match_fundamental_matrix_ransacT_match_fundamental_matrix_ransacMatchFundamentalMatrixRansacMatchFundamentalMatrixRansacmatch_fundamental_matrix_ransac — Compute the fundamental matrix for a pair of stereo images by
automatically finding correspondences between image
points.
Note the column/row ordering in the point coordinates: because the
fundamental matrix encodes the projective relation between two
stereo images embedded in 3D space, the x/y notation has to be
compliant with the camera coordinate system. So, (x,y) coordinates
correspond to (column,row) pairs.
The matching process is based on characteristic points, which can be
extracted with point operators like points_foerstnerpoints_foerstnerPointsFoerstnerPointsFoerstnerPointsFoerstnerpoints_foerstner or
points_harrispoints_harrisPointsHarrisPointsHarrisPointsHarrispoints_harris.
The matching itself is carried out 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.
Then, the RANSAC algorithm is applied to find the fundamental matrix
that maximizes the number of correspondences under the epipolar constraint.
To increase the speed of the algorithm the search area for the
matching operations can be limited. Only points within a window of 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
RowMoveRowMoveRowMoveRowMoverowMoverow_move and ColMoveColMoveColMoveColMovecolMovecol_move.
If the second camera is
rotated around the optical axis with respect to the first camera
the parameter RotationRotationRotationRotationrotationrotation 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. In this case, an angle interval should be
specified and RotationRotationRotationRotationrotationrotation is a tuple with two elements. The
larger the given interval the slower the operator is since the
RANSAC algorithm is run over all angle increments within the
interval.
The parameter EstimationMethodEstimationMethodEstimationMethodEstimationMethodestimationMethodestimation_method decides whether the relative
orientation between the cameras is of a special type and which algorithm is
to be applied for its computation.
If EstimationMethodEstimationMethodEstimationMethodEstimationMethodestimationMethodestimation_method is either 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" or
'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard" the relative orientation is arbitrary.
If left and right camera are identical and the relative orientation between
them is a pure translation then choose EstimationMethodEstimationMethodEstimationMethodEstimationMethodestimationMethodestimation_method equal to
'trans_normalized_dlt'"trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt" or 'trans_gold_standard'"trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard".
The typical application for this special motion case is the
scenario of a single fixed camera looking onto a moving conveyor belt.
In order to get a unique solution in the correspondence problem the minimum
required number of corresponding points is eight in the general case and
three in the special, translational case.
The fundamental matrix is computed by a linear algorithm if
'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" or 'trans_normalized_dlt'"trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt" is chosen.
With 'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard" or 'trans_gold_standard'"trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard"
the algorithm gives a statistically optimal result, and returns as well the
covariance of the fundamental matrix CovFMatCovFMatCovFMatCovFMatcovFMatcov_fmat.
Here, 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt" and 'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard" stand for
direct-linear-transformation and gold-standard-algorithm respectively.
The value ErrorErrorErrorErrorerrorerror indicates the overall quality of the estimation
procedure and is the mean Euclidean distance in pixels between the
points and their corresponding epipolar lines.
List of values:
'gold_standard'"gold_standard""gold_standard""gold_standard""gold_standard""gold_standard", 'normalized_dlt'"normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt""normalized_dlt", 'trans_gold_standard'"trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard""trans_gold_standard", 'trans_normalized_dlt'"trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt""trans_normalized_dlt"
DistanceThresholdDistanceThresholdDistanceThresholdDistanceThresholddistanceThresholddistance_threshold (input_control) number →HTupleUnion[float, int]HTupleHtuple (real / integer) (double / int / long) (double / Hlong) (double / Hlong)
Maximal deviation of a point from its epipolar line.
Default:
1
Value range:
0.5
≤
DistanceThresholdDistanceThresholdDistanceThresholdDistanceThresholddistanceThresholddistance_threshold
≤
5
Richard Hartley, Andrew Zisserman: “Multiple View Geometry in
Computer Vision”; Cambridge University Press, Cambridge; 2003.
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.