Abstract:
Distributed Aperture Systems use multiple staring sensors distributed around a vehicle to provide automatic detection of targets, and to provide an imaging capability at all aspects. The sensor image data is “stitched” to make the camera joints transparent to the operator. For example, images from three different cameras may be combined into a single seamless mosaic. The output mosaic is suitable for rendering on a head-steered helmet mounted display or a multifunction console display.

Description:
PRIORITY APPLICATION 
     This application incorporates by reference and hereby claims the benefit of the following provisional application under 35 U.S.C. §119(e): 
     U.S. provisional patent application Ser. No. 60/553,982, entitled “MULTI-CAMERA SEAMLESS IMAGE STITCHING FOR A DISTRIBUTED APERTURE” filed on Mar. 18, 2004. 
    
    
     STATEMENT OF GOVERNMENT INTEREST 
     This invention was made with Government support under Contract N00421-00-C-308 awarded by the Department of Defense. The Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to combining images and more particularly to forming a mosaic image from a plurality of images. The plurality of images may be substantially simultaneously generated, for example with a distributed aperture system (DAS). 
     BACKGROUND OF THE INVENTION 
     The automatic stitching of high-resolution images into a single wide-field-of-view mosaic is a capability currently being developed by researchers with disparate applications. Software has been developed to enable users to form panoramic views from individual snapshots taken by digital cameras. Typically, this type of software is employed in a non-real-time, post-processing environment to generate panoramic images or image sequences for later playback. 
     However, this type of software cannot work in a real-time, high performance environment. For example, a high performance aircraft may be provided with a multiple cameras—infrared or visible light—generating a plurality of images simultaneously or substantially simultaneously. The cameras can be distributed to provide a very wide angle of coverage. For example, six (6) cameras may provide 4π steradian coverage of the world exterior to the aircraft and a portion of may be presented to the pilot with the use of a helmet mounted display (HMD). The challenge is to create a mosaic output image from multiple cameras real-world-registered to the pilot view direction with the imagery as seamless and uniform as possible across camera boundaries. 
     SUMMARY OF THE INVENTION 
     In accordance with a first aspect of the invention, a method to combine a plurality of images into a seamless mosaic includes determining a virtual line-of-sight (LOS) and a corresponding field-of-view (FOV) of an output mosaic; obtaining a plurality of input images, wherein each image of the plurality of input images contributes to at least one output mosaic pixel; and mapping contributions from the plurality of input images for each output mosaic pixel. 
     In accordance with a second aspect of the invention, an apparatus for combining a plurality of images into a seamless mosaic includes a control processor for determining a virtual line-of-sight (LOS) and a corresponding field-of-view (FOV) of an output mosaic based on external input; a plurality of imaging sensors for generating a corresponding plurality of input images, wherein each image of the plurality of input images contributes to at least one output mosaic pixel of the output mosaic; and an image processor for mapping contributions from the plurality of input images for each output mosaic pixel. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Features and advantages of the invention will become apparent to those skilled in the art from the following description with reference to the drawings, in which: 
         FIG. 1  illustrates a multi-camera image stitch geometry according to an embodiment of the present invention; 
         FIG. 2  illustrates an exemplary seamless stitching algorithm according to an embodiment of the present invention; 
         FIG. 3A  illustrates a processing of for determining the line-of-sight and field-of-view of an output display view according to an embodiment of the present invention; 
         FIG. 3B  illustrates a processing for transforming a display-view coordinate system to a camera-view coordinate system according to an embodiment of the present invention; 
         FIG. 3C  illustrates a processing for mapping contributions from input images to arrive at the output display view according to an embodiment of the present invention; 
         FIG. 4  illustrates a diagram of a coordinate transformation process for translating pixels from a display-view-centered coordinate system to a camera-centered coordinate system according to an embodiment of the present invention; 
         FIG. 4A  illustrates a concept of contributing pixels from an input image to the output pixel of the output mosaic; 
         FIG. 5  illustrates a flow chart to determine a collection of contributing images to an output mosaic pixel according to an embodiment of the present invention; 
         FIG. 6A  illustrates a flow chart to translate an output pixel position from the output display view to the corresponding location in the camera view according to an embodiment of the present invention; 
         FIG. 6B  illustrates a flow chart to populate an output pixel position based on pixels of the input images according to an embodiment of the present invention; 
         FIGS. 7 and 7A  illustrate possible contributions to an output pixel from multiple input images according to an embodiment of the present invention; 
         FIG. 8  illustrates a seam region in a portion of an image carried out by a feathering operation in accordance with an embodiment of the present invention; 
         FIG. 9  illustrates a process to stitch an output mosaic from a plurality of input images according to an embodiment of the present invention; 
         FIG. 10  illustrates another process to stitch an output mosaic from a plurality of input images according to an embodiment of the present invention; and 
         FIG. 11  illustrates a block diagram of an apparatus for stitching an output mosaic from a plurality of input images according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     For simplicity and illustrative purposes, the principles of the invention are described by referring mainly to exemplary embodiments thereof. However, one of ordinary skill in the art would readily recognize that the same principles are equally applicable to many types image stitching devices and methods. Also, the terms “optical”, “camera”, “sensor”, “image” and the like are not to be limited to the visible spectrum. It is fully intended that non-visible spectrum—such as infrared, radar, or ultra-violet—images are to be included within the claim scope. 
     An example stitching algorithm geometry is provided in  FIG. 1 , which illustrates a spherical space in which the algorithm operates. The sphere represents an entire 4π steradian area covered, for example by a distributed aperture system (DAS). The DAS cameras, providing a plurality of simultaneous input images, may be positioned at the center of the sphere (coordinate system origin). In this instance, there may be three cameras providing the simultaneous input images. An arbitrary pointing direction or line-of-sight (LOS) for each camera—corresponding to an input image—can be described. The LOS may be described in multiple coordinate systems. An example is in Cartesian coordinates forward, right, and down (FRD). Another example is in Euler coordinate angles azimuth, elevation, and rotation (AZ, EL, ROT). 
     The three DAS cameras may be set such that the optical LOSs are set off 90 degrees relative to each other. These correspond to LOS vectors in FRD of [1, 0, 0], [0, −1, 0], and [0, 0, 1]. In other words, the LOS vectors are such that first view is straight forward (point [a]), second view is straight left (point [b]), and the third is straight down (point [c]), respectively. The camera field-of-views (FOV) may exceed 90×90 degrees to allow for image overlap between adjacent cameras or views. 
     It is intended that the LOSs of the plurality of input images can be other than purely orthogonal. It is generally sufficient the FOV of the neighboring input images are adjacent to each other for seamless stitching of images. For robust and reliable operation, it is preferred that the neighboring input images have FOVs that overlap each other. For example, the FOV of the cameras in  FIG. 1  may be 94×94 degrees. This allows for 4 degrees of overlap between the FOVs of neighboring cameras. 
       FIG. 1  also illustrates the LOS and FOV of a mosaic view (desired view) to be extracted and stitched for presentation on a video display (area [d]). The display LOS vector may be specified in Euler AZ, EL, ROT angles as shown. An exemplary stitching algorithm  200  is illustrated  FIG. 2 . Generally, the algorithm may be described as including the following steps. First, the virtual (desired) line-of-sight and field-of-view of the output mosaic may be determined (step  210 ). For example, the desired LOS and FOV specifications may be received via movement of the helmet mounted display HMD from a pilot. The specifications may also be received through a joy stick, computer mouse, game controller, or any other interfaces available. Needless to say, the LOS and FOV specification may be received through a variety of ways. 
     Then a collection of input images, for example from multiple cameras, may be obtained to generate the output mosaic (step  220 ). Finally, contributions to the output mosaic from the collection of input images may be mapped to arrive at the output mosaic (step  230 ). 
     It is preferred that each input image in the collection should contribute to at least one pixel of the output mosaic. Further, the input images in the collection may be simultaneously or substantially simultaneously captured. Then the output mosaic generated also represents a composite image at a particular moment in time. One method to capture images simultaneously is to operate multiple imaging sensors simultaneously. 
     As noted above, in step  210 , the LOS and FOV of the output mosaic may be determined. In other words, the output mosaic view coordinate system (or display view coordinate system) may be established. As an example, the display view coordinate system may be a spherical, uniform radius AZ/EL system established for a defined incremental FOV (IFOV) spacing between adjacent pixels and a defined FOV of array size (N r ×N c ), where N r  is the number of rows and N c  is the number of columns of the output mosaic array. The display pixel IFOV may be adjusted to achieve a desired zoom ratio. The following parameters, which may be externally supplied, may be used to determine the spatial position (AZ viewpixel , EL viewpixel ) of each output array pixel relative to the display center of the output mosaic (step  302 ). The parameters may include: 
     Output array size in number of rows and columns (N r , N c ); 
     Output mosaic display pixel IFOV; and 
     Desired zoom factor. 
     In short, with the parameters, the output mosaic&#39;s LOS and FOV may be fully determined.  FIG. 3A  illustrates an exemplary detailed processing of step  210  of  FIG. 2  to determine the LOS and FOV of the output display view. First, the parameters may be obtained (step  302 ), for example from a user. As noted, these parameters may include the output array size, the display pixel IFOV, and a desired zoom factor. 
     From this, the display view spatial position of each output mosaic pixel relative to the display center may be determined (AZ viewpixel , EL viewpixel ) may be calculated (step  304 ) as follows: 
                           ⁢         AZ   viewpixel     ⁡     (     r   ,   c     )       =     zoom_factor   ⋆     display_   ⁢   IFOV     ⋆     [     c   -     (       N   c     2     )     +   0.5     ]                 (   1   )                       ⁢         EL   viewpixel     ⁡     (     r   ,   c     )       =     zoom_factor   ⋆     display_   ⁢   IFOV     ⋆     [     r   -     (       N   r     2     )     +   0.5     ]                 (   2   )                   RadDist   viewpixel     ⁡     (     r   ,   c     )       =       cos     -   1       ⁡     [       cos   ⁢           ⁢     (       AZ   viewpixel     ⁡     (     r   ,   c     )       )       ⋆     cos   ⁢           ⁢     (       EL   viewpixel     ⁡     (     r   ,   c     )       )         ]               (   3   )               
where AZ viewpixel (r,c) represents the azimuth of the output pixel at position (r, c), EL viewpixel (r,c) represents the elevation of the output pixel at position (r, c), and RadDist viewpixel (r,c) represents the radial distance of the output pixel at position (r, c) from the display center.
 
     To obtain the collection of input images for the mosaic (step  220  of  FIG. 2 ), it is preferred that the display-centered coordinate system be transformed to the coordinate system of the input images, which will be termed as “camera-centered” coordinate system. It is preferred that the transform takes place for each input image. The process may include computing one or more transformation matrices so that the appropriate transformation may take place.  FIG. 3B  illustrates an exemplary processing of this transformation process. Note the process may be repeated for each camera-centered (input image) coordinate system. 
     First, parameters may be obtained to compute the transformation matrices (step  312 ) for each input image, for example from a user. In this particular instance, the parameters may be the parameters of the cameras used to generate the image. The parameters may include LOS of the camera (AZ cam , EL cam , ROT cam ), the FOV of the camera (Nrows cam ) Ncols cam ), the, camera pixel IFOV, and an optical distortion function ƒθ. While there may be multiple causes of the optical distortion, one primary source of the distortion may be due to a lens distortion of the camera. Thus, it may also be described as a camera distortion ƒθ. The parameters may also include the display view LOS (AZ view , EL view , ROT view ) determined above. 
     Next, the transformation matrices required to translate from the display-centered to the camera-centered coordinate systems may be computed (step  314 ). In this particular example, two 3×3 transform matrices (VIEWtoINS, CAMtoINS) may be calculated as follows: 
                   VIEWtoINS   =             [           (     Ce   ⋆   Ca     )           (     Ce   ⋆   Sa     )           (     -   Se     )                 (     Sr   ⋆   Se   ⋆   Ca     )     -     (     Cr   ⋆   Sa     )               (     Sr   ⋆   Se   ⋆   Ca     )     +     (     Cr   ⋆   Sa     )             (     Sr   ⋆   Ce     )                 (     Cr   ⋆   Se   ⋆   Ca     )     +     (     Sr   ⋆   Sa     )               (     Cr   ⋆   Se   ⋆   Sa     )     -     (     Cr   ⋆   Ca     )             (     Cr   ⋆   Ce     )           ]     ⁢     
     ⁢   where   ⁢           ⁢           Sa   =     sin   ⁢           ⁢     (     AZ   view     )               Ca   =     cos   ⁢           ⁢     (     AZ   view     )                               Se   =     sin   ⁢           ⁢     (     EL   view     )               Ce   =     cos   ⁢           ⁢     (     EL   view     )                               Sr   =     sin   ⁢           ⁢     (     ROT   view     )               Cr   =     cos   ⁢           ⁢     (     ROT   view     )                           ⁢     
     ⁢   and               (   4   )               CAMtoINS   =             [           (     Ce   ⋆   Ca     )           (     Ce   ⋆   Sa     )           (     -   Se     )                 (     Sr   ⋆   Se   ⋆   Ca     )     -     (     Cr   ⋆   Sa     )               (     Sr   ⋆   Se   ⋆   Ca     )     +     (     Cr   ⋆   Sa     )             (     Sr   ⋆   Ce     )                 (     Cr   ⋆   Se   ⋆   Ca     )     +     (     Sr   ⋆   Sa     )               (     Cr   ⋆   Se   ⋆   Sa     )     -     (     Cr   ⋆   Ca     )             (     Cr   ⋆   Ce     )           ]     ⁢     
     ⁢   where   ⁢     
     ⁢           Sa   =     sin   ⁢           ⁢     (     AZ   cam     )               Ca   =     cos   ⁢           ⁢     (     AZ   cam     )                   Se   =     sin   ⁢           ⁢     (     EL   cam     )               Ce   =     cos   ⁢           ⁢     (     EL   cam     )                   Sr   =     sin   ⁢           ⁢     (     ROT   cam     )               Cr   =     cos   ⁢           ⁢     (     ROT   cam     )                           (   5   )               
“INS” refers to the world coordinate system that the view display LOS and each camera LOS is referenced to. That is, the coordinate system shown in  FIG. 1 . For example, on an aircraft, the frame of reference may be with respect to the on-board Inertial Navigation System (INS). A magnetic head tracker generating the view display LOS may be aligned to the INS coordinate system. Each camera mounting position can be surveyed with respect to the INS coordinate system to establish the camera&#39;s LOS.
 
     Next, a camera coordinate system may be established for each camera (step  316 ). Like the. output mosaic display view, these coordinate systems may be spherical with uniform radius AZ/EL systems established for a defined IFOV spacing between adjacent pixels and a defined FOV of array size (NrowsCam, NcolsCam). The camera pixel IFOV may be the effective IFOV of the output camera imagery (images used to determine the mosaic). 
     For the purposes of explanation only, the cameras may be assumed to have identical device properties. In other words, the three cameras are assumed to have identical FOV, IFOV, and lens distortion ƒθ. The difference then is the LOS, i.e. the pointing direction, of each camera. 
     However, it should be noted that the device parameters of the cameras may be different and still be within the scope of the invention. 
     Next, the contributions from the input images may be mapped to the output mosaic pixels to arrive at the output mosaic as noted above (step  230  in  FIG. 2 ).  FIG. 3C  illustrates an exemplary processing to carryout step  230 . The processing may be described as: 1) determining a collection of potential contributing input images for the output pixel of interest (step  320 ); and 2) determining the mosaic pixel value based on the contributing input images (step  322 ). Note that the process illustrated in  FIG. 3C  is repeated for each mosaic output pixel (AZ viewpixel (r_idx, c_idx), EL viewpixel (r_idx, c_idx)). 
     Regarding step  320 , an input image may potentially be a contributor to a particular output mosaic pixel if the output mosaic pixel is within the input image. This is explained with reference to  FIG. 4 . In  FIG. 4 , there is a output mosaic display view  404  and a camera view  406 . The camera view  406  corresponds to a particular input image. As shown, the output mosaic pixel  402  is within the camera view  406 . Thus, in this instance, the camera view  406  may be a potential contributor to determine the value of the output display pixel  402 . 
     On the other hand, the camera view  406  cannot contribute to determine the value of the output mosaic pixel  410  since the pixel  410  lies entirely outside of the camera view  406 . 
     The process to determine whether an input image can be a contributor to a particular output mosaic pixel may begin by first applying coordinate rotation transformation to the output pixel position (AZ viewpixel , EL viewpixel ) to locate the corresponding AZ/EL position (AZ cam     —     pixel , EL cam     —     pixel ) with respect to the particular camera view  406 . In other words, the coordinate transformation translates the output mosaic pixel from a display-view-centered coordinate system to a camera-centered coordinate system as illustrated in  FIG. 4 . In  FIG. 4 , the display view pixel  402  may be transformed from the display-view-centered coordinate system  404  to the camera-centered coordinate system  406 . 
       FIG. 5  illustrates this process of determining whether an input image can contribute to the output mosaic pixel. To accomplish this task, for each output pixel, the position of the output pixel is translated to the corresponding position in the camera view  406 , as described above (step  502 ). 
     In one embodiment, the translation may be accomplished as follows. First, the output mosaic pixel position in Euler AZ/EL (AZ viewpixel , EL viewpixel ) coordinates may be converted to the corresponding Cartesian FRD coordinates (F view , R view , D view ) still within the display view coordinates system (step  602  of  FIG. 6A ) as follows: 
     
       
         
           
             
               
                 
                   L 
                   = 
                   
                     RadDist 
                     view_pixel 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     F 
                     view 
                   
                   = 
                   
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       L 
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     R 
                     view 
                   
                   = 
                   
                     
                       AZ 
                       view_pixel 
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             L 
                             ) 
                           
                         
                         L 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
             
               
                 
                   
                     D 
                     view 
                   
                   = 
                   
                     
                       EL 
                       view_pixel 
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             L 
                             ) 
                           
                         
                         L 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     The display-view-centered FRD vector of the output mosaic pixel may be transformed to a selected camera-centered FRD vector via a two-stage rotational transform process—transforming from display-view-centered  404  to INS-centered  408  and then to camera-centered  406  coordinate system (step  604 ). The following matrix multiplication may be used: 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             F 
                             cam 
                           
                         
                       
                       
                         
                           
                             R 
                             cam 
                           
                         
                       
                       
                         
                           
                             D 
                             cam 
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               CAMtoINS 
                             
                           
                           
                             
                               
                                 ( 
                                 
                                   3 
                                   × 
                                   3 
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           
                             VIEWtoINS 
                           
                         
                         
                           
                             
                               ( 
                               
                                 3 
                                 × 
                                 3 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                     ⋆ 
                     
                       [ 
                       
                         
                           
                             
                               F 
                               view 
                             
                           
                         
                         
                           
                             
                               R 
                               view 
                             
                           
                         
                         
                           
                             
                               D 
                               view 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
       FIG. 4  illustrates this two-stage process via the INS  408 . Ambiguity may be eliminated by rejecting any calculated FRD coordinates with F cam &lt;0. This may occur when one tries to transform to a camera that is actually pointing behind. Upon this condition, the camera may be eliminated from consideration as a contributor to the output mosaic pixel being processed. 
     The computed camera Cartesian FRD coordinates may be then converted to corresponding Euler AZ/EL angles (AZ campixel , EL campixel ) (step  606 ) within the camera-centered coordinate system. This conversion may take into account the distortion function fθ, which can alter the final result based on the sensor optics. The distortion may be switched in or out via configuration settings. If no distortion is incorporated, the closed form of the conversion becomes: 
     
       
         
           
             
               
                 
                   
                     AZ 
                     campixel 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             cos 
                             
                               - 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               F 
                               cam 
                             
                             ) 
                           
                         
                         
                           
                             1 
                             - 
                             
                               F 
                               cam 
                               2 
                             
                           
                         
                       
                       ] 
                     
                     ⋆ 
                     
                       R 
                       cam 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     EL 
                     campixel 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             cos 
                             
                               - 
                               1 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               F 
                               cam 
                             
                             ) 
                           
                         
                         
                           
                             1 
                             - 
                             
                               F 
                               cam 
                               2 
                             
                           
                         
                       
                       ] 
                     
                     ⋆ 
                     
                       D 
                       cam 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     In the vicinity where F cam =1, a singularity occurs. To eliminate the singularity problem, a finite series approximation may be utilized as follows:
 
 AZ   campixel =└1.543858−0.83776* F   cam +0.377929* F   cam   2 −0.084041* F   cam   3   ┘*R   cam    (13)
 
 EL   campixel =└1.543858−0.83776* F   cam +0.377929* F   cam   2 −0.084041* F   cam   3   ┘*D   cam    (14)
 
     The distortion ƒθ specifications can be incorporated into the transform to arrive at a spatially accurate result. The distortion ƒθ specifications may be incorporated by determining a 3 rd  order polynomial curve to fit to the distortion function and modifying the polynomial coefficients as appropriate. 
     Referring back to  FIG. 5 , the computed AZ/EL angles (AZ campixel , EL campixel ) may be used to determine if the output mosaic pixel is within the camera view (step  504 ). Whether a particular output mosaic pixel is “within” the input image may be determined in multiple ways. Though very small in size, each output mosaic pixel can be regarded as having a finite area—equivalent to the view display row dimension FOV divided by the number of pixel rows in the output mosaic. This pixel FOV extent is known as the incremental FOV or IFOV. Although not a requirement, output mosaic pixels are usually square to achieve a 1:1 aspect ratio in the output image. As illustrated in  FIG. 4A , the output pixel  402  (illustrated as a circle) does have a size equal to the IFOV. If the entirety of the output pixel  402  is inside the camera view  406 , the output pixel  402  may be considered to be “within” the camera view  406 . 
     However, the output mosaic pixel  412  overlaps only a portion of the camera view  406 . This can occur since the mapping of the output mosaic pixels to the input image pixels is not likely to be exactly corresponding. Depending on various factors, such partially overlapping output pixel may be considered to be within the camera view  406  or not. 
     In any case, the spatial position of the output mosaic pixel in relation to the camera view can be described as determining an incremental LOS and incremental FOV of the output mosaic pixel in the camera view  406  coordinate system. The incremental LOS provides the position of the center of the output pixel and the incremental FOV provides the extension from the center. 
     One particular method to determine whether the computed AZ/EL position (Az campixel , EL campixel ) of the output mosaic pixel is “within” is to compare the computed position to the FOV extent of the camera view  406 . This amounts to determining whether the center of the output mosaic pixel lies within the camera FOV. 
     If the computed AZ/EL angles lie outside the camera FOV, the camera, and thus the corresponding input image, may be eliminated as a contributor to the output mosaic pixel (AZ viewpixel (r_idx, c_idx), EL viewpixel (r_idx, c_idx)) presently being processed. For example, with reference to  FIG. 4 , the pixel  410  within the display view  404  is outside of the camera view  406 . This is simply a realization that not all cameras (or input images) contribute to every pixel of-the output mosaic. 
     On the other hand, if the computed AZ/EL angles lie within the camera FOV (see pixel  402 ), the camera ID (in this instance the camera corresponding to the camera view  406 ) and the computed array row/column address or addresses may be stored for further use (step  506 ). 
     It bears repeating that the steps illustrated in  FIG. 5  are repeated for each camera view. When this process completes, i.e. when step  320  completes (see  FIG. 3C ) the particular output mosaic pixel will have zero or more contributing images. Referring back to  FIG. 3C , when the collection of potentially contributing input images are determined in step  320 , then the value of the output mosaic pixel may be determined based on the collection of contributing images (step  322 ). 
     For a particular output mosaic pixel of interest, it may be that more than one pixel of a contributing input image may be able contribute to the output value. For example in  FIG. 4A , the IFOV (or area) of the mosaic pixel  402  may overlap portions of multiple of pixels of the camera view  406 . One way to account for the overlap is to determine the contribution weights of the overlapped pixels of the input image in some manner and determining the contributions of the multiple pixels based on their corresponding weights. 
     To illustrate, the pixel  402  of the display view  404  (represented as a circle in  FIG. 4A ) overlaps portions of four pixels  406 - 1 ,  406 - 2 ,  406 - 3 , and  406 - 4  of the camera view  406  (represented as squares in  FIG. 4A ). When this occurs, the contributions of the pixels  406 - 1  to  406 - 4  may be taken into account. For example, the contribution of the camera view  406  to the output pixel  402  may simply be an average value of the overlapped pixels. As another example, the contribution weights of the pixels  406 - 1  to  406 - 4  may depend on the amount of overlap. 
       FIG. 6B  illustrates an alternative method, which is to choose a single pixel—the nearest pixel—from the candidate camera view as the contributing pixel (step  610 ) for that camera view (input image). In other words, the camera view pixel closest to the calculated AZ/EL angles (Az campixel , EL campixel ) may be chosen to contribute to the output mosaic. Again referring to  FIG. 4A , the mosaic pixel  402  overlaps the camera view pixel  406 - 1  the most. To put it another way, the center of the mosaic pixel  402  is within the camera view pixel  406 - 1 . Thus, the camera view pixel  406 - 1  may be considered to be the nearest pixel. 
     The array row/column address of the contributing camera pixel may be derived from the computed AZ/EL angle using the camera IFOV as follows: 
     
       
         
           
             
               
                 
                   
                     c 
                     ⁡ 
                     
                       ( 
                       
                         
                           AZ 
                           campixel 
                         
                         , 
                         
                           EL 
                           campixel 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     round 
                     ⁢ 
                     
                       { 
                       
                         
                           [ 
                           
                             
                               EL 
                               campixel 
                             
                             
                               camera_ 
                               ⁢ 
                               IFOV 
                             
                           
                           ] 
                         
                         + 
                         
                           ( 
                           
                             
                               Ncols 
                               Cam 
                             
                             2 
                           
                           ) 
                         
                         - 
                         0.5 
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     r 
                     ⁡ 
                     
                       ( 
                       
                         
                           AZ 
                           campixel 
                         
                         , 
                         
                           EL 
                           campixel 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     round 
                     ⁢ 
                     
                       { 
                       
                         
                           [ 
                           
                             
                               AZ 
                               campixel 
                             
                             
                               camera_ 
                               ⁢ 
                               IFOV 
                             
                           
                           ] 
                         
                         + 
                         
                           ( 
                           
                             
                               Nrows 
                               Cam 
                             
                             2 
                           
                           ) 
                         
                         - 
                         0.5 
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     The above process may be repeated for each camera in the DAS system. Upon completion, a collection of candidate camera (potential contributing input images) and their contributing pixel/row addresses may be compiled for further use. Based on the spatial geometry illustrated in  FIG. 1 , one, two, or all three cameras may potentially contribute to a given pixel in the output mosaic. 
     Next, the value of the output mosaic pixel under consideration may be determined (step  612 ). In addition to  FIG. 6B , the explanation is provided with reference to  FIGS. 7 and 7A . In  FIG. 7 , the contributing input images, i.e. camera views  702 ,  704 , and  706  (in solid lines) may contribute to construct the output mosaic display view  710  (in dashes). 
     Processing may be dependent on the number of candidate pixels passing the criteria. For example, it may be that the output mosaic pixel encompasses an area where no contributing pixels exist (step  712 ). As an example, the output pixel  710 -A is in an area that does not overlap with any of the camera views  702 ,  704 , and  706 . This situation may also be caused by a failed imaging sensor. For example, if the camera: generating the image view  702  fails, then the output pixel  710 -B would have no contributors as well. If no contributing pixels exist, then a predetermined pixel value may be inserted for the output mosaic pixel (step  714 ). 
     The output mosaic pixel may overlap a single camera (step  716 ). For example, the pixel  710 -B only overlaps the contributing image view  702 . When this occurs, then the value of the selected camera pixel, i.e. the nearest pixel to the position (AZ cam     —     pixel , EL cam     —     pixel ), may be inserted directly into the output pixel at position (AZ viewpixe (r_idx, c_idx), EL viewpixel  (r_idx, c_idx)) (step  718 ). 
     The output mosaic pixel may overlap two cameras (step  720 ). In  FIG. 7 , pixel  710 -C overlaps both contributing image views  702  and  704 . If the output mosaic pixel overlaps two cameras, then the selected camera pixels from both contributing cameras (AZ cam     —     pixel , EL cam     —     pixel ) may be blended or feathered to produce a “seamless” appearance in the final image or a value. As an example, the value of the output mosaic pixel may simply be determined by averaging the values of the two contributors. As another example, the contributing values may be weighted according to one or more properties. 
     However, depending on the circumstance, one of the contributing images may be removed as a contributor and the value of the selected pixel of the remaining contributing image may be inserted as the value of the output mosaic pixel, much like the situation with a single contributor scenario discussed above. 
     The decision to remove a camera as a contributor may be based on a computed radial distance of each selected pixel to its corresponding camera-centered coordinate system origin and a seam width factor ε (step  722 ). As illustrated in  FIG. 8 , the contributing camera with the smaller radial distance may be designated as the “primary” contributor and the contributing camera with the larger radial distance may be designated as the “secondary” contributor. Pixel blending/feathering may occur when the difference of the computed radial distances of the contributing pixels is less than or equal to ε as seen in  FIG. 5  (step  724 ) where ε represents a predetermine difference threshold. 
     If the computed difference is greater than ε, the value of the selected pixel of the primary camera may be simply inserted as the value of the output mosaic pixel at position (AZ viewpixel (r_idx, c_idx), EL viewpixel (r_idx, c_idx)) (step  726 ). The rationale to remove the secondary contributor may be that the the amount of spatial overlap of 2 adjacent cameras exceeds the desired seam width ε. 
     The concept described may be represented mathematically/logically as follows:
 
 L   campixel(primary) =cos −1 [cos( AZ   campixel(primary) )*cos( EL   campixel(primary) )]  (17)
 
 L   campixel(secondary) =cos −1 [cos( AZ   campixel(secondary) )*cos( EL   campixel(secondary) )]  (18)
 
Δ L=L   campixel(secondary)   −L   campixel(secondary)    (19)
 
if (Δ L ≦ε){blend}, else{useprimary}  (20)
 
     If pixel blending is selected, then the blended value may represent a weighted contribution of the contributors. For example, the weight may be based on the respective radial distances as follows:
 
 I   viewpixel ( r   —   idx, c   —   idx )= W   primary   *I   primary ( AZ, EL )+ W   secondary   *I   secondary ( AZ, EL )   (21)
 
where
 
     I viewpixel (r_idx, c_idx) is the value of the output pixel at output pixel position (r_idx, c_idx), 
               W   primary     =     0.5   +     0.5   ⁡     [       Δ   ⁢           ⁢   L     ɛ     ]               
is the calculated contribution weight of the primary contributing image,
 
               W   secondary     =     0.5   -     0.5   ⁡     [       Δ   ⁢           ⁢   L     ɛ     ]               
is the calculated contribution weight of the secondary contributing image, I primary (AZ,EL) is the value of the selected pixel of the primary contributing image, and I secondary (AZ,EL) is the value of the selected pixel of the secondary contributing image.
 
     Once computed, the blended pixel value may be inserted into the mosaic output position (AZ viewpixel (r_idx, c_idx), EL viewpixel  (r_idx, c_idx)). 
     There may be more than two input images potentially contributing to the output mosaic pixel, i.e. the output mosaic pixel may overlap more than two cameras (NO result in step  720 ). Again referring to  FIG. 7 , pixel  710 -D overlaps all three contributing input image views  702 ,  704 , and  706 . Multiple ways exist to determine the value of the output mosaic pixel. One way is to average the values of all contributors. Another way is to weight the contributions of the input images based on some criteria. 
     Yet another way is to eliminate one or more input images as contributors. For example,  FIGS. 1 and 2 , the output mosaic pixel positions corresponding to the three-camera seam overlap a corner area, i.e. all three cameras may potentially contribute. Also see pixel point  710 -D in  FIG. 7 . 
     In this instance, the selected camera pixels from the contributing cameras may be sorted by radial distance from their respective camera-centers. The input image view with the pixel position having greatest radial distance may be eliminated, and the two remaining contributing input image views whose pixel positions have the smallest radial distances from center may be blended as described above (step  728 ). Eliminating the pixels in this manner results in a simpler calculation without much loss of accuracy. The blended value may be inserted into the mosaic output position (AZ viewpixel (r_idx, c_idx), EL viewpixel (r_idx, c_idx)). 
     The operations described above may be repeated for each output mosaic pixel position (AZ viewpixel (r_idx, c_idx), EL viewpixel (r_idx, c_idx)), wherein 0≦r_idx≦N r  and 0≦c_idx≦N c . Once all positions of the output mosaic are processed, the mosaic is complete. 
       FIGS. 9 and 10  represent an alternative perspective to the processing described with respect to  FIGS. 2-8 . 
       FIG. 11  illustrates a block diagram of an apparatus for stitching an output mosaic from a plurality of input images according to an embodiment. The apparatus  1100  may include a plurality of imaging sensors  1112 . In this instance, there are six such imaging sensors, but the invention is not so limited. Each imaging sensor  1112  has associated parameters such as FOV, LOS, IFOV, distortion fθ and the like. The imaging sensors  1112  are configured to generate a plurality of images that may be utilized to generate the stitched output mosaic display as discussed in detail above. 
     The apparatus  1110  may also include a control processor  1114 . The control processor  1114  may compute the transformation matrices for each input imaging sensor  1112  based on the platform INS and the display LOS of the output mosaic. The control processor  1114  may also calculate and output control parameters to an image processor  1116  based on the input parameters as shown. The processing steps to achieve these have been described in detail above. 
     The image processor  1116  may apply the coordinate transformation matrices, determine which input images (candidate cameras) will be utilized to generate the output mosaic, populate the output mosaic, and display the result to a display  1118 . The image processor  1116  may blend the output pixels as necessary. The processing steps to achieve these results also have been described in detail above. 
     It should be noted that the imaging sensors  1112 , the control processor  1114 , and the image processor  1116  need not all be co-located in each other&#39;s vicinity. For example, the imaging sensors may be located on a plane with images relayed to a ground station that performs the processing. This may be relevant for systems that utilize unmanned aerial vehicles or remotely controlled vehicles. 
     The present invention and particularly the control processing and image processing generally relate to methods and an apparatus for performing the methods described herein. The apparatus may be specially constructed devices for the required purposes such as a digital signal processor (DSP), application specific integrated circuit (ASIC), field programmable gate array (FPGA) special purpose electronic circuit, or it may comprise a general-purpose computer selectively activated or reconfigured by a computer program stored in the computer. Such a computer program may be stored in a computer readable storage medium, such as, but is not limited to, any type of disk including floppy disks, optical disks, CD-ROMs, and magnetic-optical disks, read-only memories (ROMs), random access memories (RAMs), EPROMs, EEPROMs, magnetic or optical cards, or any type of computer readable media suitable for storing electronic instructions. 
     The algorithms and displays presented herein are not inherently related to any particular computer or other apparatus. Various general-purpose systems may be used with programs in accordance with the teachings herein, or it may prove convenient to construct more specialized apparatus to perform the required method steps. The required structure for a variety of these systems will appear from the description herein. In addition, the present invention is not described with reference to any particular programming language. It will be appreciated that a variety of programming languages may be used to implement the teachings of the invention as described herein. 
     While the invention has been described with reference to the exemplary embodiments thereof, those skilled in the art will be able to make various modifications to the described embodiments of the invention without departing from the true spirit and scope of the invention. The terms and descriptions used herein are set forth by way of illustration only and are not meant as limitations. In particular, although the method of the invention has been described by examples, the steps of the method may be performed in a different order than illustrated or simultaneously. Those skilled in the art will recognize that these and other variations are possible within the spirit and scope of the invention as defined in the following claims and their equivalents.