Patent Publication Number: US-8532425-B2

Title: Method and apparatus for generating a dense depth map using an adaptive joint bilateral filter

Description:
BACKGROUND 
     1. Field of the Invention 
     Embodiments of the present invention generally relate to depth map generation and, more particularly, to a method and apparatus for generating a dense depth map using an adaptive, joint bilateral filter. 
     2. Description of the Related Art 
     Generally bilateral filters are used in image processing to provide edge-preserving smoothing of an image. Bilateral filters provide both domain and range filtering of images to smooth image content, yet maintain the edges of objects within the image. However, since bilateral filtering involves updating pixel values by estimating a weighted sum of pixel values over a large neighborhood of pixels, such filtering requires substantial computational resources and long periods of time to complete the calculations. 
     Further, a depth map represents depth in an image relative to a given focal plane. The focal plane is typically located upon the main subject of the image, but the plane (i.e., a reference plane when arbitrarily chosen) can be located at any arbitrary position within a scene. The depth map then represents object distance relative to the plane as a positive or negative value, with the magnitude of the value representing distance from the plane and the sign representing whether the object is in front of or behind the reference plane. Depth maps are typically created using ranging techniques such as laser or ultrasonic range finders as well as imaging techniques such as parallax processing. Depth maps may be enhanced using joint bilateral filtering. The goal of joint bilateral filtering is to both remove anomalous depth values through smoothing of depth values in flat areas and to improve the spatial resolution and depth resolution of the depth map. Generally bilateral filtering is slow and existing methods to optimize the processing utilize significant additional memory, or utilize approximations that may produce erroneous results. 
     Some image processing techniques utilize depth maps to enhance the image processing results. For example, depth maps are useful in foreground/background decomposition, face recognition, object tracking and the like. The depth map provides depth information that can be used to decompose an image into constituent components related to their depth within the image. However, using a low resolution depth map for image processing results in significant loss of quality and accuracy in the processing. 
     Accordingly, there exists a need for a method and apparatus for efficiently generating a dense depth map. 
     SUMMARY OF THE INVENTION 
     Embodiments generally include a method and apparatus for generating a dense depth map. In one embodiment, the method includes applying a joint bilateral filter to a first depth map to generate a second depth map, where at least one filter weight of the joint bilateral filter is adapted based upon content of an image represented by the first depth map, and wherein the second depth map has a higher resolution than the first depth map. 
     Notations 
     DL i, j : depth value of pixel with coordinates (i, j) in lower resolution depth map 
     DH X, Y : depth value of pixel with coordinates (X, Y) in higher resolution depth map 
     X, Y: coordinates of current pixel in higher resolution depth map 
     i, j: coordinates of pixel in refinement window in lower resolution depth map 
     IH X, Y : intensity of pixel current pixel (X, Y) from higher resolution image 
     IL i, j : intensity of pixel (i, j) from lower resolution image 
     WD X, Y, i, j : weight based on distance between pixel (X, Y) and pixel (i, j) 
     DD X, Y, i, j : distance term between pixel (X, Y) and pixel (i, j) 
     DI X, Y, i, j : difference term for intensity difference between pixel (X, Y) and pixel (i, j) 
     WI X, Y, i, j : weight based on intensity difference between pixel (X, Y) and pixel (i, j) 
     L X, Y, i, j : intensity difference between pixel (X, Y) and pixel (i, j) 
     M: resizing factor for first refinement method 
     N: resizing factor for second refinement method 
     P: resizing factor that brings image into resolution of depth map 
     hs1: half size of refinement window for first refinement method 
     hs2: half size of refinement window for second refinement method 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the above recited features of the present invention can be understood in detail, a more particular description of the invention, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments. 
         FIG. 1  is a block diagram of a system for generating a dense depth map using an adaptive bilateral filter according to one or more embodiments. 
         FIG. 2  is a functional block diagram representing a depth map refinement method according to one embodiment. 
         FIG. 3  is a flow diagram illustrating a method for processing a depth map to generate a dense depth map according to one embodiment. 
         FIG. 4  is a flow diagram illustrating a first refinement method according to one embodiment. 
         FIG. 5  is a flow diagram illustrating a method for a first uniformity test according to an embodiment. 
         FIG. 6  is a functional block diagram representing sub-sampled images used in the first refinement method according to an embodiment. 
         FIG. 7  is a flow diagram illustrating a second refinement method according to one embodiment. 
         FIG. 8  is a flow diagram illustrating a method for a second uniformity test according to an embodiment. 
         FIG. 9  is a functional block diagram representing sub-sampled images used in a second refinement method according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a block diagram of a system  100  for generating a dense depth map using an adaptive bilateral filter according to one or more embodiments. The system  100  includes a computer  110  and an image source  112  and a depth map source  114 . The computer  110  includes central processing unit (CPU)  120 , support circuits  130  and a memory  140 . The CPU  120  may comprise one or more commercially available microprocessors or microcontrollers that facilitate data processing and storage. Various support circuits  130  facilitate operation of the CPU  120  and may include clock circuits, buses, power supplies, input/output circuits and/or the like. The memory  140  includes a Read Only Memory, Random Access Memory, disk drive storage, optical storage, removable storage, and the like. The memory  140  includes an operating system  150 , a depth map processor  160 , image processor  170 , an interim depth map  182 , a first depth map  180 , a second depth map  184 , an image  190  and sub-sampled versions of the image  192 . 
     The computer  110  communicates with the image source  112  and the depth map source  114  to obtain an image  190  and a first depth map  180 , respectively. The image source  112  is a device that captures images, e.g., a digital camera, video camera, and the like. The depth map source  114  is a device or circuit that generates the first depth map  180  associated with the image  190 . The depth map source  114  may be a depth sensor circuit such as a laser or ultrasonic ranging circuit. In other embodiments, the source  114  may be a circuit that computes depth from two or more images using parallax processing. Other software and/or hardware based techniques for depth map generation may be used. 
     The first depth map  180  obtained from the depth map source  114  and the image  190  obtained from the image source  112 , are stored in the memory  140 . The depth map processor  160  is implemented by, for example, a depth map refinement method  200  with reference to  FIG. 2 . The depth map processor  160  generates an interim depth map  182  and a dense depth map  184  (also referred to herein as a second depth map). The first depth map  180  is refined by the depth map processor  160  by implementing, for example, the depth map refinement method  200 , to generate depth maps of successively higher resolution, the interim depth map  182  followed by the second depth map  184 . 
     The first depth map  180  is a low resolution depth map that, for example, represents depth in the image  190  relative to a focal plane. In other embodiments, the depth map may be represented in terms of absolute depth and an arbitrary plane may be considered as a reference plane. In the current implementation, the focal plane is typically located upon the main subject of the image  190 . However, the focal plane may be arbitrarily positioned. All pixel locations representing an object or surface behind the focal plane are allocated a polarity or sign (e.g., negative) and a value representing the distance from the focal plane. All pixel locations representing an object in front of the focal plane are allocated a polarity (e.g., positive) and a value representing the distance from the focal plane. 
     The image processor  170  generates the sub-sampled versions of image  192 . The image processor  170  encodes the image  190  by implementing sub-sampling to generate low resolution sub-sampled versions of image  192 . Those skilled in the art will appreciate that sub-sampling may be implemented by various well known sub-sampling techniques such as block-based pixel averaging, among others. The sub-sampled versions of the image  192  include sub-sampled images of varying resolution (not shown in  FIG. 1 ), such as a sub-sampled image  192   a  of, for example, a high resolution 1/P, a sub-sampled image  192   b  of, for example, a medium resolution of 1/PN and a sub-sampled image  192   c  of, for example low resolution 1/PMN (where M, N and P are integer values). In one embodiment of the invention, the sub-sampled images are used to guide (adapt) the refinement process used to create a dense depth map from the first (input) depth map. More specifically, the sub-sampled images are used to adapt a bilateral filter that is used to refine the low resolution depth map to form a dense depth map. 
     As an example M=4, N=2, P=8 such that the high resolution corresponds to ¼th resolution of the input image, medium resolution corresponds to 1/16th resolution of the input image, and low resolution corresponds to 1/64th resolution of the input image. 
       FIG. 2  is a block diagram representing a depth map refinement method  200  according to one embodiment. The input to the depth map refinement method  200  is a full resolution image  190  and the first depth map  180 . In the example illustrated in  FIG. 2 , the full size image  190  is subsampled at step  202  by 1/P to form a first sub-sampled image  192   a  (1/P image). The first sub-sampled image  192   a  is subsampled at step  204  by 1/N to form a second subsampled image  192   b  (1/PN image). The second subsampled image  192   b  is subsampled at step  206  by 1/M to form a third subsampled image  192   c  (1/PMN image). The lowest resolution subsampled image  192   c  has a resolution that matches the low resolution of the first depth map  180 . Those skilled in the art will appreciate that the resolution of the sub-sampled image  192   c  is commensurate with the resolution of the depth map being refined using the depth refinement method  200 . 
     At blocks  208   a  and  208   b , the sub-sampled image  192   c  and the first depth map  180  are padded, as needed, with pixels to create images of equal number of pixels. For example, since the sub-sampled image  192   c  and the first depth map  180  have the same resolution of 1/PMN, both the sub-sampled image  192   c  and the first depth map  180  are padded with a number of pixels and depth map values, respectively, proximate the image and depth map boundaries such that the size of each image measured in pixels and depth map values is the same. In some embodiments, padding may not be necessary. The padded sub-sampled image  210  and the second subsampled image  192   b  are used to refine the padded first depth map  212  by a first refinement process  214 . The first refinement process at step  204  is described in detail below with reference to  FIG. 4 . The first refinement process  204  produces an interim depth map  182  that has a higher resolution than the first depth map  180 . The resolution of the interim depth map  182  is, for example, 1/PN, i.e., the same resolution as the second subsampled image  192   b.    
     At step  216 , the interim depth map  182  is padded, as needed, and at step  218  the second sub-sampled image  192   b  is padded to generate an image with the same number of pixels as depth map values are contained in the interim depth map  182 . The padded depth map  220  and padded image  222  are coupled to a second refinement step  224 . At the second refinement step  224 , the padded image  222  and the first subsampled image  192   a  are used to refine the padded interim depth map  220 . The second refinement process  224  is described in detail below with reference to  FIG. 7 . The second refinement process  224  produces a second depth map  184 . The second depth map  184  has a depth map value density that is higher than both the first depth map  180  and the interim depth map  182  i.e., a resolution equal to the resolution of the first subsampled image  192   a . If necessary, the second depth map  184  and the first subsampled image  192   a  may be respectively padded at steps  226  and  228  to respectively form padded depth map  230  and padded image  232 . 
     Although, only two refinement steps are shown in the embodiment illustrated in  FIG. 2 , the depth refinement method  200  may be extended by any number of additional refinement steps, as indicated by the further refinement process  234 . Further refinement process  234  involves repeating the second refinement step for each additional desired refinement. The repetition process may involve additional adaptive parameter tuning and/or resolution change. 
       FIG. 3  is a flow diagram illustrating a method  300  for processing a depth map to generate a dense depth map according to one embodiment. The method  300  begins at step  302  and proceeds to step  304 . At step  304 , an image (for example, the image  190  of  FIG. 1 ) is accessed from memory (or delivered from the image source). At step  306 , the image is sub-sampled to generate sub-sampled versions of the image (for example, the sub-sampled versions of the image  192  of  FIG. 1 ). At step  308 , the sub-sampled versions of the image are stored in the memory. At step  310 , an appropriate sub-sampled image is selected from the sub-sampled versions. According to some embodiments, the sub-sampled image is selected according to the resolution of the depth map to be refined. For example, the third sub-sampled image  192   c  and the second subsampled image  192   b  are selected to refine the first depth map (for example, the depth map  180  of  FIG. 1 ) with a resolution of 1/PMN. At step  312 , the selected third sub-sample image  192   c  may be padded, as needed. 
     At step  314 , the first depth map  180  is accessed from memory, or otherwise provided by the depth map source. At step  316 , the first depth map  180  may be padded, as needed, to generate a padded first depth map. At step  318 , the first refinement method similar to, for example, the first refinement at step  214  of  FIG. 2  is performed. The first refinement method is described in detail below with reference to  FIG. 4 . At step  320 , the interim depth map (for example, the interim depth map  182  of  FIG. 1 ) generated by the first refinement method may be padded, as needed. At step  322 , other appropriate sub-sampled images (image  192   b  and  192   a ) are selected from the sub-sampled versions of the image. The sub-sampled images are selected at step  322  according to the resolution of the interim depth map. For example, the sub-sampled image  192   a  with a resolution of 1/P is selected to guide refinement of the interim depth map  182 . At step  324 , the selected sub-sampled image  192   b  may be padded, as needed. 
     At step  326 , the second refinement method (for example, the second refinement at step  224  of  FIG. 2 ) is performed. The second refinement method is described in detail below with reference to  FIG. 7 . At step  328 , the second depth map (for example, the second depth map  184  of  FIG. 1 ) generated by the second refinement method may be padded, as needed. At step  330 , the padded second depth map is stored for further processing and the method  300  ends at step  332 . 
       FIG. 4  is a flow diagram illustrating a first refinement method  400  implementing step  326  of  FIG. 3  according to one embodiment. The first refinement method  400  begins at step  402  and proceeds to step  404 . At step  404 , a refinement window is established in the sub-sampled image (for example, the third sub-sampled image  192   c  and second sub-sampled image  192   b  of  FIG. 2 ). At step  404 , a corresponding refinement window (a bilateral filtering window) is positioned in the first depth map (for example, the first depth map  180 ). At step  403 , a counter is set to zero. This counter value is used in a second uniformity test described below. At step  406 , a first uniformity test is optionally performed. The first uniformity test may be performed to determine whether the refinement window within the depth map contains a uniform set of a depth map values or not. The method of the first uniformity test is described below with reference to  FIG. 5 . If the method  400  deems the window content to be uniform, the method  400  proceeds to step  410 . If the window content is deemed non-uniform, the method  400  proceeds to step  418  (or optionally step  409 ) without updating a depth map value. The optional smoothing check and a method of implementation are described in detail below. 
     At step  410 , an intensity weight WI for the bilateral filter is calculated and at step  412  a distance weight WD for the bilateral filter is calculated. As such, the intensity weight WI and the distance weight WD are computed using a refinement window established in the sub-sampled image. The method of computation of WI and WD is described in detail below with reference to  FIG. 6 . However, those skilled in the art will appreciate that computing WI and WD using the sub-sampled image having a low resolution reduces the computation time and cost, since the number of pixels to be processed is smaller in the low resolution sub-sampled image. Through step  406  to  422 , depth map value at the center of the refinement window is computed using the bilateral filter equation (more general version is given by equation 1). At step  416 , the updated depth map value is temporarily stored. As each depth map value in the window is processed, the stored value of the center located value is updated. 
     At step  418 , a determination is made whether there are more depth map values in the refinement window to be processed. If there are more depth map values in the refinement window (option “YES”), the next depth map value is obtained at step  420  and the method  400  returns and repeats steps from  408  to  416 . In this embodiment, the window size is ±hs1 (±hs2 for second refinement method) locations away from the center value. In this manner, the depth map values within the window are weighted and summed to provide a new value for a denser depth map. If there are no more depth map values in the refinement window (option “NO”), the method  400  proceeds to step  422 . 
     At this point (option “NO”), the value stored in  416  is given by the term: 
     
       
         
           
             
               
                 
                   
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     At step  422 , updated depth map value from  416  is normalized using the equation: 
                     DH     X   ,   Y       =         ∑     i   =       X   /   M     -     hs   ⁢           ⁢   1             X   /   M     +     hs   ⁢           ⁢   1         ⁢           ⁢       ∑     j   =       Y   /   M     -     hs   ⁢           ⁢   1             Y   /   M     +     hs   ⁢           ⁢   1         ⁢           ⁢     (       DL     i   ,   j       ×     WI     X   ,   Y   ,   i   ,   j       ×     WD     X   ,   Y   ,   i   ,   j         )             ∑     i   =       X   /   M     -     hs   ⁢           ⁢   1             X   /   M     +     hs   ⁢           ⁢   1         ⁢           ⁢       ∑     j   =       Y   /   M     -     hs   ⁢           ⁢   1             Y   /   M     +     hs   ⁢           ⁢   1         ⁢           ⁢     (       WI     X   ,   Y   ,   i   ,   j       ×     WD     X   ,   Y   ,   i   ,   j         )                   (   2   )               
At step  424 , the normalized depth map values are stored as values of the interim depth map.
 
     At step  426 , a determination is made whether the first depth map is complete or not. If the first depth map is not complete (option “NO”), the method  400  proceeds to step  428 . At step  428 , the refinement window is repositioned in the first depth map and the next center located value is computed. In one embodiment, the method  400  shifts the window a predefined distance and proceeds to compute the next new depth map value. The predefined distance determines the pixel density of the interim depth map. For example, if the predefined distance is ½ the distance between depth map values of the first depth map, the resolution will be increased by a factor of two. If the first depth map is complete (option “YES”), the method  400  proceeds to end at step  430 . 
       FIG. 5  is flow diagram illustrating a method  500  for performing a first uniformity test (step  408  of  FIG. 4 ) according to an embodiment. As described above, the first uniformity test is used to determine the uniformity of the depth map values within the refinement window. As such, a depth map includes pixels having depth map values that are either positive or negative to indicate the distance in front of or behind a focal plane, respectively. The uniformity of the depth map values within the refinement window is determined by comparing the depth values DL i, j  within the refinement window to the depth value at the center DL X/M, Y/M  of the refinement window. Locations with depth map values significantly different from the depth map value of the central location are excluded from the first refinement method and thereby do not contribute to the bilateral filtering process applied to the depth map. The method  500  of the first uniformity test is described in detail in the following paragraphs. 
     The method  500  starts at step  504  and proceeds to step  506 . At step  506 , the depth map value for the central location DL X/M, Y/M  of the refinement window is determined. The co-ordinates of the central pixel at low resolution are represented as X/M, Y/M. The central location is described here in  FIG. 6  only as an example, and not as a limitation, of a reference location for the uniformity test being performed for the refinement window. Any location within the refinement window may be used as the reference location. 
     At step  508 , the depth map value of a location with co-ordinates DL i,j  is determined, where (i,j) are co-ordinates of a current location within the refinement window other than the central location. At step  510 , the method  500  calculates the difference DIFF between DL X,Y  and the DL i,j . 
     The value |DIFF| is used in the uniformity test of step  512 . In step  512 , a determination is made whether |DIFF| is higher than a predetermined uniformity threshold “threshold_UT” and whether the sign of DL i,j  is opposite to that of DL X/M,Y/M . If |DIFF| is less than “threshold_UT” or the sign of DL i,j  is not opposite to that of DL X/M,Y/M  (option “NO”), the method  500  deems the value at the current location to be uniform and returns to method  400  at step  410  in  FIG. 4 . If value of |DIFF| is higher than threshold_UT and the sign of DL i,j  is opposite to that of DL X/M,Y/M  (option “YES”), the region is deemed to be non-uniform and the method  500  proceeds to step  514  where the value COUNT is incremented by 1 and stored in memory (e.g., a register). The method  500  then returns to either step  409  or  418  of  FIG. 4 . A depth map value with a large difference with respect to the center value represents a boundary within the depth map. Using such a discontinuity within the window may cause an anomalous filter result. As such, the depth map value is excluded from the computation of Equation (1). 
     As is described below, the value count being generated in the first uniformity test is accessed and used in the second refinement method (for example the second refinement method  326  of  FIG. 3 ). This count represents the number of depth map values within the window that are both non-uniform and have an opposite sign to the center value, i.e., representing a depth boundary within the window. 
       FIG. 6  is a schematic representation of sub-sampled images  620  and  610 . The sub-sampled image  620  has a relatively lower resolution than the resolution of image  610 . For example, the sub-sampled image  620  is similar to, for example, the sub-sampled image  192   c  and the sub-sampled image  610  is similar to, for example the sub-sampled image  192   b . In one embodiment, the subsampled image  620  has a resolution of 58×42 and the subsampled image  610  has a resolution of 232×171. 
     A refinement window  622  of a size (2*hs1/M+1)×(2*hs1/M+1) pixels is established in the sub-sampled image  620 , which has a similar effect as having aa refinement window  612  of a size (2*hs1+1)×(2*hs1+1) in the target resolution image  610 . M is the resolution ratio of 2 sub-sampled images  620  to  610 . For example, if hs1 is 8 and M is 4, just by having 5×5 window in the lower resolution image  620 , the method can cover an area of 17×17 in the higher resolution image  610 . As such, the intensity weight WI X, Y, i, j  of the bilateral filter is calculated using the sub-sampled image  620  and the refinement window  622 . 
     Although the foregoing description utilizes a resizing factor M (as well as N and P for other subsampled images) that is equal for both the x-axis and the y-axis, in other embodiments, the resizing factor may be different for each axis, e.g., subsampling at M x- , M y , N x , N y , P x , and P y . 
     In the case when the image  620  is given in Y, Cr, Cb format (luminance, blue/yellow, red/green), the intensity difference can be computed across all three channels as given in following equation: 
                     DI     X   ,   Y   ,   i   ,   j       =         w   Y     ×            IHY     X   ,   Y       -     ILY     i   ,   j                +       w   Cb     ×            IHCb     X   ,   Y       -     ILCb     i   ,   j                +       w   Cr     ×            IHCr     X   ,   Y       -     ILCr     i   ,   j                          (   3   )               
w Y , w Cb , and w Cr  are weight coefficients of Y, Cb, and Cr, respectively. In other embodiments the image can be converted to another luminance/chrominance space such as L*a*b* and the distance can be computed in such a space using the known ΔE perceptual difference or a similar distance metric.
 
     If the image is in a grayscale format, the above equation becomes:
 
 DI   X,Yi,j   |IH   X,Y   −IL   i,j |  (4)
 
     DI X,Y,i,j  can be computed on the fly or the computation can be implemented via a lookup table, similarly to WI X,Y,i,j  in graph  670 , to find the level weight WI X,Y,i,j  to use in the refinement window  612  for the first refinement method. The WI X,Y,i,j  table contents forms one dimension of the filter function applied to the depth values in the window  612 . In one embodiment, the function is linear (as shown). In other embodiments, the function is non-linear depending upon the desired filter effect. Also, if the uniformity tests of  FIG. 5  has indicated that uniformity is broken, WI X,Y,i,j  is set to zero, and WI X,Y,i,j  value does not need to be computed for that depth map location. 
     Further, as described above with reference to  FIG. 2 , a sub-sampled image of resolution corresponding to the resolution of the interim depth map, for example, the sub-sampled image  192   b , is input to the first refinement method. The distance weight WD is, for example, calculated using the sub-sampled image  192   b . DD X,Y,i,j  is computed using the following equation: 
     
       
         
           
             
               
                 
                   
                     
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             γ=correction value for shifting the center at higher resolution
 
Other distances such as Euclidean distance can also be used for calculating DD X,Y,i,j .
 
           
         
       
    
     DD X,Y,i,j  is computed as a sum of the absolute value of a horizontal distance from the central pixel  614  (with co-ordinates X, Y) to a corresponding pixel in the target resolution of the each pixel  626  (with co-ordinates i,j) in a refinement window The term γ which may be 
               ⌈     M   2     ⌉     ⁢           ⁢   or   ⁢           ⁢     ⌊     M   2     ⌋           
depending on the indexing method used in the implementation. γ is used to compensate for shift in indices due to sub-sampling between higher resolution and lower resolution: (X, Y) are coordinates in higher resolution while (i, j) are coordinates in lower resolution.
 
     WD X,Y,i,j  can be pre-computed from DD X,Y,i,j  the means of a lookup table or computed using a mathematical formula, such as that represented by a WD X,Y,i,j  graph  660 , to find the distance weight WD X,Y,i,j  to use for the first refinement method. Although a linear relationship between distance and/or level and the filter weight is illustrated in  FIG. 6 , other relationships according to the requirement of the filtering process may be utilized. Although WD X,Y,i,j  is described here, as being calculated using the sub-sampled image  192   b , both filter weights, WD X,Y,i,j  and WI X,Y,i,j , could be calculated using very low resolution sub-sampled image such as the sub-sampled image  192   a  to further reduce the computational cost of bilateral filtering. 
     As per the foregoing description, the first refinement method computes filter weights for a first bilateral filter that is applied to the first depth map using a low resolution image to guide (adapt) the weight computation. In addition, a uniformity test is performed to exclude certain depth values from the computation, where the values are deemed to represent a boundary within a depth map. The results is a interim depth map having a higher resolution than the first depth map as well as having smooth content yet maintain the boundaries of the depth map. 
       FIG. 7  is a flow diagram illustrating a second refinement method  700  implementing step  326  of  FIG. 3  according to one embodiment. The second refinement method  700  begins at step  702  and proceeds to step  704 . At step  704 , a refinement window is established in the sub-sampled image (for example, the padded sub-sampled image  222  of  FIG. 2 ) and he padded interim depth map (for example,  220  of  FIG. 2 ). At step  708 , a second uniformity test is performed. The method of the second uniformity test is described below with, for example, a method  800  with reference to  FIG. 8 . If the region is deemed non-uniform, the method  700  the method proceeds from step  708  to step  718  (or, optional smoothing check step  709 ). Embodiments of implementations of the smoothing check of step  709  are described in detail below. If the region is deemed uniform at step  708 , the method  700  proceeds from step  708  to step  710 . 
     At step  710 , an intensity weight WI X,Y,i,j  of a second bilateral filter is calculated and at step  712  a distance weight WD X,Y,i,j  of a second bilateral filter is calculated. As such, the WI X,Y,i,j  and the WD X,Y,i,j  are computed using refinement window established in the sub-sampled image. The method of computation of WD X,Y,i,j  and the WD X,Y,i,j  is described in detail below with reference to  FIG. 9 . Through steps  706  to  722 , a depth map value at the center of the refinement window is computed using the bilateral filter equation (please see equation 1). 
     At step  716 , the center depth map value DH X,Y  is temporarily stored. As each depth map value in the window is processed, the stored value of the center located value is updated. At step  718 , a determination is made whether there are more depth map values in the refinement window that have yet to be used to contribute to the computed center depth map value. If there are more depth map values in the refinement window (option “YES”), the next depth map value is obtained at step  720  and repeats step  710  to step  716 . In this embodiment, the window size is ±hs2 values around the center pixel X,Y. In this manner, the depth map values within the window are weighed and summed to provide a new value for a denser depth map. If there are no more depth map values in the refinement window (option “NO”), the method  700  proceeds to step  722 . At step  722 , updated depth map values are normalized (please see equation 2). At step  724 , the normalized depth map values are stored in a second depth map. 
     At step  726 , a determination is made whether the second depth map is complete or not. If the depth map is not complete (option “NO”), the method  700  proceeds to step  728 . At step  728 , the refinement window is repositioned in the first depth map and the next center value is computed. In one embodiment, the method  700  shifts the window a predefined distance and proceeds to compute the next new depth map value. The predefined distance determines the pixel density of the second depth map. If the first depth map is complete (option “YES”), the method  700  proceeds to end at step  730 . The result is a second depth map having a higher resolution, where the increased resolution is defined by the predefined distance. 
       FIG. 8  is a flow diagram illustrating a method  800  implementing a second uniformity test (step  708  of  FIG. 7 ) according to an embodiment. The second uniformity test excludes a depth map value from the second refinement step according to the count generated in the first uniformity test. The method  800  starts at step  802  and proceeds to step  804 . At step  804 , the method  800  accesses the count generated by the first uniformity test (for example, uniformity test method  408  at step  518 ). The count generated in the first uniformity test provides the number of depth map values within the refinement window that are excluded from the first refinement step and do not belong to same side of a focal plane. At step  806 , a determination is made whether the count for the depth map value being processed within the refinement window exceeds a predetermined count threshold. In one embodiment, the count threshold is 30% of total number of depth values in the 2 nd  refinement window size (2*hs2+1)×(2*hs2+1). If the count exceeds the predetermined count threshold (option “YES”), the method  800  moves to step  808 , at which the distance weight WD X,Y,i,j  for the depth map value presently being processed is set to a fixed value for a sharper filter (i.e., the value WD X,Y,i,j  is multiplied by a constant H, where H&gt;1). Setting WD X,Y,i,j  to a value greater than one, defines a sharper weight than would be otherwise be used by the bilateral filter. In an embodiment, the WD X,Y,i,j  is set to four to define a distance weight four times sharper than is otherwise defined for “normal” bilateral filtering. After setting WD, the method  800  returns to method  700  at step  709  or step  718  in  FIG. 7 . If the count does not exceed the predetermined count threshold (option “NO”), the method  800  returns to method  700  at step  710  of  FIG. 7 . In this manner, the second refinement ensures the depth map values are generated using a sharp filter (less smoothing) when the value is near a boundary. 
       FIG. 9  is schematic representation of 2 sub-sampled images  920  and  910  (sub-sampled image  192   a  of  FIG. 2 ) used in a second refinement method (for example, the second refinement method  700  of  FIG. 7 .) The sub-sampled image  920  has a similar resolution as the padded interim depth map  220 , which is also an input to the second refinement process, and the sub-sampled image  910  has a similar resolution as the target depth map resolution of the second refinement process. 
     A refinement window  922  of size (2*hs2/N+1)×(2*hs2/N+1) pixels is established in the sub-sampled image  920 . A (2*hs2/N+1)×(2*hs2/N+1) refinement window in the lower resolution depth map is equivalent to a (2×hs2+1)×(2×hs2+1) window in a higher resolution depth map. M is resolution ratio between the lower resolution image  920  and the higher resolution image  910 . For example, if hs2 is 8 and N is 2, just by having 9×9 pixel refinement window on the lower resolution image we can cover about 17×17 area in the high resolution image, which reduces the amount of computations. As such, the intensity weight WI of the bilateral filter is calculated using the sub-sampled image  920  and the refinement window  922 . 
     In the case in which the image  620  is given in Y, Cr, Cb format (luminance, blue/yellow, red/green), the intensity difference can be computed across all three channels as given in following equation: 
                     DI     X   ,   Y   ,   i   ,   j       =         w   Y     ×            IHY     X   ,   Y       -     ILY     i   ,   j                +       w   Cb     ×            IHCb     X   ,   Y       -     ILCb     i   ,   j                +       w   Cr     ×            IHCr     X   ,   Y       -     ILCr     i   ,   j                          (   6   )               
w Y , w Cb , and w Cr  are weight coefficients of Y, Cb, and Cr, respectively. In other embodiments the image can be converted to another luminance/chrominance space such as L*a*b* and the distance can be computed in such a space using the known ΔE perceptual difference or a similar distance metric. If the image is in a grayscale format, the above equation becomes:
 
 DI   X,Y,i,j   =|IH   X,Y   −IL   i,j |  (7)
 
     Computing WI based on DI can be done via a lookup table or computing formula to generate values, such as that represented by graph  970 , to find the level weight WI to use in the refinement window  912 , 912  for the second refinement method. In one embodiment, the function is linear (as shown). In other embodiments the function is non-linear depending upon the desired filter effect. 
     Further, as described above with reference to  FIG. 2 , a sub-sampled image of resolution corresponding to the resolution of the interim depth map, the interim depth map, and a sub-sampled image of resolution corresponding to the target resolution of the second refinement process are input to the second refinement method. They image for example corresponds to  222 ,  220 , and  192   a  of  FIG. 2  respectively. The distance weight WD is for example, calculated using the sub-sampled image  192   a . The size of the refinement window in the depth map  220  and the sub-sampled image  222  is same. DD X,Y,i,j  is computed using the following equation: 
     
       
         
           
             
               
                 
                   
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             γ 2 =correction value for shifting the center at higher resolution
 
Other distances such as Euclidean distance can also be used for calculating DD X,Y,i,j .
 
           
         
       
    
     The term DD is computed as a sum of the absolute value of a horizontal distance from the central pixel  914  with co-ordinates (X,Y) to a corresponding pixel in the target resolution of the each pixel  926  with coordinates (i,j) in a refinement window plus the absolute value of a vertical distance of these 2 positions. The term γ 2  may be 
               ⌈     N   2     ⌉     ⁢           ⁢   or   ⁢           ⁢     ⌊     N   2     ⌋           
depending on the indexing method used in the implementation. γ 2  is used to compensate for shift in indices due to sub-sampling between higher resolution and lower resolution: (X, Y) are coordinates in higher resolution while (i, j) are coordinates in lower resolution.
 
     The term DD is used in a lookup table or mathematical formula to generate values, such as how WD graph  960 , to find the distance weight WD to use for the second refinement method. Although a linear relationship between DD distance and distance weight WD is illustrated in  FIG. 9 , other relationships according to the requirement of the filtering process may be utilized. Also, the sharpening factor from the second uniformity test is applied to WD accordingly. 
     Optional smoothing checks at steps  409  or  709  provide a smoothing check for a region deemed non-uniform by either the first or second uniformity tests. As alternative embodiments, two possible methods for smoothing are described; other smoothing techniques may be used. In a first smoothing method, if the edge strength around current pixel in the refined depth map exceeds a certain value and edge strength of the equivalent pixel in the image is below a certain threshold, the range filter (WI) is flattened by a predefined factor. Flattening of this range filter achieves the smoothing effect. 
     One way of estimating the edge strength is using gradient magnitude computed using finite central differences. Other methods for measuring edge strength are also possible. 
               EDGEDL       X   /   M     ,     Y   /   M         =           (       (       DL         X   /   M     -   1     ,     Y   /   M         -     DL         X   /   M     +   1     ,     Y   /   M           )     /   2     )     2     +       (       (       DL       X   /   M     ,       Y   /   M     -   1         -     DL       X   /   M     ,       Y   /   M     +   1           )     /   2     )     2                       EDGEIL       X   /   M     ,     Y   /   M         =           (       (       IL         X   /   M     -   1     ,     Y   /   M         -     IH         X   /   M     +   1     ,     Y   /   M           )     /   2     )     2     +       (       (       IH       X   /   M     ,       Y   /   M     -   1         -     IH       X   /   M     ,       Y   /   M     +   1           )     /   2     )     2               
First Smoothing Method:
         Compute EDGEDL X/M,Y/M  (first refinement) or EDGEDL X/N,Y/N  (second refinement)   Compute EDGEIL X/M,Y/M  (first refinement) or EDGEIL X/N,Y/N  (second refinement)   Apply smoothing:
           if EDGEDL X/M,Y/M &gt;threshold_edge_DL and EDGEIL X/M,Y/M &lt;threshold_edge_I   flatten WI X,Y,i,j  
 
Example values for thresholds are
   
           threshold_edge_DL is set to approximately 10% of absolute of maximum depth;   threshold_edge_I is set to approximately 20% of maximum intensity value.       

     In an alternative smoothing method, the edge strength is computed for the lower resolution depth map. Insufficiently strong edges in the original lower resolution depth map are determined by comparing with a threshold. For edges whose strength is determined to be smaller than a predefined threshold, smoothing is applied as defined in the first method. One way of estimating the edge strength is using gradient magnitude computed using finite central differences. Other methods for measuring edge strength are also possible. 
     Alternative Smoothing Method: 
     
         
         
           
             Compute EDGEDL X/M,Y,M  (first refinement) or EDGEDL X/N,Y/N  (second refinement) 
           
         
       
    
     
       
         
           
             
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                 Apply smoothing 
                 if EDGEDL X/M,Y/M &lt;threshold_edge_DL
 
Example values for threshold is
 
               
             
           
         
       
    
     threshold_edge_DL is set to approximately 15% of absolute maximum depth 
     The foregoing two smoothing methods are to be performed in the absence of a confidence measure in depth map and edge strength of the image. 
     In case confidence measures for the depth map as well for the image edge strength are available, a more general check for when to trigger smoothing condition (flattening WI X,Y,i,j ) can be formulated as following:
 
if ( CDL   X/M,Y/M &lt;threshold —   CDL ) or ( CEDGEIL   X/M,Y/M &lt;threshold —   CEDGE ), flatten  WI   X,Y,i,j  
         where:   CDL X/M, Y/M : confidence measure of DL X/M, Y/M  (low value indicates a low confidence in depth estimate)   CEDGEIL X/M, Y/M : confidence measure of edge strength of IL X/M, Y/M  (low value indicates a low confidence in edge strength estimate)   threshold_CDL: threshold for determining where depth map is confident or not threshold_CEDGE: threshold for determining where edge is confident or not       

     The various embodiments described herein provide several advantages. For example, using sub-sampled images of lower resolution for calculating weights of the joint bilateral filter reduces the computational cost of applying joint bilateral filters to generate a dense depth map. Further, the uniformity test used for determining the uniformity of depth map values in the refinement window allows the joint bilateral filter to adapt the refinement process to the content of the image. 
     It is to be understood that other similar embodiments may be used. Modifications/additions may be made to the described embodiments for performing the same function of the present invention without deviating therefore. Therefore, the present invention should not be limited to any single embodiment, but rather construed in breadth and scope in accordance with the recitation of the appended claims.