Apply an arbitrary affine 2D transformation to regions.

affine_trans_region applies an arbitrary affine 2D transformation, i.e., scaling, rotation, translation, and slant (skewing), to the regions given in Region and returns the transformed regions in RegionAffineTrans. The affine transformation is described by the homogeneous transformation matrix given in HomMat2D, which can be created using the operators hom_mat2d_identity, hom_mat2d_scale, hom_mat2d_rotate, hom_mat2d_translate, etc., or be the result of operators like vector_angle_to_rigid.

The components of the homogeneous transformation matrix are interpreted as follows: The row coordinate of the image corresponds to x and the col coordinate corresponds to y of the coordinate system in which the transformation matrix was defined. 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.

The parameter Interpolate determines whether the transformation is to be done by using interpolation internally. This can lead to smoother region boundaries, especially if regions are enlarged. However, the runtime increases drastically.

affine_trans_region in general is not reversible (clipping and discretization during rotation and scaling).

The used coordinate system is the same as in affine_trans_pixel. This means that in fact not HomMat2D is applied but a modified version. Therefore, applying affine_trans_region corresponds to the following chain of transformations, which is applied to each point (Row_i, Col_i) of the region (input and output pixels as homogeneous vectors):

  / RowTrans_i \   / 1 0 -0.5 \              / 1 0 +0.5 \   / Row_i \
  | ColTrans_i | = | 0 1 -0.5 | * HomMat2D * | 0 1 +0.5 | * | Col_i |
  \    1       /   \ 0 0   1  /              \ 0 0   1  /   \  1    /

As an effect, you might get unexpected results when creating affine transformations based on coordinates that are derived from the region, e.g., by operators like area_center. For example, if you use this operator to calculate the center of gravity of a rotationally symmetric region and then rotate the region around this point using hom_mat2d_rotate, the resulting region will not lie on the original one. In such a case, you can compensate this effect by applying the following translations to HomMat2D before using it in affine_trans_region:

  hom_mat2d_translate(HomMat2D, 0.5, 0.5, HomMat2DTmp)
  hom_mat2d_translate_local(HomMat2DTmp, -0.5, -0.5, HomMat2DAdapted)
  affine_trans_region(Region, RegionAffinTrans, HomMat2DAdapted, 'false')

If the matrix HomMat2D represents an affine transformation (i.e., not a projective transformation), affine_trans_region returns 2 (H_MSG_TRUE). The behavior in case of empty input (no regions given) can be set via set_system('no_object_result',<Result>), the behavior in case of an empty input region via set_system('empty_region_result',<Result>), and the behavior in case of an empty result region via set_system('store_empty_region',<true/false>). If necessary, an exception handling is raised.

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

hom_mat2d_identity, hom_mat2d_scale, hom_mat2d_translate, hom_mat2d_invert, hom_mat2d_rotate

select_shape

move_region, mirror_region, zoom_region

affine_trans_image

Foundation