Patent Publication Number: US-11049218-B2

Title: Seamless image stitching

Description:
PRIORITY 
     This application claims the benefit, under 35 U.S.C. § 119(e), of U.S. Provisional Patent Application No. 62/544,463 filed 11 Aug. 2017, which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     This disclosure generally relates to combining electronic images. 
     BACKGROUND 
     An electronic image of a scene may be captured by many different kinds of electronic devices. For example, images may be captured by a mobile device, such as a mobile phone or tablet, that has a camera built in to the device. At times, two or more images of a scene may be captured. An electronically captured image may include a portion of a scene that overlaps with a portion of a scene captured in another electronic image. However, the overlapping portions may be taken from different perspectives (e.g., different angles or distances) and so the overlapping portions of two images may not be identical. Those differences make it difficult to merge two images into one image of the scene, as it may not be possible to simply blend the images by superimposing a portion of a scene in one image over that portion of the scene in another image. In addition, even if that were possible, other portions of the scene may be distorted by taking that approach. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates example stitched images obtained using a prior/existing stitching technique and the result of an example improved stitching technique. 
         FIG. 2  illustrates an example 3-D imagery system architecture. 
         FIG. 3  illustrates an example stereoscopic pair of cameras. 
         FIG. 4  illustrates a partial plan view of an example camera configuration of a camera system. 
         FIG. 5  illustrates a plan view of an example camera system. 
         FIG. 6  illustrates an example set of images captured by cameras of a camera system. 
         FIG. 7  illustrates a side view of an example camera system. 
         FIG. 8  illustrates an example set of overlapping images captured by cameras of a camera system. 
         FIG. 9  illustrates an example method for stitching discrete images. 
         FIGS. 10 and 11  illustrate other example methods for stitching discrete images. 
         FIG. 12  illustrates example partitioning of an image. 
         FIG. 13  illustrates example feature point matching of images. 
         FIG. 14  illustrates an example top image and an example main stitched image. 
         FIG. 15  illustrates the example top image from  FIG. 14  after processing. 
         FIGS. 16 and 17  illustrate example methods for stitching discrete images. 
         FIG. 18  is a flowchart of an example method for stitching images based on grid optimization. 
         FIG. 19  is a flowchart of an example method illustrating steps involved in grid optimization. 
         FIG. 20  a flowchart of another example method for stitching images based on grid optimization. 
         FIG. 21  illustrates example discrete images for stitching. 
         FIG. 22  illustrates an example initial image with image artifacts. 
         FIG. 23  illustrates example image edges or contrast lines obtained upon edge detection in an image. 
         FIGS. 24A-24H  graphically illustrate an example grid optimization process for an example image. 
         FIG. 25  illustrates smoothening or spring constraints for controlling movements of grid points in images. 
         FIG. 26  illustrates an example seam estimation. 
         FIG. 27  illustrates an example stitched image using the image stitching technique of the present disclosure. 
         FIG. 28A  illustrates example stitched images obtained using a prior/existing stitching technique, and  FIG. 28B  illustrates the result of an example improved stitching technique. 
         FIG. 29  illustrates an example method for merging two or more images into a single image. 
         FIG. 30  illustrates an example method for adjusting portions of an image to correct misalignment between merged images. 
         FIGS. 31A-B  illustrate a set of detailed example calculations for determining an overall cost function J. 
         FIG. 32  illustrates a set of detailed example calculations for using bilinear mapping to determine the coordinates of a feature. 
         FIG. 33  illustrates an example computer system. 
     
    
    
     DESCRIPTION OF EXAMPLE EMBODIMENTS 
     Particular embodiments discussed herein relate to systems, apparatuses, and methods for seamlessly stitching or combining two or more electronic images together to produce a stitched image (e.g., a panoramic image or a 360° image). In particular embodiments, a plurality of images may be received from a camera system (e.g., images  2102 - 2116  as shown in  FIG. 21 ), from a single camera, or from a client or server device that stores the images. The images may have undergone some amount of initial stitching, for example according to the stitching techniques illustrated and described in relation to  FIGS. 8-18 . As another example, initial stitching may be performed by estimating camera parameters for all images in a scene by computing point-to-point correspondences between images and optimizing distances between them by varying various camera properties such as focal length, field of view, lens offset, etc. 
     Existing stitching techniques may not generate a smooth image and often produce image artifacts, as shown for example by reference numerals  212   a  and  214   a  in  FIG. 1 , and also image artifacts  2202 - 2210  as shown in  FIG. 22 .  FIG. 28A  also illustrates image artifacts caused by conventional stitching processes. Stitching artifacts may be introduced whenever any two types of images are stitched together, and the artifacts may be particularly acute in portions of a scene that are relatively close to the viewer and/or when stitching images that will be used to generate a 3D image. Stitching artifacts may be introduced by spatial movement of a camera taking a series of pictures or a spatial offset between multiple cameras taking different pictures. In addition, it is not always possible to compute a single 2D transformation that can satisfy all point correspondences between images such that the images perfectly align. 
     One technical improvement of the stitching techniques discussed herein is to generate a seamless smooth image and remove/minimize these image artifacts, as shown for example by reference numerals  212   b  and  214   b  in  FIG. 1 . An example stitched image generated using an example technique discussed herein is shown in  FIG. 27 . In order to stitch two images, the images may be first warped onto a sphere and defished to produce rectilinear images. Edge detection may be performed on these images using sobel gradients to calculate image edges and contrast lines (see for example  FIG. 23 ) such that images can be compared to each other. Grid optimization may be performed to minimize the difference between the normalized gradients of overlapping regions of the two images. In particular embodiments, grid optimization involves aligning the edge maps of the two images as much as possible. Specifically, grid optimization may include dividing each of the images into grid points (see for example,  FIGS. 24A-24F ) and recursively moving the grid points and corresponding portions of the images so as to minimize the difference in edge lines between features in the overlapping region of the two images or to minimize the difference between the normalized gradients of overlapping regions of the two images. In particular embodiments, a force model comprising a set of spring or smoothening constraints may be added that restricts the movement of grid points between two images or within the same image up to a certain threshold (e.g., a grid point may move only a certain pixels to the left/right/top/bottom from its original position). A pyramid level technique may be employed where the optimization (e.g., dividing image into grid regions and moving the grid points) may be done in multiple iterations or steps e.g., very coarse in the beginning (as shown for example in  FIG. 24B ) and gradually becomes finer (see for example,  FIG. 24B  to  FIG. 24C  or  FIG. 24C  to  FIG. 24D ) as pyramid level reduces. In the higher pyramid levels, the algorithm searches in a larger window, which reduces as the pyramid level reduces. New grid points may be added as the pyramid level decreases (see for example,  FIGS. 24C-F ). The new grid points&#39; initial positions may be interpolated from the positions of the previous points, and the grid may then be optimized again. This process may be repeated until the difference between the normalized gradients of overlapping regions of the two images is within or less than a certain threshold. Once the difference is within the threshold (e.g., edges or edge lines of two images overlap with one another), seam estimation and blending may be performed to produce a combined or stitched image, as shown for example in  FIG. 27 . In some embodiments, prior to seam and blending, color correction may optionally be performed on the images. Color correction may include images&#39; exposure, vignette removal, and white balance correction. The image stitching technique may be performed on a central processing unit (CPU) or a graphical processing unit (GPU) for faster implementation. The grid optimization method for image stitching discussed herein can also be applied for video stitching, for stitching a top image, and for 3D stitching. 
     In other embodiments, merging two or more images into a single image may be accomplished by adjusting the images based on a number of considerations. For example, misaligned portions of overlapping images may be corrected by adjusting (e.g., by warping or distorting) at least part of one or both of the images so as to minimize the misalignment. However, adjusting the images so that they are completely aligned may require so much adjustment that other portions of the images become misaligned and appear distorted to a viewer. Thus, considerations for merging two or more images together may include an analysis of the image distortion caused by aligning misaligned portions of an image. As explained below with reference to  FIGS. 29-32 , image distortion may include both local distortion, which refers to distortion of the image near the portions that are being aligned, and global distortion, which refers to distortion of portions of the image that are not near misaligned portions of the image. Thus, merging two or more images into a single image may balance the competing considerations of alignment and image distortion in order to reduce misalignment while also preserving image quality. 
       FIG. 2  illustrates an example 3-D imagery system architecture. In particular embodiments, a system architecture  200  for capturing, encoding, and rendering 360° 3-D video may include camera system  210 , front-end processors  220 , stitching server  230 , content server  240 , and client system  250 . Although this disclosure describes and illustrates a particular 3-D imagery system composed of particular systems, this disclosure contemplates any suitable 3-D imagery system composed of any suitable systems. Moreover, while the description below describes particular components performing particular functionality, this disclosure contemplates that any suitable components may perform any suitable functionality. For example, this disclosure contemplates that the processing described below may be performed at a server device, at a client device, or both, as appropriate. 
     Camera system  210  may include a number of pairs of cameras  212  (see  FIGS. 3-5 ) that are configured to digitally capture images. As an example and not by way of limitation, the captured images may correspond to 360° 3-D video that is captured and processed in real-time. Cameras  212  of camera system  210  may be connected (e.g., through universal serial bus (USB)) to a front-end processor  220 . Front-end processor  220  may provide initial control of cameras  212  by synchronizing the starting and stopping of the images from the various cameras  212 . Front-end processors  220  may also determine or set camera parameters, such as shutter speed or exposure time. Front-end processor  220  may normalize, correct distortion, compress or encode the incoming videos from camera system  210 . In particular embodiments, the number of front-end processors  220  may be based on the number of cameras  212  of camera system  210  as well as the size of the incoming images (e.g., frame rate or frame size). The image data from front-end processors  220  may be transferred (e.g., through a transmission-control protocol (TCP) network) to a stitching server  230  that perform the stitching of the discrete images captured by camera system  210 . 
     As described below, stitching server  230  may stitch together the discrete images from the various cameras to generate complete frames of 3-D video. In particular embodiments, stitching server  230  may compute image alignment of the discrete images and segment complete frames into vertical strips. Stitching server  230  may recompress strips at different sizes and bit rates for variable bit-rate control. A single stitching server  230  may be used when real-time performance is not needed, or up to tens or even hundreds of stitching servers  230  may be used when real-time performance on high-resolution, high-frame-rate, 3-D video is being consumed. The frames of 3-D video may be stored or transmitted to a content server  240 . 
     Content Server  240  may act as content distribution network for client systems  250  and communicate with client systems  250  to stream the appropriate parts of the requested 3-D video to the viewer. Content server  240  may transmit requested 3-D video to client systems  250  on a per-frame basis. In particular embodiments, the number of content servers  240  may be proportional to the number of client systems  250  receiving the 3-D video. 
     Client systems  250  may function as a device for users to view the 3-D video transmitted by content servers  240 . Furthermore, input from client systems  250  to content servers  240  may modify portions of the 3-D video transmitted to client systems  250 . As an example, the 3-D video may be adjusted based on data from client system  250  indicating that a user&#39;s viewing angle has changed. In particular embodiments, client system  250  may request frames that correspond to the straight-on view plus additional frames on either side. In particular embodiments, client system  250  may request low-resolution, full-frame images and reconstruct 3-D for the viewer. 
       FIG. 3  illustrates an example stereoscopic pair  300  of cameras  212 . In particular embodiments, stereoscopic pair  300  may include two cameras  212  referred to respectively as left camera L and right camera R. Left camera L and right camera R may capture images that correspond to a person&#39;s left and right eyes, respectively, and video images captured by cameras L and R may be played back to a viewer as a 3-D video. In particular embodiments, stereoscopic pair  300  may be referred to as a pair, a stereo pair, a camera pair, or a stereo pair of cameras. As described below, camera system  210  may capture 3-D images using a number of pairs  300  of digital cameras (“cameras”)  212 , where camera system  210  may use integrated digital cameras or an interface to one or more external digital cameras. In particular embodiments, a digital camera may refer to a device that captures or stores images or videos in a digital format. Herein, the term “camera” may refer to a digital camera, and the term “video” may refer to digital video, or video recorded or stored in a digital format. 
     In particular embodiments, camera  212  may include an image sensor that is configured to capture individual photo images or a series of images as a video. As an example and not by way of limitation, camera  212  may include a charge-coupled device (CCD) image sensor or a complementary metal-oxide-semiconductor (CMOS) active-pixel image sensor. In particular embodiments, an image sensor of camera  212  may have an aspect ratio (e.g., a ratio of the sensor&#39;s width to height) of approximately 16:9, 4:3, 3;2, or any suitable aspect ratio. In particular embodiments, an image-sensor width of camera  212  may be greater than an image-sensor height. In particular embodiments, a width and height of an image sensor may be expressed in terms of a number of pixels along two axes of the image sensor, and the image sensor width may represent the longer dimension of the image sensor. As an example and not by way of limitation, an image sensor may have a width or height of between 500 and 8,000 pixels. As another example and not by way of limitation, an image sensor with a width of 1,920 pixels and a height of 1,080 pixels may be referred to as an image sensor with a 16:9 aspect ratio. In particular embodiments, camera  212  may include a lens or lens assembly to collect and focus incoming light onto the focal area of the image sensor. As an example and not by way of limitation, camera  212  may include a fisheye lens, ultra wide-angle lens, wide-angle lens, or normal lens to focus light onto the image sensor. Although this disclosure describes and illustrates particular cameras having particular image sensors and particular lenses, this disclosure contemplates any suitable cameras having any suitable image sensors and any suitable lenses. 
     In particular embodiments, camera  212  may have a field of view (FOV) that depends at least in part on a position, focal length, or magnification of a lens assembly of camera  212  and a position or size of an image sensor of camera  212 . In particular embodiments, a FOV of camera  212  may refer to a horizontal, vertical, or diagonal extent of a particular scene that is visible through camera  212 . Objects within a FOV of camera  212  may be captured by an image sensor of camera  212 , and objects outside the FOV may not appear on the image sensor. In particular embodiments, FOV may be referred to as an angle of view (AOV), and FOV or AOV may refer to an angular extent of a particular scene that may be captured or imaged by camera  212 . As an example and not by way of limitation, camera  212  may have a FOV between 30° and 200°. As another example and not by way of limitation, camera  212  having a 100° FOV may indicate that camera  212  may capture images of objects located within ±50° of a direction or orientation  214  in which camera  212  is pointing. 
     In particular embodiments, camera  212  may have two particular FOVs, such as for example a horizontal field of view (FOV H ) and a vertical field of view (FOV V ), where the two FOVs are oriented approximately orthogonal to one another. As an example and not by way of limitation, camera  212  may have a FOV H  in a range of between 30° and 100° and a FOV V  in a range of between 90° and 200°. In the example of  FIG. 3 , camera  212  has a FOV H  of approximately 80°. In particular embodiments, camera  212  may have a FOV V  that is wider than its FOV H . As an example and not by way of limitation, camera  212  may have a FOV H  of approximately 45° and a FOV V  of approximately 150°. In particular embodiments, camera  212  having two unequal FOVs may be due at least in part to camera  212  having an image sensor with a rectangular shape (e.g., camera  212  may have an image sensor with a 16:9 aspect ratio). In particular embodiments, camera  212  may be positioned so that its FOV V  is aligned with or corresponds to the width of camera  212 &#39;s image sensor and its FOV H  is aligned with the height of the image sensor. As an example and not by way of limitation, an image-sensor may have a height and width, where the width represents the longer of the two image-sensor dimensions, and camera  212  may be oriented so that the width axis of its image sensor corresponds to FOV V . Although this disclosure describes and illustrates particular cameras having particular fields of view, this disclosure contemplates any suitable cameras having any suitable fields of view. 
     In particular embodiments, camera  212  may have an orientation  214  that represents an angle or a direction in which camera  212  is pointing. In particular embodiments, orientation  214  may be represented by a line or ray directed along a center of a FOV of camera  212 . In particular embodiments, orientation line  214  of camera  212  may be directed approximately along a longitudinal axis of camera  212 , approximately orthogonal to a surface of the camera&#39;s lens assembly or image sensor, or approximately orthogonal to axis  215 , where axis  215  represents a line between cameras L and R of stereoscopic pair  300 . In the example of  FIG. 3 , orientation  214 -L and orientation  214 -R are each approximately orthogonal to axis  215 , and orientations  214 -L and  214 -R are each directed approximately along a respective center of FOV H  of camera  212 . In particular embodiments, each camera  212  of a stereoscopic pair  300  may have a particular orientation  214  with respect to one another. In particular embodiments, a left and right camera  212  of stereoscopic pair  300  may each point in approximately the same direction, and orientations  214  of the left and right cameras may be approximately parallel (e.g., angle between orientations  214  may be approximately 0°). In the example of  FIG. 3 , left camera orientation  214 -L is approximately parallel to right camera orientation  214 -R, which indicates that cameras L and R are pointing in approximately the same direction. Left and right cameras  212  with parallel orientations  214  may represent cameras pointing in the same direction, and cameras L and R may be referred to as having the same orientation. In particular embodiments, left camera L and right camera R having a same orientation may refer to orientations  214 -L and  214 -R, respectively, that are parallel to one another to within ±0.1°, ±0.5°, ±1°, ±2°, ±3°, or to within any suitable angular value. In particular embodiments, an orientation of stereoscopic pair  300  may be represented by an orientation  214  of parallel left and right cameras  212 . As an example and not by way of limitation, a first stereoscopic pair  300  may be referred to as having a 30° degree orientation with respect to a second stereoscopic pair  300  when each camera of the first pair is oriented at 30° degrees with respect to the cameras of the second camera pair. 
     In particular embodiments, left camera L and right camera R may have orientations  214 -L and  214 -R with a particular nonzero angle between them. As an example and not by way of limitation, the two cameras of stereoscopic pair  300  may be oriented slightly toward or away from one another with an angle between their orientations of approximately 0.5°, 1°, 2°, or any suitable angular value. In particular embodiments, an orientation of stereoscopic pair  300  may be represented by an average of orientations  214 -L and  214 -R. Although this disclosure describes and illustrates particular cameras having particular orientations, this disclosure contemplates any suitable cameras having any suitable orientations. 
     In particular embodiments, an inter-camera spacing (ICS) between cameras  212  of a pair of cameras (e.g., L and R) may represent a distance by which the two cameras are separated from each other. In particular embodiments, stereoscopic pair  300  may have cameras  212  with an ICS between 6 and 11 cm, where ICS may be measured between two corresponding points or features of two cameras  212 . As an example and not by way of limitation, ICS may correspond to a distance between middle points of two cameras  212 , a distance between longitudinal axes of two cameras  212 , or a distance between orientation lines  214  of two cameras  212 . In particular embodiments, cameras L and R of stereoscopic pair  300  may be separated by an ICS distance along axis  215 , where axis  215  represents a line connecting cameras L and R, and camera orientations  214 -L and  214 -R are approximately orthogonal to axis  215 . In the example of  FIG. 3 , ICS is a distance between cameras L and R as measured along separation axis  215 . In particular embodiments, an ICS may correspond to an approximate or average distance between the pupils, or the inter-pupillary distance (IPD), of a person&#39;s eyes. As an example and not by way of limitation, an ICS may be between 6 and 7 cm, where 6.5 cm corresponds to an approximate average IPD value for humans. In particular embodiments, stereoscopic pair  300  may have an ICS value that is higher than an average IPD value (e.g., ICS may be 7-11 cm), and this higher ICS value may provide a scene that appears to have enhanced 3-D characteristics when played back to a viewer. Although this disclosure describes and illustrates particular camera pairs having particular inter-camera spacings, this disclosure contemplates any suitable camera pairs having any suitable inter-camera spacings. 
       FIG. 4  illustrates a partial plan view of an example camera configuration of camera system  210 . In the example of  FIG. 4 , camera system  210  includes a first camera pair  300  formed by L 1  and R 1 , a second camera pair  300  formed by L 2  and R 2 , and an n-th camera pair  300  formed by L n  and R n . In particular embodiments, camera system  210  may also include additional camera pairs, such as for example camera pair L 3 -R 3  (where camera L 3  is not shown in  FIG. 4 ) or camera pair L n−1 -R n−1  (where camera R n−1  is not shown in  FIG. 4 ). Although this disclosure describes and illustrates particular camera systems having particular numbers of camera pairs, this disclosure contemplates any suitable camera systems having any suitable numbers of camera pairs. 
     In particular embodiments, cameras  212  of camera system  210  may be arranged along a straight line, a curve, an ellipse (or a portion of an ellipse), a circle (or a portion of a circle), or along any other suitable shape or portion of any suitable shape. Camera system  210  with cameras  212  arranged along a circle may be configured to record images over a 360° panoramic view. In the example of  FIG. 4 , cameras  212  are arranged along a portion of a circle as represented by the circular dashed line in  FIG. 4 . Camera system  210  illustrated in  FIG. 4  may record images over a half circle and provide approximately 180° of angular viewing. In particular embodiments, cameras  212  of camera system  210  may each be located in the same plane. As an example and not by way of limitation, each camera  212  of camera system  210  may be located in a horizontal plane, and each camera  212  may have its FOV H  oriented along the horizontal plane and its FOV V  oriented orthogonal to the horizontal plane. In the example of  FIG. 4 , cameras  212  are each located in the same plane, and the FOV H  of each camera  212  is also oriented in that plane. In particular embodiments, cameras  212  of camera system  210  may each be located in the same plane, and orientation  214  of each camera  212  may also be located in that same plane. In the example of  FIG. 4 , cameras  212  are each located in the same plane, and camera orientations (e.g.,  214 -L 1 ,  214 -L 2 ,  214 -R 1 , and  214 -R 2 ) are also located in that same plane so that each camera points along a direction that lies in the plane. In particular embodiments, camera  212  may be positioned with the height dimension of camera  212 &#39;s image sensor oriented along the horizontal plane so that the image-sensor height is aligned with and corresponds to FOV H . Additionally, camera  212  may be positioned with the width dimension of camera  212 &#39;s image sensor oriented orthogonal to the horizontal plane so that the image-sensor width corresponds to FOV V . In particular embodiments, camera  212  may capture an image having an aspect ratio such that a vertical extent of the image is larger than a horizontal extent of the image. 
     In particular embodiments, camera system  210  may include a number of pairs  300  of cameras  212 , where the camera pairs  300  are interleaved with one another. In particular embodiments, camera pairs  300  being interleaved may refer to a camera configuration where a first camera pair has one camera located between the cameras of an adjacent second camera pair. Additionally, the second camera pair may also have one camera located between the cameras of the first camera pair. In particular embodiments, an adjacent or adjoining camera pair  300  may refer to camera pairs  300  located next to one another or arranged such that a camera of one camera pair  300  is located between the two cameras of another camera pair  300 . In particular embodiments, interleaved camera pairs  300  may refer to a camera configuration with first and second camera pairs, where the second pair of cameras are separated from each other by at least a camera of the first camera pair. Additionally, the first pair of cameras may also be separated from each other by at least a camera of the second camera pair. In the example of  FIG. 4 , camera pair L 2 -R 2  is interleaved with camera pair L 1 -R 1  and vice versa. Camera pairs L 1 -R 1  and L 2 -R 2  are interleaved such that camera R 2  is located between cameras L 1  and R 1 , and camera L 1  is located between cameras L 2  and R 2 . Similarly, camera pairs L 1 -R 1  and L n -R n  are also interleaved with one another. Camera pairs L 1 -R 1  and L n -R n  are interleaved such that cameras L 1  and R 1  are separated by at least camera L n , and cameras L n -R n  are separated by at least camera R 1 . In the example of  FIG. 4 , camera pair L 1 -R 1  is interleaved with two adjoining camera pairs, camera pair L 2 -R 2  and camera pair L n -R n . 
     In particular embodiments, camera system  210  may include a first pair  300  of cameras  212 , where the cameras of the first pair are separated from each other by at least one camera  212  of a second pair  300  of cameras  212 . In the example of  FIG. 4 , cameras L 1  and R 1  of camera pair L 1 -R 1  are separated from each other by camera R 2  of camera pair L 2 -R 2 . Additionally, the first pair of cameras may have an orientation  214  that is different from an orientation  214  of the second pair of cameras. In the example of  FIG. 4 , the orientation of camera pair L 1 -R 1  (which may be represented by orientation  214 -L 1  or  214 -R 1 ) is different from the orientation of camera pair L 2 -R 2  (which may be represented by orientation  214 -L 2  or  214 -R 2 ). In particular embodiments, camera system  210  may also include a third pair of cameras (e.g., L n -R n  in  FIG. 4 ), and the cameras of the first pair (e.g., L 1 -R 1 ) may also be separated from each other by a camera (e.g., camera L n ) of the third pair of cameras (e.g., L n -R n ). Additionally, the third pair of cameras may have an orientation  214  that is different from the orientations  214  of the first and second camera pairs. Although this disclosure describes and illustrates particular camera systems having particular cameras arranged in particular configurations, this disclosure contemplates any suitable camera systems having any suitable cameras arranged in any suitable configurations. 
     In particular embodiments, camera system  210  may include multiple interleaved camera pairs  300 , where each camera pair  300  has a particular orientation  214 . In particular embodiments, cameras  212  of each camera pair  300  may be arranged uniformly such that each camera pair  300  is oriented at an angle Θ with respect to one or more adjacent camera pairs  300 . In particular embodiments, angle Θ may correspond to an angular spacing or a difference in orientations  214  between adjacent pairs  300  of cameras  212 . In the example of  FIG. 4 , cameras L 1  and R 1  are pointing in the same direction as represented by their approximately parallel respective orientations  214 -L 1  and  214 -R 1 . Similarly, cameras L 2  and R 2  are each pointing along a direction, as represented by their approximately parallel respective orientations  214 -L 2  and  214 -R 2 , that is different from the orientation of camera pair L 1 -R 1 . In particular embodiments, angle Θ between adjacent camera pairs  300  may be approximately the same for each camera pair  300  of camera system  210  so that camera pairs  300  are arranged with a uniform difference between their respective orientations  214 . As an example and not by way of limitation, adjacent camera pairs  300  of camera system  210  may each be oriented at an angle of approximately 26°, 30°, 36°, 45°, 60°, 90°, or any suitable angle with respect to one another. In the example of  FIG. 4 , camera pair L 2 -R 2  is oriented at angle Θ≈30° with respect to camera pair L 1 -R 1 . In particular embodiments, for camera system  210  with n uniformly spaced camera pairs  300  (where n is a positive integer) arranged along a circle, angle Θ between each adjacent camera pair may be expressed as Θ≈360°/n. As an example and not by way of limitation, for camera system  210  with n=12 pairs of cameras distributed in a uniformly spaced circular configuration, angle Θ between each adjacent camera pair is approximately 360°/12=30°. As another example and not by way of limitation, for camera system  210  with n=8 pairs of cameras distributed in a uniformly spaced circular configuration, angle Θ between each adjacent camera pair is approximately 360°/8=45°. 
     In particular embodiments, a first and second camera pair  300  may be interleaved such that a right camera  212  of the second pair of cameras is adjacent to a left camera  212  of the first pair of cameras, and a center of a FOV H  of the right camera  212  of the second pair of cameras intersects a center of a FOV H  of the left camera  212  of the first pair of cameras. In the example of  FIG. 4 , first camera pair L 1 -R 1  is interleaved with second camera pair L 2 -R 2  such that right camera R 2  is adjacent to left camera L 1 , and the center of the FOV H  of camera R 2  (as represented by orientation  214 -R 2 ) intersects the center of the FOV H  of camera L 1  (as represented by orientation  214 -L 1 ). In particular embodiments, a first and third camera pair  300  may be interleaved such that a left camera  212  of the third pair of cameras is adjacent to a right camera  212  of the first pair of cameras, and a center of a FOV H  of the left camera  212  of the third pair of cameras intersects a center of a FOV H  of the right camera  212  of the first pair of cameras. In the example of  FIG. 4 , first camera pair L 1 -R 1  is interleaved with n-th camera pair L n -R n  such that left camera L n  is adjacent to right camera R n , and the center of the FOV H  of camera L n  (as represented by orientation  214 -L n ) intersects the center of the FOV H  of camera R 1  (as represented by orientation  214 -R 1 ). Although this disclosure describes and illustrates particular camera pairs interleaved in particular manners, this disclosure contemplates any suitable camera pairs interleaved in any suitable manners. 
     In particular embodiments, angle Θ between adjacent camera pairs  300  may be different for one or more camera pairs  300  of camera system  210  so that camera pairs  300  may have a nonuniform angular spacing. As an example and not by way of limitation, the angular spacing or distribution of camera pairs  300  in camera system  210  may be varied based at least in part on the FOV H  of each camera  212 . For example, some camera pairs  300  of camera system  210  with a narrower FOV H  may have an angular spacing of 30° while other camera pairs  300  with a wider FOV H  have an angular spacing of 50°. Although this disclosure describes and illustrates particular camera systems having particular camera pairs with particular angular spacings, this disclosure contemplates any suitable camera systems having any suitable camera pairs with any suitable angular spacings. 
     In particular embodiments, each FOV H  of a set of left cameras (e.g., cameras L 1 , L 2 , etc., which correspond to a person&#39;s left eye) or a set of right cameras (e.g., cameras R 1 , R 2 , R 3 , etc., which correspond to a person&#39;s right eye) may have an angular overlap  216  with neighboring cameras in the set. In the example of  FIG. 4 , angular overlap  216  represents a shared portion or an overlap between images captured by neighboring cameras R 1  and R 2 . In  FIG. 4 , cameras R 2  and R 3 , cameras R n  and R 1 , cameras L 1  and L 2 , and cameras L n  and L n−1  may also share similar angular overlaps. In particular embodiments, neighboring cameras  212  with an angular overlap  216  may have an overlap of their horizontal FOVs of between 10% and 30%. As an example and not by way of limitation, neighboring cameras with horizontal FOVs that overlap by 10-30% may each capture images that overlap by between 10% and 30%. As another example and not by way of limitation, neighboring cameras each with a FOV H ≈50° and an angular overlap  216  of approximately 10° may be referred to as having an angular overlap or an image overlap of approximately 20% (=10°/50°). In particular embodiments, and as described below, angular overlap  216  may be used to identify image features and create a stitched image that seamlessly shows an entire view as captured by camera system  210 . Although this disclosure describes and illustrates particular cameras having particular angular overlaps, this disclosure contemplates any suitable cameras having any suitable angular overlaps. 
       FIG. 5  illustrates a plan view of an example camera system  210 . As described below, camera system  210  may include a spatial arrangement of stereoscopic pairs  300  of cameras  212  configured to capture images and record or stream real-time video in 360 degrees and in stereoscopic 3-D format. In particular embodiments, camera system  210  may include 2n cameras  212  that form n camera pairs  300 , where n is a positive integer. In particular embodiments, camera system  210  may include n=1, 2, 3, 4, 6, 8, 10, 12, 14, 16, or any suitable number of camera pairs  300 . As examples and not by way of limitation, camera system  210  may include 8 cameras  212  that form n=4 camera pairs  300 , or camera system  210  may include 16 cameras  212  that form n=8 camera pairs  300 . In the example of  FIG. 5 , n equals 12, and camera system  210  includes 24 cameras  212  that form 12 camera pairs  300  (e.g., camera pair L 1 -R 1  through camera pair L 12 -R 12 ). As discussed above, camera pairs  300  of camera system  210  may be uniformly arranged so that adjacent camera pairs  300  are oriented at an angle of Θ≈360°/n with respect to one another. In the example of  FIG. 5 , n equals 12, and camera pairs  300  are oriented at approximately 30° (=360°/12) with respect to one another as represented by the 30° angles between radial lines R drawn from the center of camera system  210  to camera pairs  300 . 
     In particular embodiments, cameras  212  of camera system  210  may be configured so that the horizontal FOVs of neighboring left cameras are overlapped and, similarly, the horizontal FOVs of neighboring right cameras are overlapped. In the example of  FIG. 5 , each pair of neighboring left cameras (e.g., cameras L 1  and L 2 , cameras L 2  and L 3 , etc.) may have an overlap of their horizontal FOVs of between 10% and 30%. Similarly, each pair of neighboring right cameras (e.g., cameras R 1  and R 2 , cameras R 2  and R 3 , etc.) may have an overlap of their horizontal FOVs of between 10% and 30%. In particular embodiments, each set of left cameras (e.g., cameras L 1 -L 12  in  FIG. 5 ) may be oriented to capture a corresponding set of left images that covers a full 360° view around camera system  210 . Similarly, each set of right cameras (e.g., cameras R 1 -R 12  in  FIG. 5 ) may be oriented to capture a corresponding set of right images that covers a full 360° view around camera system  210 . 
     In particular embodiments, cameras  212  of camera system  210  may be arranged in an approximately circular configuration with cameras  212  located at or near an outer edge or circumference of camera body  218 . In particular embodiments, camera body  218  may represent a mechanical structure, enclosure, or casing that holds, contains, or encloses cameras  212  of camera system  210 , as well as other devices that are part of camera system  210 , such as for example, one or more power supplies or processors. In the example of  FIG. 5 , 14 cameras  212  of camera system  210  are arranged in a circular configuration near an outer edge of camera body  218 , which has a circular shape. In particular embodiments, each camera pair  300  of camera system  210  may be aligned so its orientation  214  is directed away from, or radially outward from, a common center point  217 . In the example of  FIG. 5 , center point  217  represents a center of body  218  of camera system  210 , and the orientation of each camera pair, as represented by radial line R, is directed radially outward from center point  217 . In particular embodiments, camera body  218  of camera system  210  may have a size, width, or diameter  219  of approximately 10 cm, 15 cm, 20 cm, 25 cm, 30 cm, or any suitable size. In the example of  FIG. 5 , camera body  218  may have an outer edge with a diameter  119  of approximately 20 cm. In particular embodiments, camera system  210  may have a size comparable to that of a human head as it turns. As an example and not by way of limitation, camera body  218  may have a diameter of approximately 20 cm, and camera pairs  300  may be positioned to correspond to the location of a person&#39;s eyes as the person rotates their head. Although this disclosure describes and illustrates particular camera systems having particular sizes, widths, or diameters, this disclosure contemplates any suitable camera systems having any suitable sizes, widths or diameters. 
     In particular embodiments, two or more cameras  212  of camera system  210  may be referred to as being adjacent to one another. In particular embodiments, two cameras  212  that are adjacent to one another may refer to two cameras located next to or nearby one another with no other camera located between the two cameras. In the example of  FIG. 5 , cameras L 1  and R 3  are adjacent to one another, and cameras L 2  and R 3  are adjacent to one another. In  FIG. 5 , camera R 1  is adjacent to camera L 11  and camera L 12 . In particular embodiments, adjacent cameras may be identified within a particular set of cameras without regard to other cameras which are not part of the set. As an example and not by way of limitation, two cameras within a set of left cameras may be identified as being adjacent to one another even though there may be a right camera located near or between the two cameras. In  FIG. 5 , for the set of left cameras (cameras L 1  through L 12 ), camera L 1  is adjacent to cameras L 2  and L 12 , and for the set of right cameras (cameras R 1  through R 12 ), cameras R 1  and R 2  are adjacent. 
       FIG. 6  illustrates an example set of images (I- 1  through I- 8 ) captured by cameras  212  of a camera system  210 . As an example and not by way of limitation, images I- 1  through I- 8  may correspond to images captured by left cameras L- 1  through L- 8 , respectively, of camera system  210 . Images I- 1  through I- 8  may represent images captured using a camera system  210  similar to that illustrated in  FIG. 4  or  FIG. 5 . In particular embodiments, a set of images captured by a set of left or right cameras  212  of camera system  210  may have overlap areas  610  between neighboring images, where overlap areas  610  represent portions or regions of neighboring images that correspond to approximately the same scene. In the example of  FIG. 6 , overlap area  610   5-6  represents an overlap between neighboring images I- 5  and I- 6 , and the captured scene in overlap area  610   5-6  includes a right portion of a cloud and part of a bridge. Similarly, overlap area  610   6-7  represents an overlap between neighboring images I- 6  and I- 7 , and the captured scene in overlap area  610   6-7  includes a bridge tower. 
     In particular embodiments, overlap area  610  may correspond to an overlap of horizontal FOVs of neighboring cameras  212 . In particular embodiments, neighboring images captured by left or right cameras  212  of camera system  210  may have an overlap of between 10% and 30%. In particular embodiments, an amount or a percentage of overlap corresponds to a ratio of a height, width, or area of overlap area  610  to a height, width, or area of a corresponding image. In the example of  FIG. 6 , an amount of overlap between images I- 5  and I- 6  is equal to width  604  of overlap area  610   5-6  divided by width  606  of image I- 5  or I- 6 . In particular embodiments, a dimension of overlap area  610  or a dimension of an image may be expressed in terms of a distance (e.g., in units of mm or cm) or in terms of a number of pixels. In the example of  FIG. 6 , if overlap-area width  604  is 162 pixels and image width  606  is 1,080 pixels, then the overlap between images I- 5  and I- 6  is 15% (=162/1080). Although this disclosure describes and illustrates particular images with particular overlap areas or overlap amounts, this disclosure contemplates any suitable images with any suitable overlap areas or overlap amounts. 
     In particular embodiments, camera  212  may be positioned to capture an image having an aspect ratio such that vertical extent  607  of the image is larger than horizontal extent  606  of the image. As an example and not by way of limitation, camera  212  may capture an image with vertical extent  607  of 1,920 pixels and horizontal extent  606  of 1,080 pixels. In the example of  FIG. 6 , image I- 6  has vertical extent  607  that is larger than horizontal extent  606 . 
     In particular embodiments, adjacent images or neighboring images may refer to images located next to one another that share a common overlap area  610 . In the example of  FIG. 6 , images I- 2  and I- 3  are adjacent, and image I- 6  is adjacent to images I- 5  and I- 7 . In particular embodiments, adjacent images may correspond to images captured by respective adjacent cameras. In the example of  FIG. 6 , images I- 1  through I- 8  may correspond to images captured by left cameras L 1  through L 8 , respectively, such as for example, left cameras L 1  through L 8  of  FIG. 5 . Images I- 1  and I- 2  are adjacent images, and these images may be captured by adjacent left cameras L 1  and L 2 , respectively. 
       FIG. 7  illustrates a side view of an example camera system  210 . In particular embodiments, camera system  210  may include one or more top cameras  212 T which create a “roof” over an otherwise cylindrical side view captured by side cameras  212  arranged along a periphery of camera system  210 . In particular embodiments, side cameras  212  may refer to cameras  212  arranged in a planar configuration with their respective orientations  214  located within the same plane, such as for example cameras  212  illustrated in  FIG. 4  or  FIG. 5 . In particular embodiments, top camera  212 T may provide an upward view that may be combined with images from side cameras  212  so that a user can look up (as well as looking to their left or right, or down within the downward extent of FOV V ) when viewing a 3-D video. In particular embodiments, camera system  210  may include one or more top cameras  212 T pointing up as well as one or more bottom cameras (not illustrated in  FIG. 7 ) pointing down. As an example and not by way of limitation, images from side cameras  212  may be combined with images from top camera  212 T and a bottom camera so that a user can look in any direction (e.g., left, right, up, or down) when viewing a 3-D video. In particular embodiments, camera system  210  may include two or more top cameras  212 T (e.g., a top-left camera and a top-right camera which may form a stereoscopic pair), and images from top cameras  212 T may be combined to enhance a user&#39;s 3-D perception while viewing a 3-D video and looking upwards. Although this disclosure describes and illustrates particular camera systems having particular top or bottom cameras, this disclosure contemplates any suitable camera systems having any suitable top or bottom cameras. 
     In particular embodiments, top camera  212 T may have a field of view FOV T  that overlaps a vertical field of view FOV V  of one or more side cameras  212 . As an example and not by way of limitation, an outer edge portion of an image from top camera  212 T may overlap an upper portion of images from cameras  212  by 10-30%. In the example of  FIG. 7 , angular overlap  216  represents an overlap between FOV T  of top camera  212 T and FOV V  of a side camera  212 . In particular embodiments, top camera  212 T may have a relatively high FOV T . As an example and not by way of limitation, top camera  212 T may include a fisheye lens and FOV T  of top camera  212 T may be in the range of 140° to 185°. In particular embodiments, camera system  210  may include a set of side cameras  212  and may not include a top camera  212 T. As an example and not by way of limitation, camera system  210  may include side cameras  212  having a FOV V  in the range of 140° to 185°, and side cameras  212  may be configured to capture all or most of a full 360° view without use of a top camera. In particular embodiments and as illustrated in  FIG. 7 , camera system  210  may include a set of side cameras  212  as well as top camera  212 T. In particular embodiments, camera system  210  having top camera  212 T may allow side cameras  212  to have a reduced FOV V  with respect to a camera system  210  without a top camera. As an example and not by way of limitation, camera system  210  may include side cameras  212  having a FOV V  in the range of 100° to 160°, where FOV V  overlaps with FOV T  of top camera  212 T. 
     In particular embodiments, top camera  212 T may be located near a top surface of camera system  210  or, as illustrated in  FIG. 7 , top camera  212 T may be recessed or indented with respect to a top surface of camera system  210 . As an example and not by way of limitation, top camera  212 T may be located in a recessed position which may provide for a larger amount of overlap with side cameras  212 . In particular embodiments, side cameras  212  of camera system  210  may each have an orientation  214  that lies in a horizontal plane of camera system  210 , and orientation  214 T of top camera  212 T may be approximately orthogonal to orientations  214 . In the example of  FIG. 7 , side cameras  212  are oriented horizontally, and top camera  212 T has a vertical orientation  214 T. Although this disclosure describes and illustrates particular camera systems with particular edge cameras and particular top cameras having particular arrangements, orientations, or fields of view, this disclosure contemplates any suitable camera systems with any suitable edge cameras and any suitable top cameras having any suitable arrangements, orientations, or fields of view. 
       FIG. 8  illustrates an example set of overlapping images captured by cameras  212  of a camera system  210 . In particular embodiments, a camera system  210  with n camera pairs  300  and one top camera  212 T may capture 2n+1 images for each frame of video. The images illustrated in  FIG. 8  may be captured using 2n side cameras  212  and top camera  212 T of camera system  210  similar to that illustrated in  FIG. 7 . In particular embodiments, n left cameras  212  and n right cameras  212  may be arranged in pairs and interleaved as described above so that left-camera images I-L 1  through I-L n  are overlapped and right-camera images I-R 1  through I-R n  are overlapped. In the example of  FIG. 8 , overlap areas  610 L represent overlapping portions of images of neighboring left cameras, and overlap areas  610 R represent overlapping portions of images of neighboring right cameras. As an example and not by way of limitation, neighboring left cameras  2  and  3  may capture images I-L 2  and I-L 3 , respectively, with corresponding overlap area  610 L 2-3 . In the example of  FIG. 8 , image I-Top represents an image captured by top camera  212 T, and overlap area  610 T represents an outer edge portion of image I-Top that overlaps with upper portions of the images from side cameras  212 . In particular embodiments, overlap area  610 T may be used to stitch top image I-Top with images from one or more side cameras  212 . 
     In particular embodiments, left and right cameras  212  may be arranged so that each left-camera overlap area  610 L is captured within a single image of a corresponding right camera  212  and each right-camera overlap area  610 R is captured within a single image of a corresponding left camera  212 . In the example of  FIG. 8 , overlap area  610 L 1-2  of images I-L 1  and I-L 2  corresponds to image I-R 1  so that the overlap between left cameras L 1  and L 2  is captured by right camera R 1 . Similarly, overlap area  610 R 2-3  of images I-R 2  and I-R 3  corresponds to image I-L 3  so that the overlap between cameras R 2  and R 3  is contained within a field of view of camera L 3 . In particular embodiments, and as described below, overlap area  610  between two images may be used to identify image features and create a stitched image. Additionally, an overlap area  610  as captured by another camera may also be used in a stitching process. In the example of  FIG. 8 , images I-R 1  and I-R 2  may be stitched together based at least in part on features located in overlap area  610 R 1-2  of the two images. Additionally, since image I-L 2  captures the same overlap area, image I-L 2  may also be used in a stitching process or to verify the accuracy of a stitching process applied to images I-R 1  and I-R 2 . Although this disclosure describes and illustrates particular camera systems configured to capture particular images having particular overlap areas, this disclosure contemplates any suitable camera systems configured to capture any suitable images having any suitable overlap areas. 
     In particular embodiments, camera system  210  may include one or more depth sensors for obtaining depth information about objects in an image. As an example and not by way of limitation, one or more depth sensors may be located between or near cameras  212  of camera system  210 . In particular embodiments, a depth sensor may be used to determine depth or distance information about objects located within a FOV of cameras  212 . As an example and not by way of limitation, a depth sensor may be used to determine that a person within a FOV of camera  212  is located approximately 1.5 meters from camera system  210  while an object in the background is located approximately 4 meters away. In particular embodiments, depth information may be determined based on a triangulation technique. As an example and not by way of limitation, two or more images captured by two or more respective cameras  212  may be analyzed using triangulation to determine a distance from camera system  210  of an object in the images. In particular embodiments, camera system  210  may include a depth sensor that operates based on a structured-light scanning technique. As an example and not by way of limitation, a structured-light 3-D scanner may illuminate a scene with a projected light pattern (e.g., a sheet of light or parallel stripes of light from an infrared light source, such as a laser or a light-emitting diode), and an image of reflected or scattered light from the projected light pattern may be captured (e.g., by a camera that is part of the depth sensor) and used to determine distances of objects in the scene. In particular embodiments, camera system  210  may include a depth sensor that operates based on a time-of-flight technique where a distance to an object is determined from the time required for a pulse of light to travel to and from the object. Although this disclosure describes particular depth sensors which operate in particular manners, this disclosure contemplates any suitable depth sensors which operate in any suitable manners. 
     In particular embodiments, a depth sensor may provide depth information about objects located near camera system  210  (e.g., within 0.1-10 meters of camera system  210 ), and the depth information may be used to enhance a stitching process. As described below, a stitching process may use correspondence between overlapped images from adjacent cameras to calculate the geometry of the scene. By using a depth sensor, the relative depth or distance of items within a FOV of one or more cameras  212  may be determined rather than assuming a single overall depth. In particular embodiments, depth-sensor information may allow near portions of an image to be stitched separately from far portions. As an example and not by way of limitation, segmentation of a scene such that near and far objects are stitched separately and then combined may provide improved stitching results by taking into account the distance between camera system  210  and objects in an image. In particular embodiments, a depth sensor may provide the ability to stretch, compress, or warp portions of an image of an object located close to camera system  210 , resulting in an improved rendering of the object in a stitched image. As an example and not by way of limitation, when an object is close to camera system  210  (e.g., a person passes within 0.5 meters of camera system  210 ), accounting for the object&#39;s distance may result in a stitched image with a reduced amount of distortion. In particular embodiments, a depth sensor may provide the ability to exclude objects from view that are within a threshold distance of camera system  210 . As an example and not by way of limitation, an object that is determined to be very close to camera system  210  (e.g., a person&#39;s hand within 0.1 meters of camera system  210 ) may be removed during image processing so that the object does not block the view of a scene. 
     In particular embodiments, camera system  210  may include one or more infrared (IR) cameras, where an IR camera may refer to a camera that is sensitive to IR light (e.g., light with a wavelength between approximately 0.8 μm and 14 μm). In particular embodiments, an IR camera may be sensitive to thermal radiation or may provide an ability to image a scene in low-light situations (e.g., a darkened room or outdoors at nighttime) where a visible camera (e.g., camera  212 ) may have reduced sensitivity. As an example and not by way of limitation, in addition to cameras  212  (which may be optimized for visible-light sensing), camera system  210  may also include one or more IR cameras, and information or images from cameras  212  and the IR cameras may be combined to improve image capture or rendering in low-light situations. As another example and not by way of limitation, camera system  210  may include a set of IR cameras arranged to capture images over a 360° panoramic view around camera system  210 . As yet another example and not by way of limitation, cameras  212  of camera system  210  may be configured to have sensitivity to visible light as well as infrared light. Although this disclosure describes and illustrates particular camera systems having particular visible or infrared cameras, this disclosure contemplates any suitable camera systems having any suitable visible or infrared cameras. 
     In particular embodiments, camera system  210  may include one or more auxiliary cameras configured to image a scene with a wider FOV or with a different view than cameras  212 . As an example and not by way of limitation, camera system  210  may include a set of cameras  212  as described above, and camera system may also include one or more fisheye cameras or stereoscopic cameras with a FOV that is wider than FOV of cameras  212 . In particular embodiments, auxiliary cameras with a wider FOV may allow captured images from cameras  212  to be successfully stitched even when viewing a large expanse of uniform color or texture (e.g., a wall). In particular embodiments, cameras  212  may be configured to have a high resolution (which may result in a relatively narrow FOV), and auxiliary cameras with a wider FOV may provide a wide-field reference that allows high-resolution images from cameras  212  to be successfully aligned and stitched together. 
     In particular embodiments, cameras  212  may capture a vertical field of view greater than or approximately equal to 180 degrees. As an example and not by way of limitation, camera system  210  may include cameras  212  with FOV V  of approximately 185°. In particular embodiments, camera system  210  may include a set of cameras  212  with FOV V  greater than or equal to 180°, and camera system  210  may not include top camera  212 T, since full viewing coverage may be provided by cameras  212 . 
     In particular embodiments, camera system  210  may include one or more fisheye cameras, where a fisheye camera may refer to a camera with a wide FOV (e.g., a FOV of greater than or equal to 180 degrees). As an example and not by way of limitation, camera system  210  may include 2, 3, or 4 fisheye cameras located near a center of camera body  218 . As another example and not by way of limitation, camera system  210  may include one or more pairs of fisheye cameras (e.g., four fisheye cameras configured as two pairs of fisheye cameras). A pair of fisheye cameras may be configured to capture 3-D images and may include two fisheye cameras separated by an ICS distance corresponding to an IPD. In particular embodiments, camera system  210  with fisheye cameras may be configured to simulate 3-D stereopsis (e.g., a perception of depth or 3-D structure) and may correspond to one or more virtual cameras located inside an image sphere. 
     In particular embodiments, camera system  210  may include cameras  212  having a relatively high FOV V  and low FOV H . As an example and not by way of limitation, cameras  212  may have a lens (e.g., an astigmatic lens) that provides a wider field of view vertically than horizontally. As another example and not by way of limitation, cameras  212  may have a FOV V  of approximately 180°, and a FOV H  of approximately 30°. In particular embodiments, a relatively narrow horizontal FOV may provide for a captured image that has relatively low distortion in the horizontal direction. In particular embodiments, distortion in the vertical direction associated with a relatively wide FOV V  may be reversed by post-capture processing based at least in part on lens-calibration information. In particular embodiments, removing distortion in the vertical direction may be a more efficient process than removing distortion along both the horizontal and vertical directions. As an example and not by way of limitation, camera  212  having a relatively low FOV H  may provide an improvement in distortion removal since the image distortion is primarily along one axis (e.g., a vertical axis). 
     In particular embodiments, camera system  210  may include two or more sets of moderate-FOV cameras  212 . As an example and not by way of limitation, cameras  212  may have a vertical and horizontal FOV of 30 to 90 degrees. In particular embodiments, camera system  210  may include two or more sets of cameras  212  with the sets arranged in rows (e.g., one set or ring of cameras  212  located above another set). Each set of cameras  212  may be configured to capture a ring of images, each ring covering a 360-degree panorama in the horizontal direction and a moderate FOV (e.g., 60 degrees) in the vertical direction. As an example and not by way of limitation, camera system  210  may include three sets of cameras  212 , each camera having a FOV V  of approximately 65 degrees that overlaps adjacent sets by approximately 15 degrees. Each set of cameras  212  may capture images at high resolution and with relatively low distortion, and the images from each ring may be combined to produce high-resolution, low-distortion images that cover a full panorama. 
     In particular embodiments, camera system  210  may include multiple cameras  212  where the cameras  212  may not being combined into stereoscopic pairs. As an example and not by way of limitation, camera system  210  may include 12 cameras arranged with overlapping horizontal FOVs so that the cameras capture a 360-degree panorama. In particular embodiments, cameras  212  may be aligned so their orientations  214  are directed away from, or radially outward from, a common center point  217  (e.g., a center of body  218  of camera system  210 ). In particular embodiments, cameras  212  may not capture 3-D images, and a 3-D effect may be produced after image capture during a stitching or reconstruction process. As an example and not by way of limitation, post-capture processing may be applied to images to simulate stereopsis. 
     In particular embodiments, a calibration procedure may be applied to cameras  212  or camera system  210 . As an example and not by way of limitation, camera  212 , camera pair  300 , or camera system  210  may have a positioning or alignment error resulting from production tolerances, and a calibration procedure may be used to correct or compensate for these errors and allow for improved stitching of images. In particular embodiments, a calibration procedure may be used to determine that a camera  212  or camera pair  300  has a position or orientation error or offset, and a corresponding error or offset in captured images may be corrected during image capture or during a post-capture process. As an example and not by way of limitation, camera pairs  300  may be manufactured to have an ICS of 6.5 mm, and from a calibration procedure, it may be determined that a camera pair  300  has an ICS of 7.0 mm. The 0.5-mm discrepancy between the ICS of camera pair  300  and a target ICS may be corrected for during image capture or with a post-capture correction process (e.g., an offset corresponding to 0.5 mm may be applied to images captured by one of the cameras  212 ). As another example and not by way of limitation, camera pairs  300  may be manufactured to have a uniform 30° angular spacing between adjacent camera pairs  300 , and from a calibration procedure, it may be determined that a camera pair  300  has a 29° angular spacing with respect to an adjacent camera pair  300 . The 1° angular error between camera pairs  300  may be corrected for while images are captured or during a post-capture correction process (e.g., an offset corresponding to a 1° rotation may be applied to captured images from one or more cameras  212 ). 
     In particular embodiments, a calibration procedure may be applied to camera system  210  after camera system  210  is manufactured, prior to camera system  210  being used, at periodic intervals (e.g., every month months), or at any suitable time or interval of time. As an example and not by way of limitation, camera system  210  may apply a calibration procedure prior to capturing a scene, which may ensure that positions and orientations of cameras  212  are known during image capture to ensure a successful stitching process. As another example and not by way of limitation, a calibration procedure may be applied to camera system  210  to correct for a misalignment of cameras  212  that may result from a temperature change, aging of camera system  210 , or a mechanical shock (e.g., if camera system  210  is dropped during transport). In particular embodiments, once a calibration procedure is performed, data regarding calibration of cameras  212  or camera pairs  300  may be stored in a non-volatile memory of camera system  210 . Although this disclosure describes particular calibration procedures performed in particular manners and at particular times, this disclosure contemplates any suitable calibration procedures performed in any suitable manners and at any suitable times. 
     In particular embodiments, cameras  212  of camera system  210  may be calibrated using projected light. In particular embodiments, projected-light calibration may be implemented using a wide angle projector, a mask in front of a lamp, or a laser scanner or reflector that projects an optical calibration pattern onto nearby surfaces. As an example and not by way of limitation, a laser beam may be reflected by a diffraction grating or a motorized mirror to produce a calibration pattern that is projected onto nearby surfaces. A projected laser pattern may be imaged by cameras  212  to determine camera calibration parameters. In particular embodiments, an optical assembly (e.g., a laser, mirror, or grating) for generating and projecting a calibration pattern may be mechanized to retract into or underneath camera-system body  218  when not in use. In particular embodiments, an optical-calibration assembly may be configured to rotate to project a calibration pattern in different directions so that different cameras  212  of camera system  210  may be calibrated. In particular embodiments, camera system  210  may be placed inside a controlled room or a spherical surface to provide an improved accuracy of calibration. Although this disclosure describes particular projected-light calibration systems, this disclosure contemplates any suitable project-light calibration systems. 
     In particular embodiments, cameras  212  of camera system  210  may be calibrated using a physical or mechanical process or structure. As an example and not by way of limitation, a mechanical calibration structure, such as for example a fan- or umbrella-like device, may be stored between cameras  212  or underneath or inside camera-system body  218 . During calibration, these physical calibrators may be mechanically deployed at a known location relative to camera system  210 . The physical calibrators may be imaged by cameras  212 , and the captured images may be compared to a known geometry to determine calibration parameters. In particular embodiments, a mechanical calibration device may be a physical device separate from camera system  210 . As an example and not by way of limitation, an external calibration device may have internal spokes that extend inward from a spherical outer body to allow camera system  210  to be held in a precise position that is known relative to the calibration device. As another example and not by way of limitation, an external calibration device may include optical sensors that allow camera system  210  to be precisely located relative to the calibration device. In particular embodiments, an interior surface of a calibration device may have calibration markings that are imaged by cameras  212 , and calibration parameters for cameras  212  or camera pairs  300  may be determined based on captured images of the calibration markings. In particular embodiments, camera system  210  may include an optical assembly that projects a calibration pattern onto an interior surface of a calibration device. Although this disclosure describes particular physical calibration systems, this disclosure contemplates any suitable physical calibration systems. 
     In particular embodiments, camera system  210  may include one or more processors integrated as part of camera system  210 , or camera system  210  may be coupled to one or more processors located external to camera system  210 . As an example and not by way of limitation, camera system  210  may include one or more front-end processors  220  located inside body  218  of camera system  210 . As another example and not by way of limitation, cameras  212  may be connected over USB to a set of one or more front-end processor machines  220 . In particular embodiments, front-end processors  220  may carry out initial control of cameras  212 , camera distortion correction, cropping of images, encoding of videos, compression of image data, or transmission of videos. As an example and not by way of limitation, camera system  210  may include independent front-end processors  220  connected to cameras  212  that carry out initial image adjustments, camera parameter control, or initial encoding of camera data to reduce the video payload for transport. In particular embodiments, the number of front-end processors associated with camera system  210  may depend at least in part on a number of cameras  212  in camera system  210  as well as a size or frame rate of video captured by cameras  212 . As an example and not by way of limitation, each camera  212  may be connected to one or more dedicated processors  220 . Although this disclosure describes and illustrates particular camera systems coupled to particular processors in particular manners, this disclosure contemplates any suitable camera systems coupled to any suitable processors in any suitable manners. 
     In particular embodiments, camera parameters (e.g., brightness, contrast, gain, exposure, white balance, saturation, focus, or aperture setting) may be calibrated, controlled, or mapped by one or more processors  220 . In particular embodiments, a white balance setting for each camera  212  may be set or controlled independent of other cameras, since each camera  212  may see a scene differently. As an example and not by way of limitation, a camera  212  positioned next to a window may see a bluish scene while an adjacent camera  212  may see reddish indoor lighting, and the two cameras may have different white balance settings. In particular embodiments, one or more camera parameters may be controlled globally to ensure that settings for adjacent cameras (e.g., adjacent left cameras  212  or adjacent right cameras  212 ) do not deviate too widely. As an example and not by way of limitation, settings for exposure or gain for a camera  212  may be based at least in part on settings for one or more adjacent cameras  212 . As another example and not by way of limitation, if exposure or gain settings are adjusted, processor  220  may ensure that settings for adjacent cameras for the same eye (e.g., adjacent left cameras  212  or adjacent right cameras  212 ) do not deviate too widely to minimize image banding or unacceptable stitching performance. In particular embodiments, a focus setting of cameras  212  may be maintained at infinity to minimize stitching errors that may result from a variation of camera focus. In particular embodiments, cameras  212  may be set to have a reduced aperture to provide a larger depth of field, which may result in a reduction in stitching errors. Although this disclosure describes particular camera parameters controlled in particular manners, this disclosure contemplates any suitable camera parameters controlled in any suitable manners. 
     In particular embodiments, an encoding process may involve one front-end processor  220  per camera  210 , or a single processor  220  (with a single core or multiple processor cores) may be shared by multiple cameras  210 . A front-end processor  220  may use accelerators, application-specific integrated-circuits (ASICs), or subprocessors to handle parts of a task of capturing, modifying, compressing, storing, or transmitting video data. Each processor  220  may run a general-purpose operating system, or may be an ASIC itself operating in complete- or near-lockstep with a central control processor. In particular embodiments, a central-control processor may act as a distributor or central control point for talking to front-end image-capture processors  220 . In particular embodiments, central processors may be implemented as parts of a single large ASIC, with duplicated resources to connect to and control each camera  212 . In such a case, multiple threads or copies of the same code or hardware-based algorithm may run to parallelize the process of capture. In particular embodiments, front-end processors  220  may use a processor-local storage system or may immediately stream data to one or more shared storage resources. In particular embodiments, decentralized storage may be utilized, and processor-local storage may be used as a buffer to the stitching system to achieve system load distribution. 
     In particular embodiments, front-end processors  220  may use a bus or network for transmission of data. The data transmission may use any suitable data-transmission format. In particular embodiments, transmission methods that guarantee receipt or otherwise notify the recipient of packet loss may be utilized. In particular embodiments, a sending component may retransmit damaged packets or may allow a receiver to insert a flag into a stored data stream indicating that packet corruption took place. In particular embodiments, a stitching system may then compensate for such damaged or lost packets as needed. 
     In particular embodiments, cameras  212  may have some lens distortion as well as some deviation relative to a target position or orientation  214 . In particular embodiments, corrections for these effects may be static, and they may be pre-calibrated and corrected using lookup tables in the front end. As an example and not by way of limitation, panorama leveling, vignette correction, lens distortion correcting, white balance correction, exposure correction and matching, or viewpoint adjustment may be applied directly to an image. In this manner, an image may be operated on before any compression-induced color or feature shifts take place, which may reduce the occurrence of visible correction artifacts. Additionally, color correction may be applied to enhance edge sharpness, overall exposure, or white balance. In particular embodiments, noise reduction may be applied to a scene in order to reduce the compressed size of an image. In particular embodiments, front-end processors  220  may downsample an image after one or more image correction or enhancement steps are applied. As an example and not by way of limitation, rather than using a processor-intensive subsampling process, an output image may be downsampled. In particular embodiments, images may be captured at a higher resolution than that used for subsequent stitching, and this high-resolution image capture may help mitigate aliasing or artifacts that may be associated with correction or enhancement steps 
     One or more initial stitching operations may be performed on a pair of images before the grid optimization stitching technique described herein is performed. In particular embodiments, stitching server  230  may determine a vertical alignment and a horizontal alignment of discrete images (e.g., images I-L 1  through I-Ln) being stitched together. In particular embodiments, images from multiple cameras may be compared, such that all left images are compared to other left images (e.g., I-L 1  through I-Ln), and all right images are compared to other right images (e.g., I-R 1  through I-Rn). In the example of  FIG. 6 , image I- 6  may be compared to adjacent images I- 5  and I- 7 . Additionally, left images may be compared to right images (e.g., I-L 1  and I-R 1 ) to make sure they are correctly aligned relative to each other. As an example and not by way of limitation, images I-L 1  through I-L 12  may correspond to images captured by left cameras L 1  through L 12 , respectively, of camera system  210  illustrated in the example of  FIG. 5 . As described above, the FOV of the cameras corresponding to each eye (e.g., L 6 ) has an overlap with its neighbors (e.g., L 5  and L 7 ), such that spatially aligning the images results in an overlap area  610  between adjacent images (e.g., I- 6  and I- 7 ). As described below, overlap area  610  of adjacent images may be used to identify image features for creating a stitched image. In particular embodiments, assumptions may be made when performing some of the stitch parameter calculations due to the known geometry of the camera system. 
       FIG. 9  illustrates an example method for stitching discrete images. The method  900  may begin at step  910 , where a number of images are received from a number of cameras  212 . In particular embodiments, the cameras may include a first camera  212  having a first orientation  214  and a second camera  212  having a second orientation  214 . In particular embodiments, the images may include a first image from the first camera  212  and a second image from the second camera  212 . At step  920 , a number of feature points are detected within the first and second images. At step  930 , one or more pairs of corresponding feature points located within an area of overlap between the first and second images are determined. In particular embodiments, the pairs of corresponding feature points include a respective one of the feature points from each of the first and second images. At step  940 , the first or second image is spatially adjusted based on a calculated offset between each pair of corresponding feature points. At step  950 , the first and second images are combined into a merged or stitched image based on the spatial adjustment. Particular embodiments may repeat one or more steps of the method of  FIG. 9 , where appropriate. Although this disclosure describes and illustrates particular steps of the method of  FIG. 9  as occurring in a particular order, this disclosure contemplates any suitable steps of the method of  FIG. 9  occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example method for stitching discrete images including the particular steps of the method of  FIG. 9 , this disclosure contemplates any suitable method for stitching discrete images including any suitable steps, which may include all, some, or none of the steps of the method of  FIG. 9 , where appropriate. Furthermore, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the method of  FIG. 9 , this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the method of  FIG. 9 . 
       FIGS. 10 and 11  illustrate other example methods  1000  and  1100 , respectively, for stitching discrete images. In particular embodiments, a method for stitching images, such as for example the methods  1000  and  1100 , illustrated in  FIG. 10  or  FIG. 11 , respectively, may provide a process for stitching images that preserves 3-D perception and is performed automatically (e.g., the process requires little or no human intervention). Although this disclosure describes and illustrates a particular flow performing particular steps in a particular order to stitch images, this disclosure contemplates any suitable flow that performs any suitable steps in a suitable order. 
     In particular embodiments, images received from front-end processors  220  of camera system  210  may be resized prior to stitching. Decreasing the resolution of the images while determining pairs of corresponding feature points, described below, may speed up the stitching process. Additionally, reduction of resolution may improve resilience to noise in low-light conditions, as well as increase overall sensitivity to small-scale textures for feature detection, described below. As an example and not by way of limitation, 2-8 megapixel (MP) images may be resized to a lower resolution that is easier to manage for a real-time 3-D stitching process. As another example and not by way of limitation, 8 MP images captured by cameras  212  may be resized to 2 MP, and the resized 2-MP images may be used as inputs to a stitching process. In particular embodiments, a resized image may be constrained to have a minimum size (e.g., 1 MP, 2 MP, or any suitable minimum size). As an example and not by way of limitation, 4 MP and 2 MP images may both be resized to 1 MP. In particular embodiments, resizing the received images may reduce noise in the images that may affect feature detection using local contrast enhancement. As an example and not by way of limitation, a scaling kernel, such as for example a Lanczos kernel, may be used to minimize kernel artifacts that may cause errors in feature detection. In particular embodiments, stitching parameters may be determined from images that are resized to a lower resolution than original images. As an example and not by way of limitation, after using a set of resized images (e.g., 2 MP images) to determine stitching parameters, a set of original, high-resolution images (e.g., 8 MP images) captured by cameras  212  may be stitched together using the determined stitching parameters. 
     In particular embodiments, images received from camera system  210  may be dewarped to stitch the images onto a rectangular plane. As an example and not by way of limitation, the received images may be super-sampled to reduce the amount of artifacts that may hinder feature detection, described below. In particular embodiments, a dewarping procedure may be combined with a scaling procedure, which may reduce the need for super-sampling. As an example and not by way of limitation, received images may undergo a combined dewarping and scaling procedure, and the combination of dewarping and scaling may reduce artifacts in the images. Alternately, the dewarping of received images may be used as a global transform as a function of position, and access to pixel data of the received images may go through a transform and super-sampling to produce suitable values. In particular embodiments, a dewarp transformation of an image may be approximated by equation (1): 
                       Image   ⁢           ⁢   dewarp   ⁢         :     ⁢           [         x           y         ]     ⁡     [           scale   ′               translate   ′               a   .           .   e           ]         →     [           x   ′               y   ′           ]       ,           (   1   )               
where x is a position along a latitude of a projected 3-D space, y is a position along a longitude of the projected 3-D space, a . . . e are camera dewarp parameters, scale′ is a scaling factor of the image, translate′ is a horizontal or vertical spatial translation parameter, and x′ and y′ are the latitude and longitude positions, respectively, after the dewarp transformation. In particular embodiments, a dewarping process may be performed using an estimated scaling factor based on the characteristics of one or more of the cameras of the camera system. In particular embodiments, a dewarp process may be performed on one or more sets of initial images, and a simplified version of the dewarp process may be applied to later images using an abstraction of the dewarp process. As an example and not by way of limitation, access to points and images may be abstracted to provide for a faster dewarping process.
 
     At step  1105 , features in received images that form a scene may be detected, as illustrated in the example of  FIG. 11 . In particular embodiments, feature detection and matching may be performed on grayscale versions of image I- 6 , and a particular contrast may be applied to images I- 6  in a separate operation or through a look-up table (LUT). In particular embodiments, feature detection may be performed globally on image I- 6  using local contrast enhancement. Local contrast enhancement increases “local” contrast, while at the same time preventing an increase in “global” contrast, thereby protecting large-scale shadow/highlight detail. As an example and not by way of limitation, local contrast gradients may be indicative of an edge, corner, or “blob” that corresponds to a feature. Features of image I- 6  may be detected using a feature detection algorithm such as for example scale-invariant feature transform (SIFT), speeded up robust features (SURF), or oriented FAST and Rotated BRIEF (ORB), where FAST stands for “features from accelerated segment test” and BRIEF stands for “binary robust independent elementary features.” In particular embodiments, a feature detection process may detect one or more feature points  614  (see  FIG. 13 ). As an example and not by way of limitation, feature points  614  may be detected by taking a difference of multiple Gaussian smoothing operations. Furthermore, the position (e.g., within the grid or within search region  612  (see  FIG. 12 )) of feature points  614  and the contrast values of each feature point  614  for each search region  612  may be stored. 
       FIG. 12  illustrates example partitioning of an image. In particular embodiments, received images (e.g., images I- 7  through I- 5 ) may be partitioned into a number of search regions  612 . As example and not by way of limitation, images I- 7  through I- 5  may correspond to images corresponding to a particular eye (e.g., all left or right images), as illustrated in the example of  FIG. 8 . In particular embodiments, the received images (e.g., I- 7  through I- 5 ) may be partitioned into 24 search regions arranged in a 4×6 rectangular grid, as illustrated in the example of  FIG. 12 . As described above, images (e.g., I- 7  through I- 5 ) from adjacent cameras corresponding to a particular eye (e.g., all left cameras) have overlap areas  610   6-7  and  610   5-6  that are proportional to angular overlap  216  between the FOV of the respective cameras. In particular embodiments, overlap areas  610   6-7  and  610   5-6  of the images (e.g., I- 7  through I- 5 ) may correspond to the right and left edges of the received images (e.g., I- 7  through I- 5 ). In particular embodiments, feature-point detection or matching may be limited to overlap areas of adjacent images. In the example of  FIG. 12 , for adjacent images I- 6  and I- 7 , feature-point detection may only be applied in overlap area  610   6-7 . Regions outside of overlap area  610  may not be considered, which may ensure that irrelevant or unnecessary points located outside an overlap area do not affect a stitching process. 
       FIG. 13  illustrates example feature point matching of images. At step  1110 , feature point matching may be performed locally on the search regions of overlap areas  610   6-7  to minimize the effect of irrelevant points on stitched image  620 , as illustrated in the example of  FIG. 11 . As an example and not by way of limitation, feature point calculations may be performed on the detected feature points  614 A-B to match a feature point  614 A of image I- 6  to a corresponding feature point  614 B of image I- 7 . The pairs of corresponding feature points  614 A-B may be detected by locally comparing the area around each detected feature point  614 A-B in search regions of overlap areas  610   6-7 . In particular embodiments, the respective contrast settings for that feature point  614 A-B in the respective images I- 7  and I- 6  may be applied as part of the matching of feature points  614 A-B. As an example and not by way of limitation, the contrast difference between images I- 7  and I- 6  may be compensated as an offset of a contrast curve. In particular embodiments, this offset of the contrast curve may be calculated with additional bits (e.g., using signed 16 bits for 8 bit values) to take this into account. A difference in the offset may cause the best match to have a uniform difference that is known ahead of time. 
     In particular embodiments, a size of an area used to match feature points  614  may be set according to a size of images. In particular embodiments, a geometry of camera system  210  may be known, and based on the known camera-system geometry, an approximate number of pixels of the search regions and overlap areas  610   6-7  of adjacent images I- 6  and I- 7  may be known a priori. As an example and not by way of limitation, since the location and orientation of cameras  212  of camera system  210  are fixed relative to one another, the overlap between adjacent left cameras (e.g., cameras L 1  and L 2 ) or adjacent right cameras (e.g., cameras R 11  and R 12 ) may be known, and similarly the overlap between adjacent left or right cameras (e.g., cameras L 1  and R 1 ) may also be known. In particular embodiments, determining corresponding pairs of feature points may be performed using a nearest-neighbor search algorithm. As an example and not by way of limitation, a nearest-neighbor search algorithm may identify patterns of feature points  614 B within each search region of overlap area  610   6-7  of image I- 7  that match corresponding patterns of feature points  614 A within each search region of overlap area  610   6-7  of image I- 6 . In particular embodiments, a nearest-neighbor algorithm may use a search radius around each feature point  614 A-B to determine the pairs of corresponding feature points  614 A-B. As an example and not by way of limitation, a search area may have a radius of 32 pixels, 64 pixels, or any suitable radius, or a search area may have a size of 32 pixels×32 pixels, 64 pixels×64 pixels, or any suitable size. In particular embodiments, a secondary refinement step may be used to realign the pairs of corresponding feature points before a final homography calculation. 
     In particular embodiments, a feature-matching procedure may use estimated parameters, and some searching may be applied within an overlap area or a search region to optimize position. In particular embodiments, a search radius may be increased as a feature search moves from a center to an edge of an image (e.g., image I- 6  or I- 7 ). As an example and not by way of limitation, a search radius may be increased due to increased errors associated with a difference between actual and estimated parameters (e.g., actual FOV versus estimated FOV). In particular embodiments, additional feature points may be added to regions  612  with fewer than a pre-determined number (e.g., 3 pairs) of pairs of corresponding feature points  614 A-B. As an example and not by way of limitation, if a feature search reveals less than 3 feature points in a particular region  612 , backup feature points from a backup feature-point set may be added to a set of features. In particular embodiments, backup, substitute, or additional feature points may be based on characteristics of camera system  210 , characteristics of each camera  212 , calibration data, or any combination thereof, and additional feature points may be indicated or marked in a data structure. 
     In particular embodiments, camera parameters or images (e.g., I- 6  and I- 7 ) may be heuristically optimized to reduce the number of free variables in a final optimization to generate stitched image  620 . As an example and not by way of limitation, heuristic optimization may be used to optimize or refine one or more camera-related parameters (e.g., FOV, orientation  214 , or location of vertical or horizontal camera center). A feature-matching procedure may use estimated camera parameters based at least in part on known camera geometry (e.g., position or orientation of cameras  212  of camera system  210 ) or on a calibration process. For example, knowing a nominal position and orientation of cameras  212  may allow estimates to be made of camera FOV, angular overlap  216 , camera orientation  214 , or camera position (e.g., location of vertical and horizontal camera center). In particular embodiments, estimated camera parameters may be optimized iteratively or by using a group numeric approach for multiple non-linear values. In particular embodiments, for each image (e.g., I- 6  and I- 7 ), the position of the pairs of corresponding feature points  614 A-B may be compared to each other and adjustments made to corresponding camera parameters based on an offset in the position of the respective feature points  614 A-B. As an example and not by way of limitation, a FOV parameter or an orientation parameter may be adjusted in response to detecting a radial offset on average between the feature points  614 A-B. As another example and not by way of limitation, a vertical or horizontal camera-position parameter may be adjusted (e.g., translated) in response to detecting a vertical or horizontal offset, respectively, on average between the feature points  614 A-B. 
     At step  1115 , an estimation of camera displacement (e.g., camera rotation or translation) between images I- 6  and I- 7  may be determined using a homography matrix based on the matched pairs of corresponding feature points, as illustrated in the example of  FIG. 11 . In particular embodiments, adjustments to images I- 6  and I- 7  may be made based on the estimated camera displacement determined by the homography matrix. The stitch parameters that are used to adjust and align images I- 6  and I- 7  to form the merged stitched image  620  may be calculated using the homography matrix. As an example and not by way of limitation, the homography matrix may be initially calculated for images I- 6  and I- 7 , and adjustment may be made to subsequent images based on the calculated homography matrix. 
     Adjustments may be made to images I- 7  and I- 6  to properly combine the images I- 7  and I- 6  into stitched image  620 . In particular embodiments, the adjustments may be made to meet one or more optimization criteria. As an example and not by way of limitation, optimization criteria may be that the vertical or horizontal offset of the pairs of corresponding feature points  614 A-B should be minimized. As another example, an optimization criteria may be that the horizontal offset of the pairs of corresponding feature points  614 A-B should be less than a maximum horizontal offset before a viewer would see double. As yet another example, an optimization criteria may be that the vertical offset of the pairs of corresponding feature points  614 A-B should be less than a maximum vertical offset. 
     In particular embodiments, the adjustments to images I- 6  and I- 7  may be performed assuming one or more initial conditions. As an example and not by way of limitation, an initial condition may assume that a first camera pair (e.g., camera pair L 1 -R 1  in  FIG. 5 ) has an orientation  214  that defines a main ray (or yaw) of camera system  210 . As another example, an initial condition may assume that the orientation  214  for the remaining camera pairs (relative to the first camera pair) about the y-axis is Y i =(i−1)×360°/n, where the y-axis is orthogonal to a plane of camera system, i=2 . . . n, and n is the number of camera pairs of the camera system. As an example and not by way of limitation, for camera system  210  with n=8 camera pairs, camera pairs  300  are oriented at 45 degrees with respect to one another. As yet another example, an initial condition may assume that cameras  212  of camera system  210  are level along the x- and z-axes (e.g., zero roll and pitch, respectively). 
     In particular embodiments, adjustments to images I- 6  and I- 7  may be determined by minimizing one or more optimization costs. As an example and not by way of limitation, a distance between pairs of corresponding feature points  614 A-B may represent a base total optimization cost. As another example, rotational adjustments along an axis may have a cost that is proportional to a weighted rotational displacement (e.g., k x (X′−X 0 ) 2  about each axis, yaw, pitch, and roll, where k x  is a weighting coefficient). Furthermore, each axis may have a particular weighting coefficient, such as for example k Y  for a yaw axis, k P  for a pitch axis, and k R  for a roll axis. In particular embodiments, FOV or translational adjustment of images I- 6  and I- 7  may have linear cost of k x |X′−X 0 | per axis. Each axis may have a particular weighting coefficient, such as for example k FOV  for a FOV adjustment, k CX  for an x-axis translation, and k CY  for a y-axis translation. In particular embodiments, the optimization costs may be functionalized, such that the optimization cost functions may be modified to deal with corner cases. 
     In particular embodiments, images (e.g., I- 6  and I- 7 ) may be stitched together by performing a global optimization using the results of the heuristic optimization, initial conditions, optimization costs, or any combination thereof. These factors may be globally optimized using, for example, Monte-Carlo, gradient descent, a sparse version of Gauss-Newton, or other suitable non-linear optimization solver. In particular embodiments, the system of parameters may be global optimized through a system of equations expressed by (2): 
                     Global   ⁢           ⁢   optimization   ⁢           ⁢         :     ⁢           [           x   ′               y   ′             0           1         ]     ⁡     [           Homography   ⁢           ⁢   Matrix   ⁢     :               YPR           scale           translate         ]         →     [           x   ″               y   ″               z   ″             1         ]             (   2   )               
where x′ and y′ are the coordinates from the dewarp operation; the homography matrix is calculated from the pairs of corresponding feature points as described above; YPR is the rotational adjustments along the yaw, pitch, and roll axis, respectively; scale is a scaling of the image; translate is a translational adjustment; and x″, y″, and z″ are the optimized coordinates.
 
     The system of equations described by equation (2) may suffer convergence failure. At step  1125 , a failed convergence on an image with more than 40% of the feature points coming from a backup source (e.g., calibration) may indicate the particular image is too white, too close, or lacks features, as illustrated in the example of  FIG. 11 . In this situation, the particular image may be adjusted in accordance with the initial conditions described above. In particular embodiments, convergence of the system of equations described by equation (2) may fail due to the substituted feature points having too large of a spatial offset. In that case, substituted feature points may have their optimization cost halved and the global optimization performed again. As an example and not by way of limitation, the reduction of the optimization and performing global optimization may be performed a pre-determined number of times (e.g., 4 cycles). Furthermore, if the equation (2) continues to fail to converge, then the contribution of the feature points may be set to zero. 
     In particular embodiments, in addition to images from adjacent cameras corresponding to a particular eye having an overlap, an image from a neighboring camera corresponding to the other eye may also have an overlap with both images. As an example and not by way of limitation, images from cameras L 1  and L 2  may have an overlap area, and a neighboring camera (e.g., camera R 1 , R 2 , or R 3 ) may also capture an image that includes the same overlap area. As illustrated in the example of  FIG. 8 , images I-L 1  and I-L 2  have overlap area  610 L 4-2 , and image I-R 1  also overlaps the two images. In particular embodiments, features of an image (e.g., image I-R 1 ) from a neighboring camera (e.g., camera R 1 ) may be detected and corresponding pairs of feature points may be determined between an overlap area (e.g., overlap area  610 L 1-2 ) of adjacent images (e.g., images I-L 1  and I-L 2 ) and the image from the neighboring camera. Furthermore, a homography matrix may be calculated based on the detected pairs of corresponding feature points of the overlap areas of adjacent cameras and the overlapping portions of the image from a neighboring camera. In particular embodiments, the results of a homography matrix corresponding to adjacent cameras (e.g., cameras L 1  and L 2 ) may be compared to a homography matrix corresponding to a neighboring camera (e.g., camera R 1 ). In addition, determining a correspondence between a stitched image corresponding to a left-eye view with a stitched image corresponding to a right-eye view may be used to stabilize the vertical offset between the stereoscopic pair of stitched images. 
     In particular embodiments, once stitch parameters or adjustments are calculated, as described above, they may be checked for correctness. In particular embodiments, a calibration may be performed using images of a known scene captured by camera system  210 . The detection of pairs of corresponding feature points of the known scene may provide a set of feature points that may be used as a basis for image adjustments to stitch images. Once the stitching server has detected the pairs of corresponding feature points within the overlapped areas, an error calculation (e.g., a sum of squares of differences) may be performed in an area around each detected feature point. If the error calculation is above a pre-determined threshold value, then the detected pair of corresponding feature points may be flagged as being suspect. If the number of pairs of corresponding feature points drops below a pre-determined threshold number of pairs, the stitching of the discrete images may be flagged. In particular embodiments, the flagged pairs of corresponding feature points may be replaced with the feature points of the calibration data, thereby forcing the homography calculation to think that the images are at calibration orientations. 
     After the homography matrices are calculated, they may be checked for correctness. At step  1135 , the difference between the yaw rotations of consecutive homography matrices may be checked, as illustrated in the example of  FIG. 11 . If the difference is within ±2-3° of the expected difference based on the calibrated data, described above, the image adjustments may be considered to be correct. As an example and not by way of limitation, the homography matrices for a 12-camera system where each camera is separated by 30° may be calculated. If the yaw rotation differences are within a pre-determined range of the expected value (e.g., between 27° and 33°), then the calculated homography matrices may be considered acceptable. In particular embodiments, the images from the cameras are used to calculate homography matrices. If the calculated homography matrices or camera positions are within ±2 degrees of the expected positions and angles, the stitch may be considered good. At step  1145 , if the stitch fails for some images, the detected pairs of corresponding feature points may be replaced with substitute feature points from calibration data and the stitching procedure re-attempted, as illustrated in the example of  FIG. 11 . At step  1155 , if the stitching procedure fails for a number of images above a pre-determined threshold number, the entire stitch may be rejected and the homography matrices from the last successful stitched frame may be used, as illustrated by the example of  FIG. 11 . In the case where a stitching failure occurs for an initial frame, homography matrices calculated based on calibration data may be used instead. 
       FIG. 14  illustrates example top image I-Top and stitched image  620 . Top image I-Top may be captured by top camera  212 T, and stitched image  620  may result from a stitching process that stitches or combines left or right images (e.g., images I-R 1  through I-Rn) together. In the example of  FIG. 14 , stitched image  620  includes images I- 1 , I- 2 , and I- 3 , which are stitched together to form stitched image  620 . In particular embodiments, after images from cameras  212  are stitched together to form stitched image  620 , top image I-Top from top camera  212 T may be stitched or added to an upper portion  610 U of stitched image  620 . Similarly, in particular embodiments, an image from a bottom camera may be stitched or added to a bottom portion of stitched image  620 . In particular embodiments, adding a top or bottom image to stitched image  620  may provide an added view to accommodate stitched image  620  that may not cover a ±90° vertical FOV. As an example and not by way of limitation, left images I-L 1  through I-Ln illustrated in the example of  FIG. 8  may be stitched together to form stitched image  620  with a vertical extent corresponding to FOV V  of cameras  212 . For example, stitched image  620  may represent a 360° horizontal panoramic view around camera system  210 , and the panoramic view may cover a ±70° vertical range (corresponding to FOV V =140°) with respect to a horizontal plane of camera system  210 . After stitched image  620  is formed, top image I-Top may be stitched to a top portion of stitched image  620 , thereby forming an image with a 360° panoramic view having a vertical extent with a range of approximately −70° to approximately +90°. Additionally, a bottom image may also be stitched to a bottom portion of stitched image  620 , thereby forming an image that extends in all directions (e.g., covers a full 360° horizontal view that extends vertically in a range from approximately −90° to approximately +90°, where −90° represents looking straight down and +90° represents looking straight up). Although this disclosure describes and illustrates particular stitched images having particular horizontal and vertical extents, this disclosure contemplates any suitable stitched images having any suitable horizontal and vertical extents. 
     In particular embodiments, portions of top image I-Top may overlap with or correspond to portions of stitched image  620 . Furthermore, particular portions of top image I-Top may be correlated with particular images (e.g., images I- 1 , I- 2 , I- 3 , etc.) based on a known configuration of cameras  212  of camera  210  as well as a known configuration of top camera  212 T. As an example and not by way of limitation, each region of top image I-Top bordered by two adjacent seam lines  617  (e.g., hatched region  619 ) may correspond to a particular image of stitched image  620 . In the example of  FIG. 14 , hatched region  619  of image I-Top may correspond to image I- 2  captured by a particular camera  212  of camera system  210 . A correspondence between images that make up stitched image  620  and portions of top image I-Top may be based on a configuration or orientation  214  of cameras  212  and a configuration of top camera  212 T. In particular embodiments, seam lines  617  in image I-Top may correspond to seams  617 M of stitched image  620 , where seams  617 M may represent a border between adjacent discrete images that form stitched image  620 . As another example and not by way of limitation, center lines  618  may correspond to an approximate center  618 M of discrete images of stitched image  620 . In particular embodiments, lines  617  and  618  may represent estimated locations for seams  617 M and centers  618 M, respectively, before top image I-Top is processed or optimized for stitching to stitched image  620 . 
     In particular embodiments, upper portion  610 U of stitched image  620  may represent an area of stitched image  620  that overlaps outer annular region  610 T of top image I-Top. For example, stitched image  620  may correspond to a FOV V  that covers for example ±70° with respect to a horizontal orientation  214 , and top image I-Top may correspond to an image that extends from a vertical direction (e.g., +90° latitude) to a latitude of +60°. The outer solid black circle of image I-Top may correspond to a latitude of +60°, and the smaller dashed circle  610 E of image I-Top may correspond to a latitude of +70°. Overlap areas  610 U and  610 T may correspond to a 10° overlap (e.g., from latitude +60° to latitude +70°) between image I-Top and stitched image  620 . In particular embodiments, an algorithm to stitch top image I-Top to stitched image  620  may include searching for features, determining pairs of corresponding feature points that are located in overlap areas  610 U and  610 T, as described above, and using those pairs of corresponding feature points to stitch image I-Top′ with stitched image  620  as described below. Although this disclosure describes and illustrates particular top and stitched images having particular portions that correspond to or overlap with one another, this disclosure contemplates any suitable top and stitched images having any suitable portions that correspond to or overlap with one another. 
       FIG. 15  illustrates the example top image from  FIG. 14  after processing. In particular embodiments, prior to being added to stitched image  620 , smaller dashed circle  610 E of top image I-Top may be processed, transformed, or optimized to form processed image I-Top′, which is then stitched or added to stitched image  620 . In particular embodiments, processing steps applied to smaller dashed circle  610 E of top image I-Top may include rotating or moving lines  617  or  618 , or warping smaller dashed circle  610 E of top image I-Top so that processed image I-Top′ matches or blends with stitched image  620 . In particular embodiments, a single processed image I-Top′ may be used with the respective stitched images  620  that correspond to the left and right views or eyes. As an example and not by way of limitation, overlap area  610 T of top image I-Top may be cropped prior to the transformation process. In particular embodiments, processed image I-Top′ may be added to a stitched image representing a left-eye view and to a stitched image representing a right-eye view. In particular embodiments, smaller dashed circle  610 E of top image I-Top may undergo two processing routines to generate separate left and right processed top images based on the stitched image that corresponds to a left-eye and right-eye view, respectively. As an example and not by way of limitation, the left processed top image may be added to the stitched image representing a left-eye view and the right processed image may be added to the stitched image representing a right-eye view. 
     In particular embodiments, processing of smaller dashed circle  610 E of top image I-Top to generate processed image I-Top′ may include detecting pairs of corresponding feature points in overlap areas  610 T and  610 U, as described above. As an example and not by way of limitation, features located near where seam lines  617  intersect an outer edge of image I-Top may be detected. One or more feature points of the detected features may be matched to corresponding feature points from stitched image  620 , and based on the matching between corresponding pairs of feature points, offsets of smaller dashed circle  610 E of image I-Top with respect to stitched image  620  may be calculated. In particular embodiments, in the case where no corresponding pairs of feature points are detected, feature points may be determined based on camera geometry, or camera calibration may be used to determine the processing performed on smaller dashed circle  610 E of top image I-Top. 
     In particular embodiments, a radial warp around a center of top image I-Top may be determined such that the center position center of top image I-Top remains fixed. Additionally, based on a determined radial warp, seam lines  617  may be rotated to intersect locations where seams  617 M of stitched image  616  end, and center lines  618  may be rotated to match any yaw adjustments performed during stitching the discrete images to generate stitched image  620 . As an example and not by way of limitation, if one of the discrete images (e.g., image I- 1 , I- 2 , or I- 3 ) forming stitched image  620  underwent a yaw adjustment of +2°, then a +2° rotation may be applied to a corresponding center line  618 . 
     In particular embodiments, one or more portions of the outer edge of smaller dashed circle  610 E of image I-Top′ may be pulled out or pulled in to match stitched image  620 . As an example and not by way of limitation, locations where seam lines  617  or center lines  618  intersect the outer edge of smaller dashed circle  610 E of image I-Top may be pulled out or pulled in to match a corresponding region of stitched image  620 . As an example and not by way of limitation, the outer edge of smaller dashed circle  610 E of image I-Top may be pulled out or pulled in by increasing or decreasing, respectively, the length of seam lines  617  or center lines  618  as appropriate. In particular embodiments, processed image I-Top′ may be saved separately as a cap image, or processed image I-Top′ may be integrated into stitched image  620 . As an example and not by way of limitation, a polar-to-rectilinear transform may be applied to processed image I-Top′, and the processed image I-Top′ may then be blended with stitched image  620 , as described below. 
     In particular embodiments, seams  617 M where the discrete images are stitched together to form stitched image  620  may be “blended” using a gradient blend. As an example and not by way of limitation, the luminance or brightness may have a gradient along a direction approaching seams  617 M. For example, the brightness may decrease moving toward seams  617 M from either lateral direction. An intersection of stitched image  620  and the outer edge of processed image I-Top′ may be blended in a similar fashion. As an example and not by way of limitation, the brightness of the intersection between stitched image  620  and the processed image I-Top′ may have a gradient proportional to the scale of stitched image  620 , such that the blending is smooth at high latitudes. 
     The blending of the discrete images may occur within the overlap areas that encompass seams  617 M. Furthermore, the blending may occur along a non-linear path to reduce visual discontinuities from the blending path. In particular embodiments, the blending algorithm may explore multiple candidate blending paths. An edge detection algorithm may be performed in area around an intersection of adjacent discrete images. If a candidate blending path hits a side edge of either image, the candidate blending path may follow the side edge in both directions until the candidate blending path is at the bottom edge of stitched image  620 . If candidate blending paths intersect, the candidate paths may continue along their current directions. In particular embodiments, selection of the blending path from the candidate blending path may be based on selecting the only candidate blending path that reaches the bottom edge of stitched image  620  or if multiple candidate blending paths reach the bottom edge, the shortest candidate blending path is selected. In particular embodiments, the candidate blending path that is the least concave with relation to the center of the image that the candidate blending path is on. For portions that are “traced” the mask gradient should be 50% directly on trace line with small blur radius. 
     In particular embodiments, a Voronoi-type seam finder may be used for spatially stable stitching. This spatial stability may ensure that shared homographic matrices and blend data may be reused, which may reduce blend-edge flickering. The Voronoi-type seam finder may be used to further refine the search areas for the feature matcher, described above, thereby improving the accuracy of the homographic matrices of feature points confined within areas (e.g., overlap areas) that are most likely to be in the output image. This data may be fed back in real-time to the front-end processors to ignore image data that may not be used in the stitching of stitched image  620 . 
     In particular embodiments, variation in the near-field depth of objects in the captured images may be a concern when generating stitched image  620 . As described above, depth information (e.g., obtained from a depth sensor or triangulation of objects in images using the stereo image pairs) may be used to segregate the feature point matching based on the proximity of the feature points to the camera. Objects closer to the viewer or camera have a different geometry for stitching than objects that are further away. In particular embodiments, the depth variation of far-field objects may have a minimal effect on stitching quality, and therefore computing resources may be focused on accounting for near-field depth variation. In particular embodiments, stitching servers  230  may determine based on depth data whether an object in one or more images is located within an area where additional measures may be taken to improve stitching quality. As an example and not by way of limitation, calculation (or recalculation) of homography matrices may then be triggered in response to detecting objects located within a pre-determined threshold distance of a camera  212  or camera system  210 . 
     In particular embodiments, the discrete images may be partitioned into multiple portions that are stitched and blended separately or near-field objects may be prioritized since these objects may have more visible stitching errors than far-field objects. As an example and not by way of limitation, near-field objects may be segregated from the far-field objects and stitched separately. In particular embodiments, the segregated near-field objects may be masked onto stitched image  620  with the far-field objects by placing the near-field objects over the far-field objects using a binary mask. Near-field objects may look very different to the cameras observing the same spot on the near-field object. In particular embodiments, the stitching server may choose to use one of the adjacent images to stitch the object in the overlap areas. As an example and not by way of limitation, a seam finder (e.g., Voronoi-type) may be used to stitch the near-field object from the image containing the majority of the near-field object&#39;s area. In particular embodiments, a non-uniform warp may be used to combine the homography matrix for the near-field object with the homography matrix for the far-field object. A mesh-based warp, for example, may transition between the two homography matrices at the edge between the near-field and far-field objects for stitching of both foreground and background of stitched image  620 . 
     Homography matrices may change significantly when objects move from far-field to near-field. In particular embodiments, calculation of homography matrices may be performed on a separate computing thread from the stitching process. As an example and not by way of limitation, one computing thread may perform stitching of the discrete images, and another computing thread may analyze the discrete images for homography data and provide updates to a shared storage. The remainder of cases may be managed by using calibration data or using the last available homography matrices. In particular embodiments, calculating the homography matrices or the stitching process may be accelerated using a graphical-processing unit (GPU). As an example and not by way of limitation, the central-processing unit (CPU) of the system may be used to calculate the homography matrices and the GPU may be used to distort and blend the discrete images. 
     In particular embodiments, one or more adjustments specific to stitching for stereoscopic video may be performed. In particular embodiments, the pairs of corresponding feature points from stitched images  620  corresponding to the left-eye and right-eye views may be projected onto a 3-D spherical projection space. In particular embodiments, there may be a difference between the starting point for the left-eye view and the right-eye view. This difference may be corrected through the initial condition that the first camera position is used as a start position and the first camera has a yaw of zero. The remaining cameras may be adjusted based on these initial conditions. 
     In particular embodiments, stitched images  620  corresponding to the left-eye view and the right-eye view may be performed using shared homography matrices. The stitching process calculating the adjustments to generate stitched image  620  corresponding to the left-eye view may communicate with the stitching process calculating the adjustments to generate stitched image  620  corresponding to the right-eye view to ensure the overall homographies and image adjustments are consistent between the left-eye view and the right-eye view. Furthermore, image parameters or exposure correction should be consistent within a reasonable range between the left-eye view and the right-eye view. In particular embodiments, stereoscopic video may have frames that are time-synchronized between left-eye view and right-eye views. 
     In particular embodiments, generating stitched images  620  for video may use a look-ahead approach. As an example and not by way of limitation, for a current frame, the stitching adjustments (e.g., homography matrices) may be calculated for the current frame and some pre-determined number of subsequent frames in the future. In particular embodiments, a full set of stitch parameters is calculated in response to detecting a substantive change in a pair of corresponding feature points (e.g., movement of an object from far-field to near-field) occurring in the future frames. Furthermore, a change flag may be set that causes the stitch parameters to be interpolated (e.g., sine easing) to the newly calculated stitching parameters, such that the stitch smoothly switches to deal with the change in the scene. The determination of the pre-determined number of subsequent frames should incorporate the time needed to calculate the new stitching adjustments. 
       FIGS. 16 and 17  illustrate example methods  1600  and  1700 , respectively, for stitching discrete images. In particular embodiments, a method  1600  for stitching of real-time 360° 3-D video is to distribute the stitching of individual frames across multiple stitching servers, as illustrated in the example of  FIG. 16 . The homography matrix management may be done either per-stitching server, or stitching servers may share homography matrices using a central homography server. In particular embodiments, the central homography server may task individual server nodes to calculate homography matrices or stitch images. The number of servers used to complete stitched images may be proportional to the desired frame rate or the throughput of the stitching servers. As an example and not by way of limitation, for a single stitching server with a 1 frame per second (FPS) throughput, 30 stitching servers may be used to produce a 30 FPS stitched video. 
     In particular embodiments, another method  1700  for stitching of real-time 360° 3-D video is to distribute the stitching of segments of video (e.g., video chunks, or multiple frames) across multiple stitching servers, as illustrated in the example of  FIG. 17 . Multiple stitching servers may concurrently handle the stitching of the video, where each stitching server generates a stitched video segment corresponding to the received segment of video. A collection server or video combiner may receive the individual video segments from the stitching servers and merge them back in order to produce the stitched video. 
     In particular embodiments, the discrete images may be manually stitched to generate a stitched image or video. The feature extraction and determination of pairs of corresponding feature points may be bypassed and manually selected pairs of corresponding feature point provided. From this point the remainder of the stitching process may be performed as described above. 
       FIG. 18  illustrates an example method  1800  for stitching at least two images. The stitching techniques described herein can be done on both the images simultaneously, or just on one, keeping the other constant. The method  1800  may begin at step  1802 , where an input is received. The input may include a number of electronic images. The images may be received from a number of cameras, such as from cameras  212 , or a single camera. As an example, the images may include images  2102 - 2116  as shown in  FIG. 21 . In particular embodiments, the cameras capturing such images may include a first camera  212  having a first orientation  214  and a second camera  212  having a second orientation  214 , and the received images may include a first image from the first camera  212  and a second image from the second camera  212 . The input may also include an initial stitched panoramic image (see for example,  FIG. 22 ) that may be generated using an initial stitching technique, such as the stitching techniques described above and illustrated in  FIGS. 18-26 . As discussed earlier, the initial stitched image may include image artifacts, such as image artifacts  2202 - 2210  as shown for example in  FIG. 22 . One technical advantage of the image stitching techniques discussed herein is to produce a seamless and smooth stitched image having fewer image artifacts, such as for example the image shown in  FIG. 27 . In particular embodiments, an initial stitched image may be used during the grid optimization step  1810  to ensure that the grid points do not move too much or to make sure that the final stitched/combined image is not too different from the initial stitched image. 
     At step  1804 , the images are defished. Defishing an image may include removing distortion from a fisheye so it looks like a conventional rectilinear image. At step  1806 , images may optionally be rescaled, for example to speed up the image stitching process and reduce the overall load on the system. In some embodiments, rescaling an image may include lowering the resolution of the image (e.g., 1920×2180 to 2124×1868) or compressing the size of the image. Rescaling the image may also sometimes reduce noise effects during edge detection. At step  1808 , image edge lines may be detected in each of the images, as shown for example in  FIG. 23 . In particular embodiments, gradient magnitudes obtained from Sobel filter is used for edge detection. Sometimes, instead of gradient magnitude, individual gradients in X and Y directions can be aligned separately. RGB colors or grayscale images can be used for aligning. Alternatively, only the features (e.g., SIFT/SURF/ORB, etc.) matches could be aligned. Other edge detectors, including for example and without limitation, Scharr, Laplacian, Roberts cross, Phase Stretch Transform (PST), Prewitt, Canny (thresholding with hysteresis) can also be used for image detection. 
     At step  1810 , grid optimization is performed. Grid optimization may include dividing each of the images into grid points (see for example,  FIGS. 24A-24F ), where each grid point corresponds to a portion of each of the images, and recursively moving the grid points and corresponding portions of the images so as to minimize the difference between the normalized gradients of overlapping regions of images. As used herein, moving a grid point in an image also references moving the portion of the image corresponding to the grid point. In other words, one or more grid points of one or more images may move (in parallel or independently) to minimize the difference in edge lines between features in the overlapping region of the images (e.g., to minimize differences between a feature in the first image and a corresponding feature in the second image, where these features appear in the region of overlap of the two images). In order to maintain image quality, grid points in non-overlapping regions of the image may also be moved. In particular embodiments, a set of spring or smoothening constraints may be added that restrict the movement of grid points between two images or within the same image up to a certain threshold (discussed in further detail below). 
     Grid points and corresponding portions of the image(s) may be moved until the edges or edge lines of two images overlap with one another. As an example and in reference to  FIG. 6 , images I- 6  and I- 7  may be first processed to detect edges in the images (e.g., similar to one as shown in  FIG. 23 ), then the two images may be divided into grid points (e.g., similar to one as shown in  FIG. 24B ), and the grid points of each of these images are moved. The images may be further divided into more grid points (e.g., similar to ones as shown in  FIGS. 24C-F ) and again grid points are moved from one position to another in each of the images until the edges of the overlapping regions  610   6-7  of the two images overlap with one another. Moving all the points together in one step can result in a very irregular mesh. For instance, if the grid points are moved all at once then the output image may look unnatural, distorted, and quite different from the original image. Therefore, a pyramid level technique may be used where the optimization (e.g., dividing image into grid regions and moving the grid points) may be done in multiple iterations or steps i.e., relatively coarser in the beginning (as shown for example in  FIG. 24B ) and gradually becoming finer (see for example,  FIGS. 24C-F ) at lower pyramid levels. In the higher pyramid levels, the algorithm searches in a larger window, which reduces as the pyramid level decreases. New grid points may be added as the pyramid level decreases (see for example,  FIGS. 24C-F ). The new grid point&#39;s positions may be interpolated from the positions of the previous points, and the grid may then be optimized again. 
     In particular embodiments, each point in the grid region of an image may be moved to minimize the difference between the normalized gradients of overlapping images in a small local area surrounding the point. The process may move down one level in the pyramid, where new grid points may be added and their positions may be interpolated using the original grid points. Each grid point&#39;s local window, and thus the maximum search distance in which to move that grid point, may decrease as the pyramid level decreases. 
     Searching for overlapping feature points can occur in grid cells at the same level (linear search) or in cells at a different pyramid level (exponential search). In particular embodiments, linear search may be used. In particular embodiments, exponential search may be used. Alternatively, particular embodiments keep the search area constant and search within that region for different pyramid levels of the image (i.e., scaled up or scaled down versions). Thus, in particular embodiments, the search can be performed with constant region and max step size on minmap of the image. 
       FIG. 19  illustrates an example method of grid optimization. In particular embodiments, steps  1902 - 1922  may be performed as part of grid optimization step  1810  and prior to proceeding to step  1812  of  FIG. 18 . 
     The method of  FIG. 19  may begin at step  1902  where a grid region and positions are set for each of the images at a desired level. The grid region for each image to be optimized may be based on its neighbor and its neighbors&#39; placement on the sphere. In particular embodiments, the area around the seam line between two images is the one which needs to be modified the most. An initial seam estimation may be performed on the images to get an idea of where the seams are located. In particular embodiments, the grid region is set based on the locations of the seam lines, keeping the seam line in the middle of the region. The number of points in the grid region is determined by the level of the pyramid set. At step  1904 , a minimum difference normal (minDiffNorm) value is initialized and iteration is set to zero. The minDiffNorm is the minimum difference or error between normalized gradients of overlapping regions of two images in order to be considered suitable for stitching. In particular embodiments, at step  1906  a determination is made whether the current iteration is less than a particular number N. N may be total possible number of movement combinations or iterations. For example, N may be 5. If the result of the determination is affirmative, then at step  1908 , the grid points are moved. The grid points may be moved between two images simultaneously or grid points may be moved in just one image while keeping the other constant. At step  1910 , a local window may be set for each grid point and then at step  1912 , gradients in the local windows are normalized. At step  1914 , difference (S) between normalized gradients of overlapping regions of images is calculated. At step  1916 , a determination is made whether the difference S is less than the minDiffNorm value that was initialized in step  1904 . If the result of the determination is affirmative, then at step  1918 , the movement and corresponding minDiffNorm is recorded and at step  1922 , the grid points are moved corresponding to the minDiffNorm value and the method ends. If, on the other hand, the difference S is greater than the minDiffNorm value, then at step  1920 , new grid points are added in each image (see for example,  FIG. 24B  to  FIG. 24C ) and iteration is incremented (e.g., from iter=0 to 1) and the steps  1906 - 1916  and  1920  are repeated until the edges or edge lines of two images overlap with one another or the difference between the two images is within or less than the minDiffNorm. 
       FIGS. 24A-H  show an example representation of the grid optimization method of  FIG. 19 .  FIG. 24A  shows an initial set of images to be stitched.  FIG. 24B  shows an initial grid applied to the images. While  FIG. 24B  shows the grid initially being arranged in a rectilinear shape, this disclosure contemplates any suitable shape for the initial grid.  FIGS. 24C-F  show the result of each iteration (i.e., pyramid level) of the grid optimization process. As shown in  FIGS. 24D-F , grid points, such as grid points in area  2410 , may be moved in an iteration, along with the portion of the image corresponding to the grid point. Once moved, the grid no longer has its same shape, e.g., the initially rectilinear grid of  FIG. 24B  is no longer so in  FIGS. 24C-F . As shown in  FIGS. 24E-F , grid points added in additional iterations of the optimization method (i.e., lower levels of the pyramid) may be added between neighboring grid points on a line between those points. Those grid points, along with the existing grid points, may be moved during future iterations of the optimization method, such that the grid point and its neighbors are no longer arranged in a line. This disclosure contemplates the grid points may be introduced in, and subsequently moved from, any suitable geometric configuration. 
     As shown in  FIGS. 24G-H , after one or more iterations of the optimization method of  FIG. 19 , the final grid (and thus, the corresponding portions of the images) has a different shape than the initial grid.  FIG. 24H  shows an example final grid after grid points and the corresponding portions of images are moved from their initial position ( FIG. 24G ) during one iteration of the optimization method of  FIG. 19 . As shown in  FIGS. 24A-H , some grid points may be moved while other are not during an iteration or during the entire optimization process of  FIG. 19 . Additional grid points that may be added after one iteration are not shown in  FIGS. 24G-H .  FIGS. 24G-H  may correspond, for example, to a grid in a region of overlap between two images being stitched. 
     Particular embodiments may repeat one or more steps of the method of  FIG. 19 , where appropriate. Although this disclosure describes and illustrates particular steps of the method of  FIG. 19  as occurring in a particular order, this disclosure contemplates any suitable steps of the method of  FIG. 19  occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example method for grid optimization, including the particular steps of the method of  FIG. 19 , this disclosure contemplates any suitable method for grid optimization, including any suitable steps, which may include all or only some of the steps of the method of  FIG. 19 , where appropriate. Furthermore, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the method of  FIG. 19 , this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the method of  FIG. 19 . For example, while the steps in  FIG. 19  may be performed by a central processing unit (CPU), any combination of those steps may be performed by any other computing system, including, e.g., a graphical processing unit (GPU), as discussed later below. 
     In particular embodiments, limiting the movement of each grid point in an iteration prevents artifacts from being introduced to the image as a result of too much movement. In particular embodiments, one or more spring or smoothening constraints may be added that restrict the movement of grid points between two images or within the same image up to a certain threshold limit. This can be thought of as minimizing the total energy of a spring system, with springs having, for example, 1) a spring constant k1, of a grid point from its origin position to its modified position, to take into consideration how much the point moves, 2) a spring constant k2, from the modified position of a grid point to the position of its neighboring grid points in that image, to take into consideration the relative displacements of points in the image, and 3) a spring constant k3, from the modified position of a grid point to a neighboring grid point in the neighboring image. In particular embodiments implementing a spring model, smoothening the displacement of grid points at an iteration (i.e., at a particular level in the pyramid) is then equivalent to a spring relation problem with spring structure as shown, for example, in  FIG. 25 . This can be done pairwise for all images. 
     As one example model of spring constraints, let the images being merged have M×N grid points each. Let the optimized displacements of the points for the first image be Pij and for the second image be Qij. Let pij and qij be the positions of points with the least energy. Let D 1  and D 2  be the original displacement vector of the points in the x and y direction respectively. Then,
 
 P   ij   −Q   ij   +q   ij   −d   ij   p   ij =0
 
⇒ d   ij   =P   ij   −Q   ij   −p   ij   +q   ij  
 
 p   ij   +r   Aij   −p   ij+1   −D   1 =0
 
⇒ r   Aij   =D   1   −p   ij   +p   ij+1  
         Similarly, for the second image, r Bij =D 1 −q ij +q ij+1  
 
 p   ij   +s   Aij   −p   i+1   j−D   2 =0
 
⇒ s   Aij   =D   2   −p   ij   +p   i+1   j  
   Similarly, for the second image, s Bij =D 2 −q ij +q i+1   j          

     The total energy of the system can be written as: 
     
       
         
           
             
               
                 
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     The total energy can also be written in matrix form as x T Ax, where x=[p 0 0 , p 0 1 , . . . , p 0 N−1 , p 1 0 , p 1 1 , . . . , p 1 N−1 , . . . , p M−1 0 , p M−1 1 , . . . , p M−1 N−1 , q 0 0 , q 0 1 , . . . , q 0 N−1 , q 1 0 , q 1 1 , q 1 N−1 , . . . , q M−1 0 , q M−1 1 , . . . , q M−1 N−1 , 1] T =[r T , 1] T , and A is a (MN+1×MN+1) symmetric positive definite matrix. Let 
               A   =     [           A   MN         b             b   T         c         ]       ,         
where A MN  is MN×MN symmetric matrix, then solution is r=A MN   −1 b.
 
     At step  1812 , color correction may optionally be performed on the images prior to seam estimation and blending. In particular embodiments, ensuring that images from all cameras have similar correction and white balance settings may result in better seam estimation and blending. For each image, the same image at different exposure settings (+1, 0, −1 exposure stops) may be fused together using standard image fusion techniques, where the weights for each exposure may be determined by contrast, saturation and well-exposedness. This may produce images with similar exposure setting which may then be easier to blend. The next step in color correction is to optimize for the images&#39; exposure, vignette removal and white balance together as a panorama. The camera response curve is used for normalizing the color space for color corrections, vignette and exposures. Let the images I 0 , I 1 , . . . , I N−1  be applied an exposure offset of log 2 (a 0 ), log 2 (a 1 ), . . . , log 2 (a N−1 ). To solve for a 0 , a 1 , a N−1 , the pixel difference using the modified exposures need to be minimized at the overlapping regions. To minimize x T Ax, such that Π i=0   N x i =1 where x=[a 0 , a 1 , . . . , a N−1 , 1] T =[r T , 1] T  and A is a (N+1×N+1) symmetric positive-semidefinite matrix: 
     Let 
               A   =     [           A   N         b             b   T         c         ]       ,         
where A N  is N×N symmetric matrix, then solution is r=A N   −1 b, normalized so that Π i=0   N−1 r i =1
 
Vignette and white balance correction can be performed in a similar way.
 
     At step  1814 , seam estimation may be performed to get a seamless stitch, e.g., without any ghosting. In particular embodiments, an energy map between two adjacent images may be calculated from the absolute difference of gradient magnitude between the images. For calculating the energy map, the energy at each pixel can be a weighted average of the neighboring pixels. The path from top to bottom with the least energy is considered as the seam line between the two images (see for example,  FIG. 26 ). Alternatively, a weighted combination of seam finding algorithms can also be used. At every pixel, weights are given based on the distance of the point from the center of the image, gradient difference, etc. and the seam with minimum energy is chosen. Each image may contribute twice in the seam estimation process. The area between the two paths is considered to the seam mask for that image. It should be noted that the seam estimation is not limited to the process discussed here and other seams finding algorithms, such as graph-cut technique can also be used for seam estimation. 
     At step  1816 , images may be blended to produce a combined or panoramic image, as shown for example in  FIG. 27 . Blending may be performed using multiband blending. Image pyramids may be built for images as well as the seam masks and each level of the pyramid may be blended independently. The resulting panorama is recovered from all the blended pyramid levels. In particular embodiments, blend width may be scaled to latitude values so that smooth blends can be achieved at higher latitudes. This keeps the blend width almost constant when the panorama is projected on the sphere. Let Ø be the latitude of a point along the seam line, d be the desired blend width when projected on the sphere. Then the blend width at the point should be 
     
       
         
           
             
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     Particular embodiments may repeat one or more steps of the method  1800  of  FIG. 18 , where appropriate. Although this disclosure describes and illustrates particular steps of the method of  FIG. 18  as occurring in a particular order, this disclosure contemplates any suitable steps of the method of  FIG. 18  occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example method for stitching images based on grid optimization, including the particular steps of the method of  FIG. 18 , this disclosure contemplates any suitable method for stitching images based on grid optimization, including any suitable steps, which may include all, some, or none of the steps of the method of  FIG. 18 , where appropriate. Furthermore, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the method of  FIG. 18 , this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the method of  FIG. 18 . For example, while the steps in  FIG. 18  may be performed by a central processing unit (CPU), any combination of those steps may be performed by any other computing system, including, e.g., a graphical processing unit (GPU) as discussed later below. 
     In particular embodiments, the grid optimization technique discussed herein can be applied to video stitching, i.e., to stitching image frames in a video. Optimizations may be performed multiple times during the video stitching. The frequency of optizmiation may depend on the time cost of single optimization. After each optimization, pixel movement may be recorded as a transform map. The transform map may be applied for subsequent frames until next optimization. Between two adjacent transform maps, the recorded pixel movement may be interpolated to make transition smooth. 
     In particular embodiments, the grid optimization technique discussed herein can be applied for stitching a top image. The top image with estimated image parameters may be placed on the optimized panorama (obtained after the blending step  1816 ). Grid optimization may be applied between the optimized panorama and the warped top image to stitch the top image. 
     In particular embodiments, the grid optimization discussed herein can be applied for 3D stitching. For a good 3D stitch, the vertical offset between left and right panoramas should be close to zero. The vertical offset for each grid point in the left and right images may be calculated by recording the y-axis movement in the pyramid search. The grid optimization should be applied to the adjacent pairs of both left and right panoramas together, with the constraint that the difference between the y-axis movements should be limited by the vertical offset, and that the difference between the x-axis movements should not exceed a constant EX,MAX (the maximum horizontal offset that can occur before a user sees double, i.e., two separate images rather than one 3D image). The seam estimation can be applied to the adjacent pairs of both left and right panoramas together to have a better 3D viewing experience. 
       FIG. 20  illustrates another example method  2000  of stitching images based on grid optimization. The method  2000  may begin at step  2002 , where a first image and a second image are accessed or received. In some embodiments, the first image is an image that may be received from a first camera  212  having a first orientation and the second image is an image that may be received from a second camera  212  having a second orientation. In some embodiments, the first and second images may be received from the same camera. In particular embodiments, at least part of the first image overlaps with at least part of the second image, or the first and the second images have an overlapping region in between. As an example, in reference to  FIG. 6 , the first and the second camera images may be I- 6  and I- 7 , respectively, having an overlapping region  610   6-7 . In some embodiments, one or more of the first and second images may be rescaled, which may include lowering the resolution or compressing the size of the images to speed up the overall process and reduce system load, as discussed elsewhere herein. 
     At step  2004 , each of the first image and the second image is divided into a first set of grid points, as shown for example in  FIG. 24B . In particular embodiments, each grid point corresponds to a portion of the first image or the second image. At step  2006 , differences in the region of overlap between the first and second images are determined. In particular embodiments, to determine the differences, edge detection is performed on the images to calculate image edges and/or contrast lines (e.g., see  FIG. 23 ) and then differences in edge lines between a feature in the first image and a corresponding feature in the second image are determined. Edge detection may be performed using sobel gradients as discussed elsewhere herein. At step  2008 , one or more grid points and corresponding portions of the first image or the second image are moved relative to other grid points to minimize the differences between the first image and the second image. In particular embodiments, moving the one or more grid points includes moving the grid points from one position to another in order to minimize the difference in edge lines between features in the overlapping region of the first and second images, as shown for example in  FIGS. 24C-F . 
     In particular embodiments, a local window may be defined for each grid point and movement of each of the one or more grid points may be constrained within its respective local window. The local window for each of the grid points may be located in the region of overlap between the first and second images. In some embodiments, the grid points of the first and second mages may be moved simultaneously or independent of one another. The grid points may be moved based at least in part on a force model comprising a set of spring or smoothening constraints, which may be configured to resist movement of the grid points, as discussed elsewhere herein. For instance, the set of spring constraints may define one or more of how much (e.g., pixels) a first grid point should move relative to a second grid point within the same image, how much a grid point in the first image should move relative to a grid point in the second image, and how much a grid point in the first image should move relative to its origin position, as shown and discussed, for example, in reference to  FIG. 25 . 
     At step  2010 , after the grid points and corresponding portions of the first and/or second images are moved, differences in the region of overlap between the two images are again determined. At step  2012 , a determination is made whether at least one difference in the overlapping region is greater than a predetermined threshold. If the result of the determination is positive, then at step  2013 , a second/subsequent set of grid points or new grid points is added to each of the first and second images, as shown for example from  FIG. 24B to 24C or 24C  to  FIG. 24D . In particular embodiments, the size of the local window for each grid point is reduced as subsequent/new grid points are added into the images. Steps  2008 - 2012  may be repeated until the at least one difference in the region of overlap becomes less than the predetermined threshold. In particular embodiments, this difference is less than the predetermined threshold when the edges or edge lines of the first and second images overlap with each other. For example, as shown in elements  102   a  and  104   a  of  FIG. 1 , edges between the hand rails in two overlapping images may not align. If the result of the determination in step  2012  is negative or once the difference(s) in the overlapping region between the first and second images is less than predetermined threshold, then at step  2014 , the first image and the second image are combined to produce a merged image (e.g., a panoramic image), as shown for example in  FIG. 27 . For example, as shown in elements  102   b  and  104   b  of  FIG. 1 , edges between the hand rails in two overlapping images be sufficiently aligned as a result of iterative grid optimization. In particular embodiments, combining the first and second camera images may include identifying a seam line between the two images (as discussed above in step  1814  of  FIG. 18 ) and then blending the images along the seam line to produce the merged image (as discussed above in step  1816  of  FIG. 18 ). 
     Particular embodiments may repeat one or more steps of the method  2000  of  FIG. 20 , where appropriate. Although this disclosure describes and illustrates particular steps of the method of  FIG. 20  as occurring in a particular order, this disclosure contemplates any suitable steps of the method of  FIG. 20  occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example method for stitching images based on grid optimization, including the particular steps of the method of  FIG. 20 , this disclosure contemplates any suitable method for stitching images based on grid optimization, including any suitable steps, which may include all, some, or none of the steps of the method of  FIG. 20 , where appropriate. Furthermore, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the method of  FIG. 20 , this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the method of  FIG. 20 . For example, while the steps in  FIG. 20  may be performed by a central processing unit (CPU), any combination of those steps may be performed by any other computing system, including, e.g., a graphical processing unit (GPU) as discussed below. 
     In order to decrease the time cost of single time optimization and increase the frequency of optimizations, particular embodiments may use a graphical processing unit (GPU) to accelerate the grid optimization (step  1810 ), seam estimation (step  1814 ), and blending (step  1816 ). As an example and not by way of limitation, when running these steps on a GPU like Nvidia GTX 980, the performance is about 6-18 times faster than a single thread CPU version running on Xeon 3.10 GHz. Each of the GPU-based grid optimization, seam estimation, and blending steps is discussed in detail below. 
     When doing grid optimization step  1810  on a GPU, for each grid point, a thread block may be assigned for calculation. When optimizing a particular grid point, such as grid point A, for each pixel or each pile of pixels in a local window WA around grid point A, a separate thread may be assigned for calculation. Using a reduction algorithm, minimum and maximum values in the local window WA may be obtained for normalization, and also their sum S A  in W A . Movement of grid points may be recorded using minimum S A . New grid points may be interpolated in two steps. If the pyramid level has not reached a minimum level (as discussed above in relation to  FIGS. 18 and 19 ), then level may be decreased and local window W A  may be reduced to obtained a new set of min and max values in W A  and the subsequent steps are repeated until the pyramid level reaches the minimum level. 
     Since sobel difference and pixel energy are both in-place calculation and calculation for each pixel is independent from others, assigning one thread per pixel can utilize the parallel capacity of a GPU. For seam finding, two alternative approaches may be used. In the first approach, kernel functions may be launched on every row sequentially. After calculating one row, current kernel function is stopped and another one is started for next row. In the second approach, only one kernel is used for every row, and inside the kernel, one thread is used for one column. Threads in the block may be synced after calculating each row. In particular embodiments, since the seam finding region is limited to 512 columns around seam line, and the number of threads per block can be 2124, the second method is preferred over the first one. 
     In particular embodiments, a reduction method may be used on the first row to find the start pixel of the seam line with minimum energy. A seam map may be copied to a CPU and seam line finding may be done by the CPU because this requires only one thread. A seam mask may be filled among all seam lines. A first channel may be used to record the index of the image and a second channel may be used to record the pixel weight for blending. 
     In particular embodiments, a pyramid for all images including seam mask may be built. For each pixel, one thread is assigned. After one level of pyramid has been built, threads with an index bigger than the pixel level in current level are killed or terminated. Images may be blended in every level. For every pixel, the image is chosen based on the first channel value of the seam mask in the current level. The image from the pyramid may be recovered by launching kernel for each level sequentially, from bottom to top. 
     In particular embodiments, merging two or more images into a single image may be accomplished by adjusting the images based on a number of considerations. For example, misaligned portions of overlapping images may be corrected by adjusting (e.g., by warping or distorting) at least part of one or both of the images so as to minimize the misalignment. However, adjusting the images so that they are completely aligned may require so much adjustment that other portions of the images become misaligned and appear distorted to a viewer. Thus, considerations for merging two or more images may include an analysis of the image distortion caused by aligning misaligned portions of an image. As explained below, image distortion may include both local distortion, which refers to distortion of the image near the portions that are being aligned, and global distortion, which refers to distortion of portions of the image that are not near misaligned portions of the image. Thus, merging two or more images into a single image may balance the competing considerations of alignment and image distortion in order to reduce misalignment while also preserving image quality. 
       FIG. 29  illustrates an example method  2900  for merging two or more images into a single image. Step  2905  involves accessing two or more images having an overlapping area, i.e., that each contain the same portion of a scene. For example, the images may be captured by the cameras described herein. 
     Method  2900  may include step  2910 , in which features may be identified in the images accessed in step  2905 . The features may be identified in the region of overlap of two images. In particular embodiments, features may be identified when one or more adjacent or nearby pixels in an image have some difference between them, such as a difference in color gradient, brightness, or other patterns. In particular embodiments, a feature in one image may be associated with a corresponding feature in another image. For example, the discontinuity in the left-side handrail shown in element  104   a  in  FIG. 1  may be an image feature and the discontinuity in the right-side handrail may be a corresponding image feature. In particular embodiments, feature points may be used to identify the location of a feature in an image. For example, the coordinates of a feature may be determined based on the coordinates of an associated feature point. 
     In particular embodiments, other parameters in addition to features may be identified in step  2910 . For example, in particular embodiments step  2910  may include accessing or determining camera properties of the camera(s) that took the images accessed in step  2905 . In particular embodiments, camera properties may be estimated. For example, distance minimization techniques using software such as PTGUI, Hugin, Autopano Kolor, or Panorama studio may be used. As another example, software libraries like Libpano may be used to compute a direct perspective/homography transformation between images and then adjust those images depending upon the projection and lens type. Software libraries such as OpenCV, VLFeat, and the like may utilize perspective estimation algorithms that can be used to perform, or assist in performing, such adjustments. 
     In particular embodiments, identifying features may include receiving an identification of features. In particular embodiments, identifying features may include computing or estimating such features. For example, DLT may be used to compute a base perspective transform. This disclosure contemplates that other methods may be used in addition or the alternative. For example, RANSAC may be used to filter outliers, and other algorithms such as least median of squares can also be used. This disclosure contemplates that any suitable method or algorithms may be used to identify features in a set of images. 
     Method  2900  may include step  2915 , in which all or part of the images are divided into regions. Such regions are referred to herein as “cells.” In particular embodiments, each cell may correspond to a region that is capable of being adjusted. In other words, each cell can be considered to be a variable capable of being adjusted in order to achieve the best fit between two or more images. Thus, in particular embodiments, more control over image adjustments may be obtained by dividing an image into more cells, thus introducing more variables that can be varied. Because the number of variables may provide more control but may also require more processing power, in particular embodiments the number of cells may be based on the features identified in the images, the type of image at issue (e.g., 2D vs 3D images, real-time vs. recorded images), the alignment (or lack thereof) between images, and/or the processing capabilities of a device. 
     In particular embodiments, a cell may be defined by a grid or mesh.  FIG. 24G  illustrates an example mesh and an example grid. Each point  2415  may be considered to be a grid point and each segment  2420  may be considered to be part of a mesh. Cell  2425  illustrates an example of a cell defined by grid points and/or by a mesh. In particular embodiments, each segment of a mesh or grid point in a grid may be independently variable. In particular embodiments, the number of variables may be determined by the size of cells, by the number of mesh segments defining the cells, and/or by the number of grid points defining the cells. Where this disclosure discusses grids and grid points this disclosure contemplates that meshes and segments can also or in the alternative be used as appropriate, and vice versa. 
     This disclosure contemplates that a cell may be defined by any suitable number and shape of grid points. For example, in  FIG. 24G  the grid points define cells that are square. In other words, each grid point defines a corner, or vertex, of a square. However, this disclosure contemplates that cells may take other shapes, such as for example rectangles or triangles. This disclosure contemplates that the size or shape of cells in an image may vary. For example, a grid could be used that has a varying density of grid points in different parts of the image. For example, if the center of an image is the focus of the stitching techniques described herein, then cells may be smaller in the center of the image and gradually grow bigger towards the edges. As another example, objects in an image may be identified, and cells may be defined such that grid points go around objects and do not pass through them. As another example, the size or shape of a cell may vary based on the feature(s) identified or discontinuities (e.g., edges) of one or more pixel attributes. This disclosure contemplates that cells may take any suitable size or shape and may be defined by any suitable number and shape of grid points or mesh segments. 
     In particular embodiments, the images accessed in step  2905  may be projected to a coordinate system that corresponds to the parameters of the cameras used to take the pictures. For example, a camera may use a “fisheye lens” to take a picture such that the field of view is different in, e.g., the vertical and horizontal dimensions.  FIG. 23  illustrates an example of transforming an image to its original coordinate system, which may also be referred to herein as “dewarping” or “defishing.” In particular embodiments, an image may be divided into cells (e.g. by defining a grid) after an image is defished. In particular embodiments, an image may be divided into cells before an image is defished, and thus the grid will be “defished” as well (i.e., will be transformed from the coordinate system in which it was initially placed to the images&#39; coordinate system). 
     In particular embodiments, the images accessed in step  2905  may undergo an initial stitching or merging process. For example, the accessed images may be aligned or stitched. This disclosure contemplates any suitable method for an initial alignment and stitching, such as but not limited to the alignment and stitching techniques described in connection with  FIGS. 8-18  herein. In particular embodiments, initial alignment and stitching may be performed after accessing the images in step  2905 , for example after defishing a set of images. In particular embodiments, the images accessed in step  2905  may have already undergone initial alignment and stitching. Thus, method  2900  may occur after an initial alignment and stitching, or alignment and stitching may be a part of method  2900 . 
     In particular embodiments, method  2900  may include adjusting one or more cells in step  2920  based on misalignment between features in the image and based on image distortion caused by adjusting an image.  FIG. 30  illustrates an example method for adjusting image cells based on these considerations. In particular embodiments, adjusting a cell may include adjusting one or more grid points or meshes defining the cell, and thus adjusting the portion of the image associated with the grid point or mesh. 
     In particular embodiments, adjustments made be made to one or both images being merged together. In particular embodiments, when more than two images are being merged together, one image may be kept constant (e.g., as a reference image) and any or all of the remaining images may be adjusted in accordance with step  2920 . In particular embodiments, when more than two images are being merged together, step  2920  may be sequentially performed for each pair of images. In other words, the adjustments to a pair of images may be calculated, and then adjustments for the next pair of images may be calculated. For example, with reference to  FIG. 6 , adjustments made be made to images I- 8  and I- 7 , then to images I- 7  and I- 6 , and so on. In particular embodiments, when more than two images are being merged together, step  2920  may be performed in parallel for each pair of images. For example, with reference to  FIG. 6 , adjustments may be made to all of the images at the same time based on the features identified in the regions of overlap  610  between the images. 
     In particular embodiments, method  2900  may include performing step  2920  several times. For example, the example method of  FIG. 30  may be iteratively repeated 100 or 1000 times in order to adjust a set of images. In particular embodiments, step  2920  may be performed a predetermined number of times. In other embodiments, step  2920  may be performed until a certain amount of alignment is achieved or until some other parameter, such as the example cost function J described below, achieves a predetermined value. In particular embodiments, step  2920  may be performed until the amount of change of alignment or of some other parameter, such as the example cost function J described below, changes less than certain amount in each successive performance of step  2920 . In particular embodiments, step  2920  may be performed until user input is received indicating that adjustment of the image(s) should no longer occur. 
     Method  2900  may include step  2925  in which the adjusted images are rendered. In particular embodiments, step  2920  may output coordinates for the adjusted images, such as for example by outputting mesh or grid point coordinates corresponding to particular portions of the images. For example, step  2925  may compute and output mesh coefficients, for example using the same interpolation technique used to render the mesh. For example, if bilinear interpolation is used to compute coefficients then bilinear coefficients may be used. Other interpolation techniques like nearest neighbor, bicubic, or spline may be used to compute and render a mesh. In particular embodiments, step  2920  may output a description of the cells to modify and how those cells are modified from the input images. In particular embodiments, step  2920  may output the images as adjusted. 
     This disclosure contemplates that step  2925  may include processing the rendered images. For example, step  2925  may include blending the rendered images together, e.g., to reduce the appearance of seams in the images. For example, the blending may be performed by using a graph cut segmentation algorithm or a seam cut and multiband blending algorithm. This disclosure contemplates any suitable method or technique for blending adjusted images. For example, enblend may be used to estimate the seam between images. Other algorithms like voronoi or variants of the graph-cut seam finding algorithm may be used. Algorithms such as a multiband blending algorithm, a linear algorithm, or a Laplacian algorithm may be used to blend the images. This disclosure also contemplates that any other suitable processing may be performed in step  2925 . 
     This disclosure contemplates that “rendering” images may involve processing the images and storing them in a data store, such as a server or a data store of a user&#39;s client device. This disclosure contemplates that step  2925  may include displaying the images, such as on a display of a client device, including the client device described herein. This disclosure contemplates that method  2900  may be performed in real time, e.g., to display images from a live event. This disclosure also contemplates that method  2900  may be performed and the resulting images stored for later use. 
     Particular embodiments may repeat one or more steps of the method of  FIG. 29 , where appropriate. Although this disclosure describes and illustrates particular steps of the method of  FIG. 29  as occurring in a particular order, this disclosure contemplates any suitable steps of the method of  FIG. 29  occurring in any suitable order. Moreover, although this disclosure describes and illustrates an example method for adjusting images, including the particular steps of the method of  FIG. 29 , this disclosure contemplates any suitable method for adjusting images according to the considerations described herein, including any suitable steps, which may include all or only some of the steps of the method of  FIG. 29 , where appropriate. Furthermore, although this disclosure describes and illustrates particular components, devices, or systems carrying out particular steps of the method of  FIG. 29 , this disclosure contemplates any suitable combination of any suitable components, devices, or systems carrying out any suitable steps of the method of  FIG. 29 . For example, while the steps in  FIG. 29  may be performed by a central processing unit (CPU), any combination of those steps may be performed by any other computing system, including, e.g., a graphical processing unit (GPU). As another example, the steps of  FIG. 29  may be performed by a server, a client device, or some combination thereof. 
       FIG. 30  illustrates an example method  3000  for performing step  2920  in  FIG. 29 . In particular embodiments, method  3000  evaluates potential adjustments to an image, such warping of an image by moving a particular grid point corresponding to that portion. Method  3000  may begin with step  3005 , which calculates the misalignment of feature points in the images being analyzed. For example, the misalignment may be calculated based on a distance between a feature point in one image and the corresponding feature point in a second image with which it should align. Herein, the alignment between feature points may be referred to as “local alignment.” 
     Local alignment may be quantitatively represented as the sum of squared distances between a feature point in an image and a corresponding feature point in an overlapping image. The sum may be over all features points that are misaligned. In other words, if there are j feature points F j ( i ) in image (i) then there are j corresponding feature points F j    (i+l)  in corresponding image (i+l). Thus, the total local misalignment J local  for those two images may be represented as the sum of squared distances between the j features in image (i) and the j corresponding features in the overlapping image (i+l). 
     In embodiments in which the cells are defined by a grid, the local alignment term can be represented as: 
     
       
         
           
             
               
                 
                   J 
                   local 
                 
                 = 
                 
                   
                     ∑ 
                     
                       k 
                       = 
                       1 
                     
                     j 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           F 
                           k 
                         
                         
                           ( 
                           i 
                           ) 
                         
                       
                       - 
                       
                         
                           F 
                           k 
                         
                         
                           ( 
                           
                             i 
                             + 
                             1 
                           
                         
                       
                     
                     ) 
                   
                 
               
               ) 
             
             2 
           
         
       
     
     where F j    (i)  represents the coordinates of the j th  feature point in the i th  image.  FIG. 32  illustrates an example method for determining the coordinates of the feature points using bilinear mapping in the cell in which the j th  feature point is located. When computing J local , any suitable method for finding the containing cell for each feature can be used, as well as any method for computing coefficients for bilinear mapping. If an alternative method for texture interpolation is used, then bilinear mapping might be replaced by the corresponding interpolation map. 
     The above term J local  quantifies the total misalignment of the features in two overlapping images. If multiple overlapping images are considered, the J local  is the sum of the J local  values of each pair of overlapping images begin merged together. 
     Method  3000  may include step  3010 , in which distortions of image cells that are not near a feature point are determined. Such distortions may be referred to as “global alignment.” When a grid is used to define cells, the global alignment term J global  is equal to the square of the distance between initial, pre-adjustment positions of grid points and their final, adjusted positions. Thus, the term J global  penalizes misalignments between two images as initially aligned and stitched compared to the two images after adjustment. In particular embodiments, preserving the initial alignment is desired in areas with no features. In particular embodiments, preserving the initial alignment is desired in areas where a feature point and its corresponding feature point are very close to being aligned. 
     In particular embodiments, J global  is the sum of the square of distances between the coordinates of a warped vertex (grid point) warp (i) (V (i) ) and the vertex&#39;s original coordinates V (i) . In particular embodiments, each term in the sum may be weighted by a weight T. Thus, J global  may be represented as: 
     
       
         
           
             
               J 
               global 
             
             = 
             
               
                 ∑ 
                 
                   i 
                   , 
                   
                     V 
                     i 
                   
                 
               
               ⁢ 
               
                   
               
               ⁢ 
               
                 
                   
                     τ 
                     V 
                   
                   i 
                 
                 ⁢ 
                 
                   
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                           warp 
                           
                             ( 
                             i 
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                         ⁡ 
                         
                           ( 
                           
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                           ( 
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                           ) 
                         
                       
                     
                      
                   
                   2 
                 
               
             
           
         
       
     
     In particular embodiments, the weight τ may be 0 if no cell defined by the vertex being considered contains a feature point. In particular embodiments, the weight may depend on the distance the cell is from a cell containing a feature, with the weight decreasing with increasing distance. In particular embodiments, the weight τ may be determined by: 
     
       
         
           
             
               τ 
               
                 V 
                 
                   ( 
                   i 
                   ) 
                 
               
             
             = 
             
               min 
               ⁢ 
               
                   
               
               ⁢ 
               
                 ( 
                 
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                       j 
                     
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                                 ( 
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                               F 
                               j 
                               
                                 ( 
                                 
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                                   + 
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                                 ( 
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     Method  3000  may include step  3015 , which seeks to preserve the geometry of cells by determining the geometric distortion caused by an adjustment. That determination may also be referred to as the “smoothness term” J smoothness . In particular embodiments, a distortion of a shape within a cell or partly defined by a cell may be used to calculate the parameter J smoothness . For example, J smoothness  may represent the distortion of a shape of a triangle formed by three vertices (grid points) defining the cell. For example, for each vertex V 1 ( i ), and each triangle it forms with vertices in adjacent cells ΔV i V 2 V 3 ( i ), J smoothness  may be equal to the squared distance between the warped position of the vertex warped( i )(V 1    (i) ), and the point V V     1     ,ΔV     1     V     2     V     3   ( i ) that will make the warped triangle similar to the original triangle. In particular embodiments: 
     
       
         
           
             
               J 
               smoothness 
             
             = 
             
               
                 ∑ 
                 
                   i 
                   , 
                   
                     V 
                     1 
                     
                       ( 
                       i 
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                     ⁢ 
                     
                         
                     
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                         warp 
                         
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     where: 
     
       
         
           
             
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     where the weighting term describes the saliency value of the cell the feature lies in. In particular embodiments, J smoothness  is summed over all vertices and all triangles in the grid. 
     Method  3000  may include step  3020 , in which an overall cost function J is calculated by adding together the terms quantifying the local alignment, the global alignment, and the smoothness. In particular embodiments, J may be a weighted sum of those terms. In particular embodiments, the weights may be normalized to the weight given to J local  such that: 
     
       
         
           
             J 
             = 
             
               
                 J 
                 local 
               
               + 
               
                 
                   α 
                   global 
                 
                 ⁢ 
                 
                   J 
                   global 
                 
               
               + 
               
                 
                   α 
                   smooth 
                 
                 ⁢ 
                 
                   J 
                   smooth 
                 
               
             
           
         
       
     
     In particular embodiments, α global =0.01 and α smooth =0.001. In particular embodiments the weights may be determined based on cell size and/or on the distribution of features. 
     Method  3000  may include step  3025 , which involves adjusting the cells so as to minimize the overall cost function J. In particular embodiments, the overall cost function J is quadratic with respect to the warped positions of mesh vertices. In particular embodiments, a direct solution to 
                 ∂   J       ∂   V       =   0         
can be found, although if the number of variables is relatively large then a direct solution may not be feasible. In such circumstances, a gradient method may be used to find a solution. For example, gradient descent or conjugate gradient based algorithms and its variants may be used.
 
       FIGS. 31A-B  illustrate a set of detailed example calculations for determining J local , J global , J smoothness , and the overall cost function J. However, this disclosure contemplates any suitable method for calculating those terms. For example, the smoothness term may be calculated using different techniques for calculating the position of V V     1     ,ΔV     1     V     2     V     3   . In particular embodiments, the saliency coefficient can be expanded to include L 2  norm of the RGB color values of the cell, the abundance of edges, and/or the number of edges spanning into adjacent cells. 
       FIG. 32  illustrates a set of detailed example calculations for using bilinear mapping to determine the coordinates of a feature based on the coordinates of vertices X, Y, Z, and W of cell containing a feature j in an image (i). The output of  FIG. 32  determines the coefficients α referenced in  FIGS. 31A-B  to calculate the J local  term. 
       FIG. 33  illustrates an example computer system  3300 . In particular embodiments, one or more computer systems  3300  perform one or more steps of one or more methods described or illustrated herein. In particular embodiments, one or more computer systems  3300  provide functionality described or illustrated herein. In particular embodiments, software running on one or more computer systems  3300  performs one or more steps of one or more methods described or illustrated herein or provides functionality described or illustrated herein. Particular embodiments include one or more portions of one or more computer systems  3300 . Herein, reference to a computer system may encompass a computing device, and vice versa, where appropriate. Moreover, reference to a computer system may encompass one or more computer systems, where appropriate. 
     This disclosure contemplates any suitable number of computer systems  3300 . This disclosure contemplates computer system  3300  taking any suitable physical form. As example and not by way of limitation, computer system  3300  may be an embedded computer system, a system-on-chip (SOC), a single-board computer system (SBC) (such as, for example, a computer-on-module (COM) or system-on-module (SOM)), a desktop computer system, a laptop or notebook computer system, an interactive kiosk, a mainframe, a mesh of computer systems, a mobile telephone, a personal digital assistant (PDA), a server, a tablet computer system, or a combination of two or more of these. Where appropriate, computer system  3300  may include one or more computer systems  3300 ; be unitary or distributed; span multiple locations; span multiple machines; span multiple data centers; or reside in a cloud, which may include one or more cloud components in one or more networks. Where appropriate, one or more computer systems  3300  may perform without substantial spatial or temporal limitation one or more steps of one or more methods described or illustrated herein. As an example and not by way of limitation, one or more computer systems  3300  may perform in real time or in batch mode one or more steps of one or more methods described or illustrated herein. One or more computer systems  3300  may perform at different times or at different locations one or more steps of one or more methods described or illustrated herein, where appropriate. 
     In particular embodiments, computer system  3300  includes a processor  3302 , memory  3304 , storage  3306 , an input/output (I/O) interface  3308 , a communication interface  3310 , and a bus  3312 . Although this disclosure describes and illustrates a particular computer system having a particular number of particular components in a particular arrangement, this disclosure contemplates any suitable computer system having any suitable number of any suitable components in any suitable arrangement. 
     In particular embodiments, processor  3302  includes hardware for executing instructions, such as those making up a computer program. As an example and not by way of limitation, to execute instructions, processor  3302  may retrieve (or fetch) the instructions from an internal register, an internal cache, memory  3304 , or storage  3306 ; decode and execute them; and then write one or more results to an internal register, an internal cache, memory  3304 , or storage  3306 . In particular embodiments, processor  3302  may include one or more internal caches for data, instructions, or addresses. This disclosure contemplates processor  3302  including any suitable number of any suitable internal caches, where appropriate. As an example and not by way of limitation, processor  3302  may include one or more instruction caches, one or more data caches, and one or more translation lookaside buffers (TLBs). Instructions in the instruction caches may be copies of instructions in memory  3304  or storage  3306 , and the instruction caches may speed up retrieval of those instructions by processor  3302 . Data in the data caches may be copies of data in memory  3304  or storage  3306  for instructions executing at processor  3302  to operate on; the results of previous instructions executed at processor  3302  for access by subsequent instructions executing at processor  3302  or for writing to memory  3304  or storage  3306 ; or other suitable data. The data caches may speed up read or write operations by processor  3302 . The TLBs may speed up virtual-address translation for processor  3302 . In particular embodiments, processor  3302  may include one or more internal registers for data, instructions, or addresses. This disclosure contemplates processor  3302  including any suitable number of any suitable internal registers, where appropriate. Where appropriate, processor  3302  may include one or more arithmetic logic units (ALUs); be a multi-core processor; or include one or more processors  3302 . Although this disclosure describes and illustrates a particular processor, this disclosure contemplates any suitable processor. 
     In particular embodiments, memory  3304  includes main memory for storing instructions for processor  3302  to execute or data for processor  3302  to operate on. As an example and not by way of limitation, computer system  3300  may load instructions from storage  3306  or another source (such as, for example, another computer system  3300 ) to memory  3304 . Processor  3302  may then load the instructions from memory  3304  to an internal register or internal cache. To execute the instructions, processor  3302  may retrieve the instructions from the internal register or internal cache and decode them. During or after execution of the instructions, processor  3302  may write one or more results (which may be intermediate or final results) to the internal register or internal cache. Processor  3302  may then write one or more of those results to memory  3304 . In particular embodiments, processor  3302  executes only instructions in one or more internal registers or internal caches or in memory  3304  (as opposed to storage  3306  or elsewhere) and operates only on data in one or more internal registers or internal caches or in memory  3304  (as opposed to storage  3306  or elsewhere). One or more memory buses (which may each include an address bus and a data bus) may couple processor  3302  to memory  3304 . Bus  3312  may include one or more memory buses, as described below. In particular embodiments, one or more memory management units (MMUs) reside between processor  3302  and memory  3304  and facilitate accesses to memory  3304  requested by processor  3302 . In particular embodiments, memory  3304  includes random access memory (RAM). This RAM may be volatile memory, where appropriate, and this RAM may be dynamic RAM (DRAM) or static RAM (SRAM), where appropriate. Moreover, where appropriate, this RAM may be single-ported or multi-ported RAM. This disclosure contemplates any suitable RAM. Memory  3304  may include one or more memories  3304 , where appropriate. Although this disclosure describes and illustrates particular memory, this disclosure contemplates any suitable memory. 
     In particular embodiments, storage  3306  includes mass storage for data or instructions. As an example and not by way of limitation, storage  3306  may include a hard disk drive (HDD), a floppy disk drive, flash memory, an optical disc, a magneto-optical disc, magnetic tape, or a Universal Serial Bus (USB) drive or a combination of two or more of these. Storage  3306  may include removable or non-removable (or fixed) media, where appropriate. Storage  3306  may be internal or external to computer system  3300 , where appropriate. In particular embodiments, storage  3306  is non-volatile, solid-state memory. In particular embodiments, storage  3306  includes read-only memory (ROM). Where appropriate, this ROM may be mask-programmed ROM, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), electrically alterable ROM (EAROM), or flash memory or a combination of two or more of these. This disclosure contemplates mass storage  3306  taking any suitable physical form. Storage  3306  may include one or more storage control units facilitating communication between processor  3302  and storage  3306 , where appropriate. Where appropriate, storage  3306  may include one or more storages  3306 . Although this disclosure describes and illustrates particular storage, this disclosure contemplates any suitable storage. 
     In particular embodiments, I/O interface  3308  includes hardware, software, or both, providing one or more interfaces for communication between computer system  3300  and one or more I/O devices. Computer system  3300  may include one or more of these I/O devices, where appropriate. One or more of these I/O devices may enable communication between a person and computer system  3300 . As an example and not by way of limitation, an I/O device may include a keyboard, keypad, microphone, monitor, mouse, printer, scanner, speaker, still camera, stylus, tablet, touch screen, trackball, video camera, another suitable I/O device or a combination of two or more of these. An I/O device may include one or more sensors. This disclosure contemplates any suitable I/O devices and any suitable I/O interfaces  3308  for them. Where appropriate, I/O interface  3308  may include one or more device or software drivers enabling processor  3302  to drive one or more of these I/O devices. I/O interface  3308  may include one or more I/O interfaces  3308 , where appropriate. Although this disclosure describes and illustrates a particular I/O interface, this disclosure contemplates any suitable I/O interface. 
     In particular embodiments, communication interface  3310  includes hardware, software, or both providing one or more interfaces for communication (such as, for example, packet-based communication) between computer system  3300  and one or more other computer systems  3300  or one or more networks. As an example and not by way of limitation, communication interface  3310  may include a network interface controller (NIC) or network adapter for communicating with an Ethernet or other wire-based network or a wireless NIC (WNIC) or wireless adapter for communicating with a wireless network, such as a WI-FI network. This disclosure contemplates any suitable network and any suitable communication interface  3310  for it. As an example and not by way of limitation, computer system  3300  may communicate with an ad hoc network, a personal area network (PAN), a local area network (LAN), a wide area network (WAN), a metropolitan area network (MAN), body area network (BAN), or one or more portions of the Internet or a combination of two or more of these. One or more portions of one or more of these networks may be wired or wireless. As an example, computer system  3300  may communicate with a wireless PAN (WPAN) (such as, for example, a BLUETOOTH WPAN), a WI-FI network, a WI-MAX network, a cellular telephone network (such as, for example, a Global System for Mobile Communications (GSM) network), or other suitable wireless network or a combination of two or more of these. Computer system  3300  may include any suitable communication interface  3310  for any of these networks, where appropriate. Communication interface  3310  may include one or more communication interfaces  3310 , where appropriate. Although this disclosure describes and illustrates a particular communication interface, this disclosure contemplates any suitable communication interface. 
     In particular embodiments, bus  3312  includes hardware, software, or both coupling components of computer system  3300  to each other. As an example and not by way of limitation, bus  3312  may include an Accelerated Graphics Port (AGP) or other graphics bus, an Enhanced Industry Standard Architecture (EISA) bus, a front-side bus (FSB), a HYPERTRANSPORT (HT) interconnect, an Industry Standard Architecture (ISA) bus, an INFINIBAND interconnect, a low-pin-count (LPC) bus, a memory bus, a Micro Channel Architecture (MCA) bus, a Peripheral Component Interconnect (PCI) bus, a PCI-Express (PCIe) bus, a serial advanced technology attachment (SATA) bus, a Video Electronics Standards Association local (VLB) bus, or another suitable bus or a combination of two or more of these. Bus  3312  may include one or more buses  3312 , where appropriate. Although this disclosure describes and illustrates a particular bus, this disclosure contemplates any suitable bus or interconnect. 
     Herein, a computer-readable non-transitory storage medium or media may include one or more semiconductor-based or other integrated circuits (ICs) (such, as for example, field-programmable gate arrays (FPGAs) or application-specific ICs (ASICs)), hard disk drives (HDDs), hybrid hard drives (HHDs), optical discs, optical disc drives (ODDs), magneto-optical discs, magneto-optical drives, floppy diskettes, floppy disk drives (FDDs), magnetic tapes, solid-state drives (SSDs), RAM-drives, SECURE DIGITAL cards or drives, any other suitable computer-readable non-transitory storage media, or any suitable combination of two or more of these, where appropriate. A computer-readable non-transitory storage medium may be volatile, non-volatile, or a combination of volatile and non-volatile, where appropriate. 
     Herein, “or” is inclusive and not exclusive, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, “A or B” means “A, B, or both,” unless expressly indicated otherwise or indicated otherwise by context. Moreover, “and” is both joint and several, unless expressly indicated otherwise or indicated otherwise by context. Therefore, herein, “A and B” means “A and B, jointly or severally,” unless expressly indicated otherwise or indicated otherwise by context. 
     This scope of this disclosure encompasses all changes, substitutions, variations, alterations, and modifications to the example embodiments herein that a person having ordinary skill in the art would comprehend. The scope of this disclosure is not limited to the example embodiments described or illustrated herein. Moreover, although this disclosure describes or illustrates respective embodiments herein as including particular components, elements, functions, operations, or steps, any of these embodiments may include any combination or permutation of any of the components, elements, functions, operations, or steps described or illustrated anywhere herein that a person having ordinary skill in the art would comprehend. Furthermore, reference in the appended claims to an apparatus or system or a component of an apparatus or system being adapted to, arranged to, capable of, configured to, enabled to, operable to, or operative to perform a particular function encompasses that apparatus, system, component, whether or not it or that particular function is activated, turned on, or unlocked, as long as that apparatus, system, or component is so adapted, arranged, capable, configured, enabled, operable, or operative.