Compute the disparities of a rectified image pair.

binocular_disparity computes pixel-wise correspondences between two epipolar images using correlation techniques. Different from binocular_distance the results are not transformed into distance values.

The algorithm requires a reference image Image1 and a search image Image2 which must be rectified, i.e., corresponding epipolar lines are parallel and lie on identical image rows ( r1=r2 ). In case this assumption is violated the images can be rectified by using the operators binocular_calibration, gen_binocular_rectification_map, and map_image. Hence, given a pixel in the reference image Image1 the homologous pixel in Image2 is selected by searching along the corresponding row in Image2 and matching a local neighborhood within a rectangular window of size MaskWidth and MaskHeight. The pixel correspondences are returned in the single-channel Disparity image d(r1,c1) which specifies for each pixel (r1,c1) of the reference image Image1 a suitable matching pixel (r2,c2) of Image2 according to the equation c2 = c1 + d(r1,c1) . A quality measure for each disparity value is returned in Score, containing the best result of the matching function S of a reference pixel. For the matching, the gray values of the original unprocessed images are used.

The used matching function is defined by the parameter Method allocating three different kinds of correlation:

'sad': Summed Absolute Differences  
       S(r1,c1,d) := SUM(|g1(r1',c1')-g2(r1',c1'+d)|), 0=<=S<=255,
'ssd': Summed Squared Differences   
       S(r1,c1,d) := SUM((g1(r1',c1')-g2(r1',c1'+d))²), 0<=S<=65025, 
'ncc': Normalized Cross Correlation 
       S(r1,c1,d) :=
          SUM(g1(r1',c1')-gm1(r1,c1))*(g2(r1',c1'+d)-gm2(r1,c1+d)))/
          SQRT(SUM((g1(r1',c1')-gm1(r1,c1))²)*
               SUM((g2(r1',c1+d)-gm2(r1,c1+d))²)),
       -1.0<=S<=1.0,

whereas SUM(x) is the averaged summation of x within a window of
size (2m+1) x (2n+1). Especially gm(r,c) is the mean value of
g(r',c') within this window at row r and column c. g1 and g2 are the gray
values of the unprocessed input image.

The size of the correlation window, referenced by 2m+1 and 2n+1, has to be odd numbered and is passed in MaskWidth and MaskHeight. The search space is confined by the minimum and maximum disparity value MinDisparity and MaxDisparity. Due to pixel values not defined beyond the image border the resulting domain of Disparity and Score is not set along the image border within a margin of height (MaskHeight-1)/2 at the top and bottom border and of width (MaskWidth-1)/2 at the left and right border. For the same reason, the maximum disparity range is reduced at the left and right image border.

Since matching turns out to be highly unreliable when dealing with poorly textured areas, the minimum statistical spread of gray values within the correlation window can be defined in TextureThresh. This threshold is applied on both input images Image1 and Image2. In addition, ScoreThresh guarantees the matching quality and defines the maximum ('sad','ssd') or, respectively, minimum ('ncc') score value of the correlation function. Setting Filter to 'left_right_check', moreover, increases the robustness of the returned matches, as the result relies on a concurrent direct and reverse match, whereas 'none' switches it off.

The number of pyramid levels used to improve the time response of binocular_disparity is determined by NumLevels. Following a coarse-to-fine scheme disparity images of higher levels are computed and segmented into rectangular subimages of similar disparity to reduce the disparity range on the next lower pyramid level. TextureThresh and ScoreThresh are applied on every level and the returned domain of the Disparity and Score images arises from the intersection of the resulting domains of every single level. Generally, pyramid structures are the more advantageous the more the disparity image can be segmented into regions of homogeneous disparities and the bigger the disparity range is specified. As a drawback, coarse pyramid levels might loose important texture information which can result in deficient disparity values.

Finally, the value 'interpolation' for parameter SubDisparity performs subpixel refinement of disparities. It is switched off by setting the parameter to 'none'.

// ...
// read the internal and external stereo parameters
read_cam_par ('cam_left.dat', CamParam1)
read_cam_par ('cam_right.dat', CamParam2)
read_pose ('relpos.dat', RelPose)

// compute the mapping for epipolar images   
gen_binocular_rectification_map (Map1, Map2, CamParam1, CamParam2, RelPose, 
  'geometric', 'bilinear', CamParamRect1,CamParamRect2, Cam1PoseRect1, 
  Cam2PoseRect2,RelPoseRect)

// compute the disparities in online images 
while 1
  grab_image_async (Image1, FGHandle1, -1)
  map_image (Image1, Map1, ImageMapped1)

  grab_image_async (Image2, FGHandle2, -1)
  map_image (Image2, Map2, ImageMapped2)

  binocular_disparity(ImageMapped1, ImageMapped2, Disparity, Score, 'sad',
    11, 11, 20, -40, 20, 2, 25, 'left_right_check','interpolation')
endfor

binocular_disparity returns 2 (H_MSG_TRUE) if all parameter values are correct. If necessary, an exception handling is raised.

binocular_disparity is reentrant and automatically parallelized (on domain level).

map_image

threshold, disparity_to_distance

binocular_distance

map_image, gen_binocular_rectification_map, binocular_calibration

3D Metrology