Patent Publication Number: US-9842423-B2

Title: Systems and methods for producing a three-dimensional face model

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to electronic devices. More specifically, the present disclosure relates to systems and methods for producing a three-dimensional (3D) face model. 
     BACKGROUND 
     In the last several decades, the use of electronic devices has become common. In particular, advances in electronic technology have reduced the cost of increasingly complex and useful electronic devices. Cost reduction and consumer demand have proliferated the use of electronic devices such that they are practically ubiquitous in modern society. As the use of electronic devices has expanded, so has the demand for new and improved features of electronic devices. More specifically, electronic devices that perform new functions and/or that perform functions faster, more efficiently or with higher quality are often sought after. 
     Some electronic devices (e.g., cameras, video camcorders, digital cameras, cellular phones, smart phones, computers, televisions, etc.) capture or utilize images. For example, a digital camera may capture a digital image. 
     New and/or improved features of electronic devices are often sought for. As can be observed from this discussion, systems and methods that add new and/or improved features of electronic devices may be beneficial. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating components for producing a three-dimensional (3D) face model; 
         FIG. 2  illustrates a process for producing an inverse depth map; 
         FIG. 3  is a flow diagram illustrating a method for producing a 3D face model; 
         FIG. 4  illustrates two tilted images; 
         FIG. 5  is a flow diagram illustrating another method for producing a 3D face model; 
         FIG. 6  is a flow diagram illustrating a method for tilting an inverse depth map; 
         FIG. 7  illustrates a process for normalizing an inverse depth map; 
         FIG. 8  is a flow diagram illustrating another method for producing a 3D face model; 
         FIG. 9  is a flow diagram illustrating a method for normalizing an inverse depth map; and 
         FIG. 10  illustrates certain components that may be included within an electronic device. 
     
    
    
     SUMMARY 
     A method for three-dimensional face generation is described. An inverse depth map is calculated based on a depth map and an inverted first matrix. The inverted first matrix is generated from two images in which pixels are aligned vertically and differ horizontally. The inverse depth map is normalized to correct for distortions in the depth map caused by image rectification. A three-dimensional face model is generated based on the inverse depth map and one of the two images. 
     A first matrix that corresponds to a first image of the two images may be obtained. A second matrix that corresponds to a second image of the two images may be obtained. The first matrix may be applied to the first image to obtain a first rectified image. The second matrix may be applied to the second image to obtain a second rectified image. The first matrix may be a homographic matrix corresponding to the first image and the second matrix may be a homographic matrix corresponding to the second image. 
     Calculating the inverse depth map may include inverting the first matrix to obtain the inverted first matrix and applying the inverted first matrix to the depth map. The depth map may be determined from the first rectified image and the second rectified image. A fundamental matrix may be determined from the two images. Obtaining the first matrix and the second matrix may include decomposing the fundamental matrix. 
     The two images may be different perspectives relative to a human face. Normalizing the inverse depth map may include normalizing a subset of pixels in the inverse depth map. Normalizing the inverse depth map may include one of rotating, tilting and scaling the inverse depth map. 
     Tilting the inverse depth map may include determining depth derivatives for each column of pixels in a subset selection of the inverse depth map, determining a mean value of all the depth derivatives for the subset selection, comparing the mean value to a threshold value and tilting the inverse depth map based on the comparison. The subset selection may include a rectangular area. The subset selection may include a first area and a second area. Comparing the mean value to a threshold value may also include comparing a difference between the mean value of the first area and the mean value of the second area to a threshold value. 
     Rotating the inverse depth map may include detecting symmetrical features in the inverse depth map, the symmetrical features having a left feature and a right feature, and adjusting the inverse depth map proportionally to make the left feature and the right feature horizontally level. 
     Scaling the inverse depth map may include detecting symmetrical features in the inverse depth map, the symmetrical features having a left feature and a right feature, and adjusting the inverse depth map to make the left feature and the right feature proportionally even and at the same depth level. 
     An apparatus for three-dimensional face generation is also described. The apparatus includes a processor and executable instructions stored in memory that is in electronic communication with the processor. The apparatus calculates an inverse depth map based on a depth map and an inverted first matrix. The inverted first matrix is generated from two images in which pixels are aligned vertically and differ horizontally. The apparatus also normalizes the inverse depth map to correct for distortions in the depth map caused by image rectification. The apparatus further generates a three-dimensional face model based on the inverse depth map and one of the two images. 
     Another apparatus for three-dimensional face generation is described. The apparatus includes means for calculating an inverse depth map based on a depth map and an inverted first matrix. The inverted first matrix is generated from two images in which pixels are aligned vertically and differ horizontally. The apparatus also includes means for normalizing the inverse depth map to correct for distortions in the depth map caused by image rectification. The apparatus further includes means for generating a three-dimensional face model based on the inverse depth map and one of the two images. 
     A computer-program product for three-dimensional face generation is described. The computer-program product includes a non-transitory computer-readable medium with instructions thereon. The instructions include code for causing an electronic device to calculate an inverse depth map based on a depth map and an inverted first matrix. The inverted first matrix is generated from two images in which pixels are aligned vertically and differ horizontally. The instructions also include code for causing the electronic device to normalize the inverse depth map to correct for distortions in the depth map caused by image rectification. The instructions further include code for causing the electronic device to generate a three-dimensional face model based on the inverse depth map and one of the two images. 
     DETAILED DESCRIPTION 
     A three-dimensional (3D) face model can be used for different applications, such as virtual reality and face recognition. 3D models may be generated from a set of two-dimensional (2D) images. For example, a set of 2D pictures displaying an image of a face may be used to create a 3D rendering of the face. For instance, 3D face model reconstruction using two images captured by a phone may provide a low-cost solution compared with studio environments. 
     In one known approach, a 3D face model is constructed from two stereo images. In this approach, camera calibration is not necessary. But this approach uses epipolar geometry to estimate the depth directly. To find the corresponding epipolar lines between two images, it requires face images to be taken in front of a white board. On the white board, a black rectangle must be included and is positioned such that the height of the target face fits within the black rectangle. In this approach, the images must be manually hand-coded for any extreme color on the four corners of the rectangle. Accordingly, this approach has limited applications and requires substantial user interaction. 
     In other known stereo camera-based 3D face reconstruction approaches, the stereo camera hardware and camera require calibration. Camera calibration can be complex, costly and time consuming, and it may require substantial user interaction. 
     In another known approach, a generic face model and several 2D face images are used to construct a 3D face. The facial features are matched and the generic face model is fitted to these feature points. The structure of the face depth is then computed. But this approach depends on the architecture of the generic face model, facial feature detection, etc. This approach may not capture the subject&#39;s natural face. In other words, this approach may distort a subject&#39;s face in applying it to the general face model. 
     Similarly, in another known approach involving 3D face reconstruction with a single view camera, a face is reconstructed into a 3D structure using a single 2D image. This approach employs a database of the objects (e.g., face models) containing example patches. In this approach, the data sets used in practice do not guarantee the presence of objects sufficiently similar to the query for accurate reconstructions. 
     Many current 3D image-generating methods, however, use an image rectification process that causes distortions to a subject&#39;s face when rendered as a 3D face model. Image rectification generally includes detection and matching of a set of corresponding points between a pair of 2D images. Under this approach, the rectified images are left skewed and distorted. In other approaches, manual modifications and corrections are required to eliminate distortion caused by image rectification. 
     Therefore, the present systems and methods may provide improved methods and configurations for automatically producing a 3D face model from two 2D images, for example, taken by a single camera. In some configurations, an inverse matrix may be employed to automatically correct image distortion with minimal user interaction. In some configurations, rotating, tilting and scaling may correct image distortion. Systems and methods for 3D face generation and producing a 3D face model are explained in greater detail below. 
       FIG. 1  is a block diagram of a method  100  illustrating components for producing a 3D face model. Each component may be implemented in hardware or software. For example,  FIG. 1  may be implemented on an electronic device (not shown). Examples of electronic devices include laptop or desktop computers, cellular phones, smart phones, wireless devices, e-readers, tablet devices, gaming systems, etc. Some of these devices may operate in accordance with one or more industry standards. 
     Components in  FIG. 1  include an image receiver  102 , a feature detector/matcher  104 , a fundamental matrix estimator  106 , a homographic matrix decomposer  108 , an image rectifier  110 , a depth estimator  112  and a 3D face modeler  114 .  FIG. 1  also illustrates a homographic matrix inverter  116 , an inverse depth map calculator  118 , an inverse depth map normalizer  120  and a symmetrical feature detector  122 . The components may be implemented on a single device or may be implemented on multiple devices. Each of these components will be discussed below in greater detail. 
     The image receiver  102  may receive a set of two images (e.g., raw data) of a subject&#39;s face. The two images may be different perspectives relative to a face. In other words, the images may be such that the pixels in the two images are different vertically and horizontally. In one configuration, the image receiver  102  may be a single camera that takes two pictures. The first picture and the second picture may be taken at the same horizontal level, but the camera may be slightly moved or rotated left or right along a horizontal axis, thus producing slightly different images. 
     In another configuration, the image receiver  102  may be a module that receives image input from an exterior device. For example, the image receiver  102  may be implemented on an electronic device and receive an image taken by a camera phone or tablet device. In some configurations, the image receiver  102  may be located on the same electronic device that captures the set of images. 
     The feature detector/matcher  104  may correlate the pixels of the first image with corresponding pixels of the second image. For instance, the feature detector/matcher  104  may detect facial features such as eyes, nose, mouth, etc., in each of the two images and match pixels from one feature in the first image to corresponding pixels of the same feature in the second image. 
     The fundamental matrix estimator  106  may generate a fundamental matrix (H). A fundamental matrix may be a 3×3 matrix that relates to corresponding points in stereo images, e.g., the set of two images. The fundamental matrix may be estimated based on a number of matched features, points or pixels between the two images. In general, a fundamental matrix may be estimated based on at least seven corresponding points, however, more or fewer corresponding points may be employed in estimating a fundamental matrix. 
     In some configurations, a matrix estimator may generate another type of matrix from two images in which pixels are aligned vertically and differ horizontally. In other words, another type of matrix that is generated from two stereo images, other than a fundamental matrix, may be used. 
     The homographic matrix decomposer  108  may decompose one or more homographic (i.e., projective transformation) matrices from a fundamental matrix, such as a 3×3 homographic matrix, for example. A homographic matrix may provide rotation and translation information of a camera between two images. A pair of homographic matrices, such as a first homographic matrix (P L ) and a second homographic matrix (P R ), may be decomposed from a fundamental matrix. The first homographic matrix may correspond to the first image and the second homographic matrix may correspond to the second image. 
     The image rectifier  110  may rectify the two images by projecting the two images onto a common image plane. For example, the image rectifier  110  may apply the first homographic matrix to the first image and the second homographic matrix to the second image. The image rectifier  110  may produce rectified images (e.g., a first rectified image and a second rectified image). In some configurations, the image rectifier  110  projects stereo images onto a common image plane parallel to a line between optical centers in such a way that the corresponding points have the same row coordinates. In this manner, the problem associated with 2D stereo correspondence is reduced to a one dimensional (1D) problem. 
     The depth estimator  112  may determine a depth map. A depth map may be an image or image channel that includes information relating to the distance of the surfaces of scene objects from a viewpoint, such as a camera. A depth map may provide depth values indicating the differences in depths between two rectified images. The depth estimator  112  may generate a depth map from a set of two rectified images. 
     The 3D face modeler  114  may generate a 3D face model based on a depth map and one of the two images. For example, the 3D face modeler  114  may align detected features in an image with a depth map. In some configurations, the 3D face modeler  114  may employ an inverse depth map in generating a 3D face model. 
     The homographic matrix inverter  116  may invert a homographic matrix. The homographic matrix inverter  116  may inverse a homographic matrix to obtain an inverted homographic matrix, such as a 3×3 inverted homographic matrix, for example. The homographic matrix inverter  116  may obtain an inverted first homographic matrix (P L   −1 ) and an inverted second homographic matrix (P R   −1 ). 
     The inverse depth map calculator  118  may calculate or map an inverse depth map. For example, the inverse depth map calculator  118  may map a depth map to an inverted homographic matrix to obtain an inverse depth map. An inverse depth map may correct for some distortions in the depth map caused by image rectification. 
     The inverse depth map normalizer  120  may adjust and normalize an inverse depth map. The normalizations may include tilting, rotating, scaling, etc., an inverse depth map. For example, the inverse depth map normalizer  120  may detect distortions in an inverse depth map and may perform adjustments accordingly. In some configurations, the inverse depth map normalizer  120  may adjust a subset of pixels in the inverse depth map. In some configurations, the inverse depth map normalizer  120  may normalize a non-inverted depth map. In other words, the inverse depth map normalizer  120  may normalize the depth map  242  directly. 
     The symmetrical feature detector  122  may detect symmetrical features in an image, such as a human face. For example, the symmetrical feature detector  122  may detect symmetrical features such as eyes, ears, lips, a nose, forehead areas, cheeks, glasses, eyebrows, etc. 
     The components illustrated in  FIG. 1  may produce a 3D face model. For example, given two stereo images of a face, a depth map may be estimated and the background part of the depth map can be set as the flat plane. With a known depth value, the 3D coordinates of the face points may be calculated and the 3D face may be reconstructed as a 3D face model. 
     In one approach, the image receiver  102  may receive a set of images. The set of images may include a first image and a second image, a left image and a right image, a top image and a bottom image, two stereo images, etc. The two images in the set of images may include corresponding pixels that are aligned vertically, but differ horizontally. In some configurations, the pixels between the two images may be aligned horizontally, but not vertically. 
     The image receiver  102  may provide the set of images to the feature detector/matcher  104 . For example, the image receiver  102  may send the images over a wired connection, wirelessly or via a storage medium. 
     The feature detector/matcher  104  may identify corresponding features in the two images and may match the corresponding images together. An illustration of feature matching is shown in  FIG. 2 , described below. 
     The feature detector/matcher  104  may provide correlated and matched images to the fundamental matrix estimator  106 . Once a certain number of pixels have been matched, the feature detector/matcher  104  may provide this data to the fundamental matrix estimator  106 . 
     The fundamental matrix estimator  106  may estimate a fundamental matrix (H) based on the correlated images. The fundamental matrix may then be decomposed by the homographic matrix decomposer  108  to obtain two homographic matrices (P L  and P R ). In other words, the projective transformation matrices P L  and P R  for rectifying stereo images may be computed based on the fundamental matrix H. 
     The image rectifier  110  may use the homographic matrix matrices P L  and P R  to rectify the first image and second image. For example, the first homographic matrix P L  may be mapped to a left image to produce a first rectified image and the second homographic matrix P R  may be mapped to a right image to produce a second rectified image. 
     An example of the image rectification process will now be given. In one configuration, image rectification includes detecting and matching a set of corresponding points between the two images by the feature detector/matcher  104 . The correctly matched points are used to compute the fundamental matrix H by the fundamental matrix estimator  106  such that X R   T HX L =0, where X L  is a point (e.g., pixel) in a left image and X R  is a corresponding point (e.g., pixel) in a right image. In other words, X L  and X R  may each represent a 2D point that can be written as a 3D column vector in a [x, y, 1] format. T may represent a matrix transpose. Thus, when the 3D column vector is transposed, the result is a 3D row vector, written as [x, y, 1] (e.g., column vector [x, y, 1] T =row vector [x, y, 1]). 
     In this configuration, P L  and P R  are 3×3 matrices decomposed from a 3×3 fundamental matrix H by the homographic matrix decomposer  108 . Given P L  and P R , the image rectifier  110  applies 2D projective transformations on the two images. Here, rectifying the images changes each image pixel (X) from a raw data pixel, written as X=[x, y, 1] T , to a rectified image pixel, written as X L ′=P L X L  or X R =P R X R . Further, in this configuration, there is no need for camera intrinsic and extrinsic parameters. 
     However, in this configuration, the pair of homographic matrices P L  and P R  is not unique because the two stereo-rectified images are stereo-rectified under a common rotation. In other words, the pair of homographic matrices P L  and P R  share a common rotation, based on the difference between the two images, rotated around a common baseline. As a result, undesirable distortion to the rectified images, specifically skewness and aspect/scale distortions may be introduced. An illustration of this distortion is shown and described below in  FIG. 2 . 
     Once the set of images are rectified, the two rectified images may be used by the depth estimator  112  to determine a depth map. In other words, given the reconstructed stereo images, a depth reconstruction may be determined. But if the rectified images are distorted, the depth map may be similarly distorted. Thus, under this approach, image rectification causes undesirable distortions in the depth map, which may lead to a distorted 3D face model if not corrected. 
     To correct for the distortion in the depth map caused by image rectification, an inverse depth map may be generated by the inverse depth map calculator  118 . The inverse depth map calculator  118  may obtain a depth map from the depth estimator  112  and an inverted homographic matrix from the homographic matrix inverter  116 . The homographic matrix inverter  116  may invert the homographic matrix obtained from the homographic matrix decomposer  108  as described above. 
     The inverse depth map calculator  118  may map the depth map to the inverted homographic matrix to produce an inverse depth map. For example, given a depth map (M) estimated from the two rectified stereo images, M may be inversely mapped to one of original images by applying an inverse matrix such as P L  or P R . In this example, a pixel (m) in M, written as m=[x, y, z] T , will become a new pixel (m′), written as m′=P L   −1  m. Thus, after inverse mapping, m′, [x′, y′, z′] as part of an inverse depth map (M′). In the above examples, z represents a pixel value in the depth map and z′ represents a pixel value in the inverse depth map. 
     Inverting the depth map may partially correct distortions in the depth map caused by the image rectification process. For example, skewness and aspect/scale distortions may be corrected. In addition to partially correcting for distortions in the depth map caused by the image rectification process, normalizations to the depth map/inverse depth map may be performed by the inverse depth map normalizer  120 . Normalization may correct the inverse depth map to prevent the 3D face model from being improperly tilted, rotated and/or scaled. For example, the normalized pixel may be written as [x a , y a ] where x a =x′/z′ and y a =y′/z′. Accordingly, after normalization, the depth map may be on the same plane as the original image. Further, distortion on the 2D plane may be removed. 
     The inverse depth map normalizer  120  may receive input from the symmetrical feature detector  122 . For example, the symmetrical feature detector  122  may send detected symmetrical features and patterns to the inverse depth map normalizer  120 . The inverse depth map normalizer  120  may use the detected symmetrical features to perform adjustments to ensure that the detected symmetrical features are correctly proportioned. Additional detail regarding image normalization is discussed in greater detail below. 
     Once the inverse depth map is corrected and normalized, the 3D face modeler  114  may generate a 3D face model. The 3D face modeler  114  may map one of the original images to the inverse depth map, applying the detected features sent from the symmetrical feature detector  122  with corresponding points on the inverse depth map. 
     According to the systems and methods presented herein, it may be beneficial to invert the depth map and modify the inverse depth map based on face specific characteristics to reduce undesirable distortions during image rectification. Specifically, existing approaches, as descried previously, cause image distortion in the image rectification process and often require substantial user interaction. The systems and methods presented herein improve existing methods by inverting the depth map to partially account for distortion introduced in the image rectification process. Further corrections are applied by modifying and normalizing the inverse depth map based on face specific characteristics to improve the quality of the 3D face model. Moreover, the systems and methods presented herein require minimal user interaction. 
       FIG. 2  illustrates a process  200  for producing an inverse depth map  242 . The process  200  may be implemented in hardware or software. For example, the process  200  may be implemented on an electronic device. In some configurations, the process  200  may correspond to the components described in connection with  FIG. 1 . 
       FIG. 2  illustrates a first image  230  and a second image  232 . The first image  230  and the second image  232  may make up a set of stereo images. For example, the two images may be of a single face taken from different viewpoints. In some configurations, an object other than a face may be used. 
     In some configurations, more than two images may be employed. For example, any number of images, where the vertical pixels are all aligned, may be used. The images may be provided to an image receiver  102 . 
     Given the two images taken of a human face from different viewpoints (e.g., the first image  230  and the second image  232 ), the raw, uncalibrated stereo images may be rectified. In rectifying the two images, the first image  230  may first be correlated with the second image  232  resulting in a combined correlated image  234 . For instance, a feature detector/matcher  104  may detect and match the first image  230  and the second image  232 . Then, a fundamental matrix estimator  106  may calculate a fundamental matrix based on linear projections of the matched points, as shown in the combined correlated image  234 . 
     The first image  230  and the second image  232  may be used via the combined correlated image  234  to produce a first rectified image  236  and a second rectified image  238 . For example, an image rectifier  110  may perform part of the image rectification process as described above. The first rectified image  236  and the second rectified image  238  may be distorted during the image rectification process, as shown in  FIG. 2 . 
     A depth map  240  may be determined from the first rectified image  236  and the second rectified image  238 . For instance, a depth estimator  112  may generate the depth map  240 . The depth map  240  may be distorted as a result of the first rectified image  236  and the second rectified image  238  being distorted. 
     To correct for this distortion, an inverse depth map  242  may be calculated. For example, an inverse depth map calculator  118  may calculate an inverse depth map  242 . The inverse depth map  242  may be calculated by applying an inverted homographic matrix (e.g., P L   −1  or P R   −1 ) to the depth map  240 . As illustrated in  FIG. 2 , the inverse depth map  242  may correct distortions such as skewness in the depth map  240  caused by image rectification. 
       FIG. 3  is a flow diagram illustrating a method  300  for producing a 3D face model. The method  300  may be implemented in hardware or software. For example, the method  300  may be implemented on an electronic device. An electronic device may obtain  302  two images, such as a first image  230  and a second image  232 . The two images may be two stereo images received by an image receiver  102 . 
     The electronic device may determine  304  a fundamental matrix from the first image  230  and the second image  232 . The fundamental matrix (H) may be a 3×3 matrix that tracks corresponding points in the two stereo images. The fundamental matrix may be generated by a fundamental matrix estimator  106  based on a combined correlated image  234 . 
     The electronic device may decompose  306  a first matrix corresponding to the first image  230  from the fundamental matrix. The electronic device may also decompose  306  a second matrix corresponding to the second image  232  from the fundamental matrix. For example, the first matrix and the second matrix may be homographic matrices P L  and P R , respectively, as described above. In some configurations, the first matrix and the second matrix may be P R  and P L , respectively, or some other matrices. In some configurations, the first and second matrices may be decomposed from a homographic matrix decomposer  108 . 
     The electronic device may apply  308  the first matrix to the first image  230  to obtain a first rectified image  236 . The electronic device may apply  308  the second matrix to the second image  232  to obtain a second rectified image  238 . For example, an image rectifier  110  may map or project the first matrix to the first image  230  to produce a first rectified image  236 . The second rectified image  238  may be generated similarly. Distortions may be introduced during image rectification. 
     The electronic device may determine  310  a depth map  240  from the first rectified image  236  and the second rectified image  238 . The depth map  240  may be determined by a depth estimator  112 . If the first rectified image  236  and the second rectified image  238  are distorted and skewed, then the depth map  240  will likely also be distorted and skewed. The depth map  240  may provide depth values indicating the differences in depths based on the first rectified image  236  and the second rectified image  238 . 
     The electronic device may calculate  312  an inverse depth map  242 . The inverse depth map  242  may be calculated by inverting the first matrix (or the second matrix) and applying the inverted matrix to the depth map  240 . For example, an inverse depth map calculator  118  may perform these calculations. The inverted first matrix or inverted second matrix may be an inverted homographic matrix such as P L   −1  or P R   −1 . A homographic matrix inverter  116  may provide the inverted first matrix or the inverted second matrix to the inverse depth map calculator  118  to obtain the inverse depth map  242 . 
     The electronic device may normalize  314  the inverse depth map  242  to correct for distortions in the depth map caused by image rectification. An inverse depth map normalizer  120  may adjust for distortions, for example. Additional detail regarding normalization will be described in greater detail below. 
     The electronic device may generate  316  a 3D face model based on the inverse depth map  242  and one of the two images (e.g., the first image  230  or the second image  232 ). For instance, the 3D face modeler  114  may map one of the original images to the inverse depth map  242 , which has been normalized. In generating the 3D face model, detected features from a symmetrical feature detector  122  may be mapped to corresponding points on the inverse depth map  242 . The 3D face model does not include at least some of the distortions caused by image rectification because of the corrections performed by this method  300 . 
     While calculating an inverse depth map may correct for some distortion, other distortions, such as skewness, scaling and rotating distortions, may still affect the inverse depth map. These distortions may be caused by depth dimension distortion created during image rectification. For example, the left eye may be distorted from the rectification process and the left eye may have a larger depth value than the right eye. Normalization may correct distortions not corrected by creating an inverse depth map. 
     To refine the depth map, face characteristics may be used. For example, left and right symmetrical features may be considered. As another example, tilting may be adjusted based on forehead and mouth areas. Scaling and rotation may also be adjusted based on symmetrical facial features, such as eyes, ears, lips, a nose, forehead areas, cheeks, glasses, eyebrows, etc.  FIGS. 4-9  will describe various normalization processes in greater detail, such as tilting, scaling and rotating. 
       FIG. 4  illustrates two tilted images. The tilted images may be based on the inverse depth map  242 . Over tilt in the tilted images may be corrected for by comparing different depth values in various parts of the inverse depth map  242 , as will be described below. Adjusting and refining the tilting of the inverse depth map  242  may be one method of normalizing the inverse depth map  242 . 
     The two tilted images in  FIG. 4  may include a first tilted image  444  and a second tilted image  454 . A first ellipse  452  may be modeled to match the perimeter of the face in the first tilted image  444 . The first ellipse  452  may include a first major axis (a)  448  and a first minor axis (b)  450  and may help in detecting distortions, such as over tilt in the first tilted image  444 . For example, over tilt may be detected by employing a first subset selection window  446 . Over tilt may indicate that the image is tilted in either direction beyond an acceptable amount. In other words, an over tilted image may be tilted too far forward or tilted too far back about the first minor axis (b)  450 . 
     The first subset selection window  446  may be rectangular; however, other shapes may be employed. In one configuration, the first subset selection window  446  may have a height of a/2 and a width of b/3. Other dimensions may be employed. In some configurations, the first subset selection window  446  may be co-centered with the first ellipse  452 . In some configurations, the first subset selection window  446  may be centered with the nose area of the face on the first tilted image  444 . 
     The second tilted image  454  may similarly include a second ellipse  462  that includes a second major axis (a)  458  and a second minor axis (b)  460 . The second ellipse  462  may be modeled to correspond to the face in the second tilted image  454 . 
     The second tilted image  454  may also include a second subset selection  456  and a third subset selection  466 . The height and width of the second subset selection  456  and the third subset selection  466  may be equal; however, in some configurations, they may vary from one another. For example, the second subset selection  456  and the third subset selection  466  may have a height of a/4 and width of b/3. The second subset selection  456  and the third subset selection  466  may each be rectangular, or may be another type of shape, such as an ellipse. Further, the second subset selection  456  and the third subset selection  466  may be different shapes. 
     The second subset selection  456  may be positioned over the forehead area and the third subset selection  466  may be located over the mouth area of the second tilted image  454 . In an ideal image used for rendering a 3D face model, the forehead and the mouth of a subject&#39;s face are located in the same plane. Thus, the second subset selection  456  and the third subset selection  466  may be compared to determine the tilt angle. 
     Determining tilt angle based on the first subset selection  446  or from the comparison of the second subset selection  456  and the third subset selection  466  is discussed below in  FIGS. 5 and 6 . 
     While normalizing (e.g., tilting, rotating, scaling, adjusting, etc.) the inverse depth map  242 , the image foreground and background should be considered so that adjustments may be focused on a subject&#39;s face and not the background. In addition, distinguishing between the foreground and the background allows for smoothing between the two surfaces. 
     In one configuration, this may be performed by calculating a mean value of the face depth f m . The mean value of the face depth may be used to set the background depth d, which should be a flat plane behind the 3D face model. The background depth should be less than the mean face depth, however, the difference should not vary significantly. If d&lt;w*f m , the image depth may be adjusted. Here, w is a coefficient to control a threshold so as to prevent the face depth from being adjusted when the image depth is being adjusted. In this way, the background and the face boundary may be merged smoothly so that there is no strong blur on the boundary. 
       FIG. 5  is a flow diagram illustrating another method  500  producing a 3D face model. The method  500  may be implemented in hardware or software. In some configurations, the method  500  may be implemented on an electronic device. The electronic device may calculate  502  an inverse depth map  242 . 
     The electronic device may determine  504  depth derivatives for each column of pixels in a subset selection of the inverse depth map  242 . For example, the subset selection may be a first subset selection  446 , a second subset selection  456  or a third subset selection  466 . The depth derivative may be computed for each vertical column in a subset selection. For example, each vertical column may be computed from the top to the bottom for each subset selection. 
     In one configuration, the electronic device may use  506  a single rectangular subset selection (e.g., the first subset selection  446 ). In this configuration, the electronic device may determine  508  a mean value (m) for the subset selection, i.e., for all depth derivatives in the single subset selection. In other words, each depth derivative may be averaged to calculate m. 
     The electronic device may compare  510  the mean value to a threshold value (t 1 ). If |m|&gt;t 1 , the face in the inverse depth map  242  may be classified as over-tilted and adjustments may be made until the condition of |m|≦t 1  is satisfied. In other words, the electronic device may tilt  518  the inverse depth map  242  based on the comparison. The electronic device may generate  520  a 3D face model based on the inverse depth map  242  and one of the two images, as described above. 
     In another configuration, the electronic device may use  512  use two rectangular subset selections (e.g., the second subset selection  456  and the third subset selection  466 ). The two rectangular subset selections may represent a first subset selection area and a second subset selection area. 
     The electronic device may determine  514  a mean value (m) for each subset selection. For example, the electronic device may determine  514  a first mean value (m 1 ) for the first subset selection area and a mean value (m 2 ) for the second subset selection area. 
     The electronic device may compare  516  the difference between the first area mean value and the second area mean value to a threshold value (t 2 ). For example, |m 1 −m 2 | may equal a difference value (diff); duff may be compared to t 2 . If |diff|&gt;t 2 , the inverse depth map  242  may be classified as over-tilted and adjustments may be made until the condition of |diff|≦t 2  is satisfied. In other words, the electronic device may tilt  518  the inverse depth map  242  based on the comparison. The threshold values (i.e., t 1  and t 2 ) may be based on empirical data, user preference, historical values, etc. 
     The electronic device may generate  520  a 3D face model based on the inverse depth map  242  and one of the two images. This may be performed as described above. 
       FIG. 6  is a flow diagram illustrating a method  600  for tilting an inverse depth map  242 . The method  600  may be implemented in hardware or software. For example, the method  600  may be implemented on an electronic device. This method  600  may be one example of normalizing an inverse depth map  242 . 
     The electronic device may initiate  602  tilt adjustments. The electronic device may perform  604  face detection and eye detection. For example, face detection and eye detection may be performed on an inverse depth map  242  or one of the raw input images. In some configurations, performing  604  face detection and eye detection may be performed by a symmetrical feature detector  122 . 
     The electronic device may model  606  the face as an ellipse with major axis a and minor axis b. For example, the ellipse may be like the first ellipse  452  or the second ellipse  462  described above in connection with  FIG. 4 . 
     In one configuration, the electronic device may set  608  one rectangle, co-centered with the ellipse. The rectangle may have a width of b/3 and a height of a/2. For example, the rectangle may be like the first subset selection  446  of  FIG. 4 . 
     The electronic device may calculate  610  an average derivative value (m) along the vertical direction of the face. The electronic device may compare  612  if |m|&gt;threshold t 1  (i.e., the image is over tilted). In this case, the electronic device may adjust  614  the depth value along the vertical direction (e.g., about the minor axis (b)) of the face until |m|&lt;=t 1 . 
     In another configuration, the electronic device may set  616  two rectangles, each with width b/3 and height a/2, centered at the forehead and mouth areas in the ellipse. For example, the two rectangles may be like the second subset selection  456  and the third subset selection  466  of  FIG. 4 . The electronic device may calculate  618  an average depth value (m 1  and m 2 ) for each of the two rectangles. This may be performed as described in connection with  FIG. 5  above. The electronic device may compare  620  if |m 1 −m 2 |&gt;threshold t 2  (i.e., the image is over tilted). In this case, the electronic device may adjust  622  the depth value along the vertical direction (e.g., about the minor axis (b)) of the face until |m 1 −m 2 |≦t 2 . 
       FIG. 7  illustrates a process  700  for normalizing an inverse depth map  742 . The process  700  may be implemented in hardware or software. For example, the process  700  may be implemented on an electronic device. In some configurations, the process  700  may correspond to the components described in connection with  FIG. 1 . 
       FIG. 7  illustrates an inverse depth map  742 , which may correspond to the inverse depth map  242  described above.  FIG. 7  also illustrates a detected image  774 , a normalized inverse depth map  778  and a 3D face model  780 . The inverse depth map  742  may have been previously adjusted and corrected for over tilt. In other approaches, tilting may be adjusted later on. 
     In some configurations, the positions of the face area and the eyes may be detected, as shown in a detected symmetrical feature  776 . Based on the left/right eye detection, the inverse depth map  742  may be adjusted proportionally to make the left and right sides on the same depth level. In other words, the detected image  774  may include a detected symmetrical feature  776 , such as a pair of eyes. Other symmetrical features may include ears, lips, a nose, forehead areas, cheeks, glasses, eyebrows, etc. 
     The detected image  774  may be generated by a symmetrical feature detector  122 . The detected image  774  may employ a first image  230  or a second image  232  from the set of stereo images. Alternatively, the detected image  774  may be a depth map  240  or an inverse depth map  742 . 
     The inverse depth map  742  and the detected image  774  may be used in obtaining the normalized inverse depth map  778 . For example, an inverse depth map normalizer  120  may generate a normalized inverse depth map  778  using the inverse depth map  742  and/or the detected image  774 . 
     The 3D face model  780  may be generated based on the inverse depth map  742  and one of the two images (e.g., the first image  230  or the second image  232 ). For example, a 3D face modeler  114  may generate a 3D face model  780  to align detected symmetrical features  776  in an image with the inverse depth map  742 . 
       FIG. 8  is a flow diagram illustrating another method  800  for producing a 3D face model  780 . The method  800  may be implemented in hardware or software. For example, the method  800  may be implemented on an electronic device. 
     An electronic device may calculate  802  an inverse depth map  742 , as described above. The electronic device may determine  804  symmetrical features in the inverse depth map  742 . For example, a left feature symmetric with a right feature may be determined  804 . The left feature and the right feature may be included as a detected symmetrical feature  776 . Symmetrical features may be matched by a symmetrical feature detector  122 . Symmetrical features may be based on known facial features or calculated from symmetrical-like features on corresponding sides of an image. 
     The left feature and the right feature may be, for example, a pair of eyes. The pair of eyes may not be proportional to each other. In other words, the left eye in the inverse depth map  742  may have a larger depth value than the right eye. 
     In one configuration, the electronic device may adjust  806  the inverse depth map  742  proportionally to make the left feature and the right feature horizontally level. For example, inverse depth map  742  may be rotated about an axis running perpendicular to the image to align the left feature and the right feature until they are horizontally level. This is explained in greater detail below in connection with  FIG. 9 . 
     In some configurations, the electronic device may adjust  808  the inverse depth map  742  to make the left feature and the right feature proportionally even and at the same depth level. In one example, the inverse depth map  742  may be rotated about a vertical axis until the left feature and the right feature are even. 
     In another example, the pixels in one or both features may be adjusted until the left feature and the right feature are proportionally even. For instance, given a set of eyes where the left eye is larger than the right eye, the depth level of the left eye may be decreased and/or the depth level of the right eye may be increased. In another instance, the size or scale of the left eye may be decreased and/or the size or scale of the right eye may be increased. A combination of adjustments may be performed to make the left feature and the right feature proportionally even and at the same depth level. In this manner the inverse depth map  742  may be adjusted until the left feature and the right feature are on the same plane. The electronic device may generate  810  a 3D face model  780  based on the inverse depth map  742  and one of the two images. This may be performed as described above. 
       FIG. 9  is a flow diagram illustrating a method  900  for normalizing an inverse depth map  742 . The method  900  may be implemented in hardware or software. For example, the method  900  may be implemented on an electronic device. In some configurations, this method  900  may be employed in connection with method  600  described in connection with  FIG. 6  for tilting an inverse depth map  742 . 
     The electronic device may initiate  902  rotation adjustments. The electronic device may perform  904  face detection and eye detection. For example, face detection and eye detection may be performed on an inverse depth map  742  or one of the raw input images. In some configurations, performing  904  face detection and eye detection may be performed by a symmetrical feature detector  122 . 
     The electronic device may model  906  the face as an ellipse with major axis a and minor axis b. In one configuration, the ellipse may be similar to the first ellipse  452  or the second ellipse  462  described above in connection with  FIG. 4 . 
     In some configurations, the electronic device may set  908  two rectangles, one centered at the left eye and one centered at the right eye. Each rectangle may have a width of b/4 and a height of a/8. Other dimensions and shapes may be employed. For example, the two rectangles may each have a width of b/3 and a height of a/2. As another example, the two rectangles may have different dimensions from each other. Further, shapes other than rectangles may be employed. 
     The two rectangles may be like the second subset selection  456  and the third subset selection  466  of  FIG. 4 , but positioned over the eyes and having different dimensions. 
     The electronic device may calculate  910  the average depth value (m 1  and m 2 ) for the two rectangles. This may be performed as described in connection with  FIG. 5  above. The electronic device may compare  912  if |m 1 −m 2 |&gt;threshold t (i.e., the image is over rotated). In this case, the electronic device may adjust  914  the depth value along the horizontal direction (e.g., about the major axis) of the face until |m 1 −m 2 |≦t. 
       FIG. 10  illustrates certain components that may be included within an electronic device  1001 . One or more of the electronic devices described above may be configured similarly to the electronic device  1001  that is shown in  FIG. 10 . 
     The electronic device  1001  includes a processor  1009 . The processor  1009  may be a general purpose single- or multi-chip microprocessor (e.g., an ARM), a special purpose microprocessor (e.g., a digital signal processor (DSP)), a microcontroller, a programmable gate array, etc. The processor  1009  may be referred to as a central processing unit (CPU). Although just a single processor  1009  is shown in the electronic device  1001  of  FIG. 10 , in an alternative configuration, a combination of processors (e.g., an ARM and DSP) could be used. 
     The electronic device  1001  also includes memory  1003  in electronic communication with the processor  1009  (i.e., the processor  1009  can read information from and/or write information to the memory  1003 ). The memory  1003  may be any electronic component capable of storing electronic information. The memory  1003  may be random access memory (RAM), read-only memory (ROM), magnetic disk storage media, optical storage media, flash memory devices in RAM, on-board memory included with the processor, programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable PROM (EEPROM), registers, and so forth, including combinations thereof. 
     Instructions  1005   a  and data  1007   a  may be stored in the memory  1003 . The instructions  1005   a  may include one or more programs, routines, sub-routines, functions, procedures, code, etc. The instructions  1005   a  may include a single computer-readable statement or many computer-readable statements. The instructions  1005   a  may be executable by the processor  1009  to implement one or more of the methods  300 ,  500 ,  600 ,  800  and  900 , described above. Executing the instructions  1005   a  may involve the use of the data  1007   a  that is stored in the memory  1003 .  FIG. 10  shows some instructions  1005   b  and data  1007   b  being loaded into the processor  1009  (which may come from instructions  1005   a  and data  1007   a ). 
     In some configurations, the electronic device  1001  may include one or more image capture components  1017  for capturing images. In one configuration, an image capture component  1017  may be a camera or a photo cell for capturing images, such as stereo images. 
     The electronic device  1001  may also include one or more communication interfaces  1013  for communicating with other electronic devices. The communication interfaces  1013  may be based on wired communication technology, wireless communication technology, or both. Examples of different types of communication interfaces  1013  include a serial port, a parallel port, a Universal Serial Bus (USB), an Ethernet adapter, an IEEE 1394 bus interface, a small computer system interface (SCSI) bus interface, an infrared (IR) communication port, a Bluetooth wireless communication adapter, and so forth. 
     The electronic device  1001  may also include one or more input devices  1015  and one or more output devices  1019 . Examples of different kinds of input devices  1015  include a keyboard, mouse, microphone, remote control device, button, joystick, trackball, touchpad, lightpen, etc. For instance, the electronic device  1001  may include one or more image capture components  1017  for capturing images. 
     Examples of different kinds of output devices  1019  include a speaker, printer, 3D printer, etc. One specific type of output device  1019  which may be typically included in an electronic device  1001  is a display  1023 . A display  1023  used with configurations disclosed herein may utilize any suitable image projection technology, such as a cathode ray tube (CRT), liquid crystal display (LCD), light-emitting diode (LED), gas plasma, electroluminescence, or the like. For example, 3D face models may be displayed on the display  1023 . A display controller  1025  may also be provided for converting data stored in the memory  1003  into text, graphics and/or moving images (as appropriate) shown on the display  1023 . 
     The electronic device  1001  may also include a transmitter (not shown) and a receiver (not shown) to allow transmission and reception of signals between the electronic device  1001  and a remote location (e.g., another electronic device, a wireless communication device, etc.). The transmitter and receiver may be collectively referred to as a transceiver. An antenna (not shown) may be electrically coupled to the transceiver. The electronic device  1001  may also include (not shown) multiple transmitters, multiple receivers, multiple transceivers and/or multiple antenna. 
     The various components of the electronic device  1001  may be coupled together by one or more buses, which may include a power bus, a control signal bus, a status signal bus, a data bus, etc. For simplicity, the various buses are illustrated in  FIG. 10  as a bus system  1011 . 
     In one configuration, a circuit may be adapted to generate a three-dimensional face. A first section of the circuit may be adapted to calculate an inverse depth map based on a depth map and an inverted first matrix. The inverted first matrix may be generated from two images in which pixels are aligned vertically and differ horizontally. In addition, the same circuit, a different circuit, a section of a different circuit or a second section of the same circuit may be adapted to normalize the inverse depth map to correct for distortions in the depth map caused by image rectification. Further, the same circuit, a different circuit, a section of a different circuit, or a third section of the same circuit may be adapted to generate a three-dimensional face model based on the inverse depth map and one of the two images. 
     In the above description, reference numbers have sometimes been used in connection with various terms. Where a term is used in connection with a reference number, this may be meant to refer to a specific element that is shown in one or more of the Figures. Where a term is used without a reference number, this may be meant to refer generally to the term without limitation to any particular Figure. 
     The term “determining” encompasses a wide variety of actions and, therefore, “determining” can include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Also, “determining” can include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Also, “determining” can include resolving, selecting, choosing, establishing and the like. 
     The phrase “based on” does not mean “based only on,” unless expressly specified otherwise. In other words, the phrase “based on” describes both “based only on” and “based at least on.” 
     The term “processor” should be interpreted broadly to encompass a general purpose processor, a central processing unit (CPU), a microprocessor, a digital signal processor (DSP), a controller, a microcontroller, a state machine and so forth. Under some circumstances, a “processor” may refer to an application specific integrated circuit (ASIC), a programmable logic device (PLD), a field programmable gate array (FPGA), etc. The term “processor” may refer to a combination of processing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. 
     The term “memory” should be interpreted broadly to encompass any electronic component capable of storing electronic information. The term memory may refer to various types of processor-readable media such as random access memory (RAM), read-only memory (ROM), non-volatile random access memory (NVRAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable PROM (EEPROM), flash memory, magnetic or optical data storage, registers, etc. Memory is said to be in electronic communication with a processor if the processor can read information from and/or write information to the memory. Memory that is integral to a processor is in electronic communication with the processor. 
     The terms “instructions” and “code” should be interpreted broadly to include any type of computer-readable statement(s). For example, the terms “instructions” and “code” may refer to one or more programs, routines, sub-routines, functions, procedures, etc. “Instructions” and “code” may include a single computer-readable statement or many computer-readable statements. 
     The functions described herein may be implemented in software or firmware being executed by hardware. The functions may be stored as one or more instructions on a computer-readable medium. The terms “computer-readable medium” or “computer-program product” refers to any tangible non-transitory storage medium that can be accessed by a computer or a processor. By way of example, and not limitation, a computer-readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk and Blu-ray® disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. 
     The methods disclosed herein include one or more steps or actions for achieving the described method. The method steps and/or actions may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of steps or actions is required for proper operation of the method that is being described, the order and/or use of specific steps and/or actions may be modified without departing from the scope of the claims. 
     Further, it should be appreciated that modules and/or other appropriate means for performing the methods and techniques described herein, such as those illustrated by  FIGS. 3, 5-6 and 8-9 , can be downloaded and/or otherwise obtained by a device. For example, an electronic device may be coupled to a server to facilitate the transfer of means for performing the methods described herein. Alternatively, various methods described herein can be provided via a storage means (e.g., random access memory (RAM), read-only memory (ROM), a physical storage medium such as a compact disc (CD) or floppy disk, etc.), such that a device may obtain the various methods upon coupling or providing the storage means to the device. 
     It is to be understood that the claims are not limited to the precise configuration and components illustrated above. Various modifications, changes and variations may be made in the arrangement, operation and details of the systems, methods and apparatus described herein without departing from the scope of the claims.