Compute a projective transformation matrix between two images by finding correspondences between points.

Given a set of coordinates of characteristic points (Cols1,Rows1) and (Cols2,Rows2) in both input images Image1 and Image2, proj_match_points_ransac automatically determines corresponding points and the homogeneous projective transformation matrix HomMat2D that best transforms the corresponding points from the different images into each other. The characteristic points can, for example, be extracted with points_foerstner or points_harris.

The transformation is determined in two steps: First, gray value correlations of mask windows around the input points in the first and the second image are determined and an initial matching between them is generated using the similarity of the windows in both images.

The size of the mask windows is MaskSize x MaskSize. Three metrics for the correlation can be selected. If GrayMatchMethod has the value 'ssd', the sum of the squared gray value differences is used, 'sad' means the sum of absolute differences, and 'ncc' is the normalized cross correlation. This metric is minimized ('ssd', 'sad') or maximized ('ncc') over all possible point pairs. A thus found matching is only accepted if the value of the metric is below the value of MatchThreshold ('ssd', 'sad') or above that value ('ncc').

To increase the algorithm's performance, the search area for the matchings can be limited. Only points within a window of 2*RowTolerance x 2*ColTolerance points are considered. The offset of the center of the search window in the second image with respect to the position of the current point in the first image is given by RowMove and ColMove.

If the transformation contains a rotation, i.e., if the first image is rotated with respect to the second image, the parameter Rotation may contain an estimate for the rotation angle or an angle interval in radians. A good guess will increase the quality of the gray value matching. If the actual rotation differs too much from the specified estimate the matching will typically fail. The larger the given interval, the slower the operator is since the entire algorithm is run for all relevant angles within the interval.

Once the initial matching is complete, a randomized search algorithm (RANSAC) is used to determine the transformation matrix HomMat2D. It tries to find the matrix that is consistent with a maximum number of correspondences. For a point to be accepted, its distance from the coordinates predicted by the transformation must not exceed the threshold DistanceThreshold.

Once a choice has been made, the matrix is further optimized using all consistent points. For this optimization, the EstimationMethod can be chosen to either be the slow but mathematically optimal 'gold_standard' method or the faster 'normalized_dlt'. Here, the algorithms of vector_to_proj_hom_mat2d are used.

Point pairs that still violate the consistency condition for the final transformation are dropped, the matched points are returned as control values. Points1 contains the indices of the matched input points from the first image, Points2 contains the indices of the corresponding points in the second image.

The parameter RandSeed can be used to control the randomized nature of the RANSAC algorithm, and hence to obtain reproducible results. If RandSeed is set to a positive number, the operator yields the same result on every call with the same parameters because the internally used random number generator is initialized with the seed value. If RandSeed = 0, the random number generator is initialized with the current time. Hence, the results may not be reproducible in this case.

proj_match_points_ransac is reentrant and automatically parallelized (on tuple level).

points_foerstner, points_harris

projective_trans_image, projective_trans_image_size, projective_trans_region, projective_trans_contour_xld, projective_trans_point_2d, projective_trans_pixel

hom_vector_to_proj_hom_mat2d, vector_to_proj_hom_mat2d

Richard Hartley, Andrew Zisserman: ``Multiple View Geometry in Computer Vision''; Cambridge University Press, Cambridge; 2000.

Olivier Faugeras, Quang-Tuan Luong: ``The Geometry of Multiple Images: The Laws That Govern the Formation of Multiple Images of a Scene and Some of Their Applications''; MIT Press, Cambridge, MA; 2001.

Matching