gen_binocular_proj_rectification — Compute the projective rectification of weakly calibrated binocular
stereo images.
gen_binocular_proj_rectification( : Map1, Map2 : FMatrix, CovFMat, Width1, Height1, Width2, Height2, SubSampling, Mapping : CovFMatRect, H1, H2)
A binocular stereo setup is called weakly calibrated if the fundamental matrix, which describes the projective relation between the two images, is known. Rectification is the process of finding a suitable set of transformations, that transform both images such that all corresponding epipolar lines become collinear and parallel to the horizontal axes. The rectified images can be thought of as acquired by a stereo configuration where the left and right image plane are identical and the difference between both image centers is a horizontal translation. Note that rectification can only be performed if both of the epipoles are located outside the images.
Typically, the fundamental matrix is calculated beforehand with
match_fundamental_matrix_ransac and FMatrix is the basis
for the computation of the two homographies H1 and H2,
which describe the rectifications for the left image and the right image
respectively. Since a projective rectification is an underdetermined
problem,
additional constraints are defined: the algorithm chooses the set
of homographies that minimizes the projective distortion induced by the
homographies in both images. For the computation of this cost function the
dimensions of the images must be provided in Width1,
Height1, Width2, Height2. After rectification
the fundamental matrix is always of the canonical form
In the case of a known covariance matrix CovFMat of the
fundamental matrix FMatrix, the covariance matrix
CovFMatRect of the
above rectified fundamental matrix is calculated. This can help for an
improved stereo matching process because the covariance matrix defines in
terms of probabilities the image domain where to find a corresponding match.
Similar to the operator gen_binocular_rectification_map the
output images Map1 and Map2 describe the transformation,
also called mapping, of the original images to the rectified ones.
The parameter Mapping specifies whether bilinear interpolation
('bilinear_map') should be applied between the pixels in the input
image or whether the gray value of the nearest neighboring pixel should be
taken ('nn_map').
The size and resolution of the maps and of the transformed
images can be adjusted by the parameter SubSampling, which applies
a sub-sampling factor to the original images. For example, a factor of two
will halve the image sizes. If just the two homographies are required
Mapping can be set to 'no_map' and no maps will be
returned.
For speed reasons, this option should be used if for a
specific stereo configuration the images must be rectified only once.
If the stereo setup is fixed, the maps should be generated only once
and both images should be rectified with map_image;
this will result in the smallest computational cost for on-line
rectification.
Map1 and Map2 are single channel images if
Mapping is set to 'nn_map' and five channel images if
it is set to 'bilinear_map'. In the first channel, which is of type
int4, the pixels contain the linear coordinates of their reference pixels
in the original image. With Mapping equal to 'no_map'
this reference pixel is the nearest neighbor to the back-transformed pixel
coordinates of the map.
In the case of bilinear interpolation the reference pixel is the next upper
left pixel relative to the back-transformed coordinates.
The following scheme shows the ordering of the pixels in the original image
next to the back-transformed pixel coordinates, where the reference pixel
takes the number 2.
| 2 | 3 |
| 4 | 5 |
The channels 2 to 5, which are of type uint2, contain the weights of the relevant pixels for the bilinear interpolation.
Based on the rectified images, the disparity be
computed using binocular_disparity.
In contrast to stereo with fully calibrated cameras, using the operator
gen_binocular_rectification_map and its successors, metric depth
information can not be derived for weakly calibrated cameras.
The disparity map gives just a qualitative depth ordering of the
scene.
Map1 (output_object) image(-array) → object (int4 / uint2)
Image coding the rectification of the 1. image.
Map2 (output_object) image(-array) → object (int4 / uint2)
Image coding the rectification of the 2. image.
FMatrix (input_control) hom_mat2d → (real / integer)
Fundamental matrix.
CovFMat (input_control) number-array → (real / integer)
9x9 covariance matrix of the fundamental matrix.
Default: []
Width1 (input_control) integer → (integer)
Width of the 1. image.
Default: 512
Suggested values: 128, 256, 512, 1024
Restriction:
Width1 > 0
Height1 (input_control) integer → (integer)
Height of the 1. image.
Default: 512
Suggested values: 128, 256, 512, 1024
Restriction:
Height1 > 0
Width2 (input_control) integer → (integer)
Width of the 2. image.
Default: 512
Suggested values: 128, 256, 512, 1024
Restriction:
Width2 > 0
Height2 (input_control) integer → (integer)
Height of the 2. image.
Default: 512
Suggested values: 128, 256, 512, 1024
Restriction:
Height2 > 0
SubSampling (input_control) number → (integer / real)
Subsampling factor.
Default: 1
List of values: 1, 2, 3, 1.5
Mapping (input_control) string → (string)
Type of mapping.
Default: 'no_map'
List of values: 'bilinear_map', 'nn_map', 'no_map'
CovFMatRect (output_control) number-array → (real)
9x9 covariance matrix of the rectified fundamental matrix.
H1 (output_control) hom_mat2d → (real)
Projective transformation of the 1. image.
H2 (output_control) hom_mat2d → (real)
Projective transformation of the 2. image.
* Rectify an image pair using a map.
get_image_size (Image1, Width1, Height1)
get_image_size (Image2, Width2, Height2)
points_harris (Image1, 3, 1, 0.2, 10000, Row1, Col1)
points_harris (Image2, 3, 1, 0.2, 10000, Row2, Col2)
match_fundamental_matrix_ransac (Image1, Image2, Row1, Col1, Row2, Col2, \
'ncc', 21, 0, 200, 20, 50, 0, 0.9, \
'gold_standard', 0.3, 1, FMatrix, \
CovFMat, Error, Points1, Points2)
gen_binocular_proj_rectification (Map1, Map2, FMatrix, [], Width1, \
Height1, Width2, Height2, 1, \
'bilinear_map', CovFMatRect, H1, H2)
map_image (Image1, Map1, Image1Rect)
map_image (Image2, Map2, Image2Rect)
* Rectify an image pair without using a map.
get_image_size (Image1, Width1, Height1)
get_image_size (Image2, Width2, Height2)
points_harris (Image1, 3, 1, 0.2, 10000, Row1, Col1)
points_harris (Image2, 3, 1, 0.2, 10000, Row2, Col2)
match_fundamental_matrix_ransac (Image1, Image2, Row1, Col1, Row2, Col2, \
'ncc', 21, 0, 200, 20, 50, 0, 0.9, \
'gold_standard', 0.3, 1, FMatrix, \
CovFMat, Error, Points1, Points2)
gen_binocular_proj_rectification (Map1, Map2, FMatrix, [], Width1, \
Height1, Width2, Height2, 1, \
'no_map', CovFMatRect, H1, H2)
* Determine the maximum extent of the two rectified images.
projective_trans_point_2d (H1, [0,0,Height1,Height1], \
[0,Width1,0,Width1], [1,1,1,1], R1, C1, W1)
R1 := int(floor(R1/W1))
C1 := int(floor(C1/W1))
projective_trans_point_2d (H2, [0,0,Height2,Height2], \
[0,Width2,0,Width2], [1,1,1,1], R2, C2, W2)
R2 := int(floor(R2/W2))
C2 := int(floor(C2/W2))
WidthRect := max([C1,C2])
HeightRect := max([R1,R2])
projective_trans_image_size (Image1, Image1Rect, H1, 'bilinear', \
WidthRect, HeightRect, 'false')
projective_trans_image_size (Image2, Image2Rect, H2, 'bilinear', \
WidthRect, HeightRect, 'false')
match_fundamental_matrix_ransac,
vector_to_fundamental_matrix
map_image,
projective_trans_image,
binocular_disparity
gen_binocular_rectification_map
J. Gluckmann and S.K. Nayar: “Rectifying transformations that minimize resampling effects”; IEEE Conference on Computer Vision and Pattern Recognition (CVPR) 2001, vol I, pages 111-117.
3D Metrology