hom_vector_to_proj_hom_mat2dT_hom_vector_to_proj_hom_mat2dHomVectorToProjHomMat2dHomVectorToProjHomMat2d (Operator)

Name

hom_vector_to_proj_hom_mat2dT_hom_vector_to_proj_hom_mat2dHomVectorToProjHomMat2dHomVectorToProjHomMat2d — Compute a homogeneous transformation matrix using given point correspondences.

Signature

Description

hom_vector_to_proj_hom_mat2dhom_vector_to_proj_hom_mat2dHomVectorToProjHomMat2dHomVectorToProjHomMat2dHomVectorToProjHomMat2d determines the homogeneous projective transformation matrix HomMat2DHomMat2DHomMat2DHomMat2DhomMat2D that optimally fulfills the following equations given by at least 4 point correspondences

In contrast to vector_to_proj_hom_mat2dvector_to_proj_hom_mat2dVectorToProjHomMat2dVectorToProjHomMat2dVectorToProjHomMat2d, hom_vector_to_proj_hom_mat2dhom_vector_to_proj_hom_mat2dHomVectorToProjHomMat2dHomVectorToProjHomMat2dHomVectorToProjHomMat2d uses homogeneous coordinates for the points, and hence points at infinity (PwPwPwPwpw = 0 or QwQwQwQwqw = 0) can be used to determine the transformation. If finite points are used, typically PwPwPwPwpw and QwQwQwQwqw are set to 1. In this case, vector_to_proj_hom_mat2dvector_to_proj_hom_mat2dVectorToProjHomMat2dVectorToProjHomMat2dVectorToProjHomMat2d can also be used. vector_to_proj_hom_mat2dvector_to_proj_hom_mat2dVectorToProjHomMat2dVectorToProjHomMat2dVectorToProjHomMat2d has the advantage that one additional optimization method can be used and that the covariances of the points can be taken into account. If the correspondence between the points has not been determined, proj_match_points_ransacproj_match_points_ransacProjMatchPointsRansacProjMatchPointsRansacProjMatchPointsRansac should be used to determine the correspondence as well as the transformation.

If the points to transform are specified in standard image coordinates, their row coordinates must be passed in PxPxPxPxpx and their column coordinates in PyPyPyPypy. This is necessary to obtain a right-handed coordinate system for the image. In particular, this assures that rotations are performed in the correct direction. Note that the (x,y) order of the matrices quite naturally corresponds to the usual (row,column) order for coordinates in the image.

Attention

It should be noted that homogeneous transformation matrices refer to a general right-handed mathematical coordinate system. If a homogeneous transformation matrix is used to transform images, regions, XLD contours, or any other data that has been extracted from images, the row coordinates of the transformation must be passed in the x coordinates, while the column coordinates must be passed in the y coordinates. Consequently, the order of passing row and column coordinates follows the usual order (RowRowRowRowrow,ColumnColumnColumnColumncolumn). This convention is essential to obtain a right-handed coordinate system for the transformation of iconic data, and consequently to ensure in particular that rotations are performed in the correct mathematical direction.

Furthermore, it should be noted that if a homogeneous transformation matrix is used to transform images, regions, XLD contours, or any other data that has been extracted from images, it is assumed that the origin of the coordinate system of the homogeneous transformation matrix lies in the upper left corner of a pixel. The image processing operators that return point coordinates, however, assume a coordinate system in which the origin lies in the center of a pixel. Therefore, to obtain a consistent homogeneous transformation matrix, 0.5 must be added to the point coordinates before computing the transformation.

Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Multithreading scope: global (may be called from any thread).
• Processed without parallelization.

Parameters

Possible Predecessors

proj_match_points_ransacproj_match_points_ransacProjMatchPointsRansacProjMatchPointsRansacProjMatchPointsRansac, proj_match_points_ransac_guidedproj_match_points_ransac_guidedProjMatchPointsRansacGuidedProjMatchPointsRansacGuidedProjMatchPointsRansacGuided, points_foerstnerpoints_foerstnerPointsFoerstnerPointsFoerstnerPointsFoerstner, points_harrispoints_harrisPointsHarrisPointsHarrisPointsHarris

Possible Successors

projective_trans_imageprojective_trans_imageProjectiveTransImageProjectiveTransImageProjectiveTransImage, projective_trans_image_sizeprojective_trans_image_sizeProjectiveTransImageSizeProjectiveTransImageSizeProjectiveTransImageSize, projective_trans_regionprojective_trans_regionProjectiveTransRegionProjectiveTransRegionProjectiveTransRegion, projective_trans_contour_xldprojective_trans_contour_xldProjectiveTransContourXldProjectiveTransContourXldProjectiveTransContourXld, projective_trans_point_2dprojective_trans_point_2dProjectiveTransPoint2dProjectiveTransPoint2dProjectiveTransPoint2d, projective_trans_pixelprojective_trans_pixelProjectiveTransPixelProjectiveTransPixelProjectiveTransPixel

Alternatives

vector_to_proj_hom_mat2dvector_to_proj_hom_mat2dVectorToProjHomMat2dVectorToProjHomMat2dVectorToProjHomMat2d, proj_match_points_ransacproj_match_points_ransacProjMatchPointsRansacProjMatchPointsRansacProjMatchPointsRansac, proj_match_points_ransac_guidedproj_match_points_ransac_guidedProjMatchPointsRansacGuidedProjMatchPointsRansacGuidedProjMatchPointsRansacGuided

References

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.

Module

Calibration