affine_trans_image — Apply an arbitrary affine 2D transformation to images.
affine_trans_image applies an arbitrary affine 2D transformation, i.e., scaling, rotation, translation, and slant (skewing), to the images given in Image and returns the transformed images in ImageAffinTrans. 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 column 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 domain of the input image is ignored, i.e., assumed to be the full rectangle of the image. The domain of the output image is the intersection of the transformed rectangle and the rectangle of the ouput image.
Generally, transformed points will lie between pixel coordinates. Therefore, an appropriate interpolation scheme has to be used. The interpolation can also be used to avoid aliasing effects for scaled images. The quality and speed of the interpolation can be set by the parameter Interpolation:
Nearest-neighbor interpolation: The gray value is determined from the nearest pixel's gray value (possibly low quality, very fast).
Bilinear interpolation. The gray value is determined from the four nearest pixels through bilinear interpolation. If the affine transformation contains a scaling with a scale factor < 1, no smoothing is performed, which may cause severe aliasing effects (medium quality and run time).
Bilinear interpolation. The gray value is determined from the four nearest pixels through bilinear interpolation. If the affine transformation contains a scaling with a scale factor < 1, a kind of mean filter is used to prevent aliasing effects (medium quality and run time).
Bilinear interpolation. The gray value is determined from the four nearest pixels through bilinear interpolation. If the affine transformation contains a scaling with a scale factor < 1, a kind of Gaussian filter is used to prevent aliasing effects (best quality, slow).
In addition, the system parameter 'int_zooming' (see set_system) affects the accuracy of the transformation. If 'int_zooming' is set to 'true', the transformation for byte, int2 and uint2 images is carried out internally using fixed point arithmetic, leading to much shorter execution times. However, the accuracy of the transformed gray values is smaller in this case. For byte images, the differences to the more accurate calculation (using 'int_zooming' = 'false') is typically less than two gray levels. Correspondingly, for int2 and uint2 images, the gray value differences are less than 1/128 times the dynamic gray value range of the image, i.e., they can be as large as 512 gray levels if the entire dynamic range of 16 bit is used. Additionally, if a large scale factor is applied and a large output image is obtained, then undefined gray values at the lower and at the right image border may result. The maximum width B_max of this border of undefined gray values can be estimated as B_max = 0.5 * S * I / 2^15, where S is the scale factor in one dimension and I is the size of the output image in the corresponding dimension. For real images, the parameter 'int_zooming' does not affect the accuracy, since the internal calculations are always done using floating point arithmetic.
The size of the target image can be controlled by the parameter AdaptImageSize: With value 'true' the size will be adapted so that no clipping occurs at the right or lower edge. With value 'false' the target image has the same size as the input image. Note that, independent of AdaptImageSize, the image is always clipped at the left and upper edge, i.e., all image parts that have negative coordinates after the transformation are clipped.
The region of the input image is ignored.
affine_trans_image does not use the HALCON standard coordinate system (with the origin in the center of the first pixel), but instead uses the same coordinate system as in affine_trans_pixel, i.e., the origin lies in the upper left corner of the first pixel. Therefore, applying affine_trans_image corresponds to a chain of transformations (see affine_trans_pixel), which is applied to each point of the image (input and output pixels as homogeneous vectors). As an effect, you might get unexpected results when creating affine transformations based on coordinates that are derived from the image, e.g., by operators like area_center_gray. For example, if you use this operator to calculate the center of gravity of a rotationally symmetric image and then rotate the image around this point using hom_mat2d_rotate, the resulting image 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_image:
hom_mat2d_translate(HomMat2D, 0.5, 0.5, HomMat2DTmp) hom_mat2d_translate_local(HomMat2DTmp, -0.5, -0.5, HomMat2DAdapted) affine_trans_image(Image, ImageAffinTrans, HomMat2DAdapted, 'constant', 'false')
Input transformation matrix.
Type of interpolation.
Default value: 'constant'
List of values: 'bilinear', 'constant', 'nearest_neighbor', 'weighted'
Adaption of size of result image.
Default value: 'false'
List of values: 'false', 'true'
* Reduction of an image (512 x 512 Pixels) by 50%, rotation * by 180 degrees and translation to the upper-left corner: hom_mat2d_identity(Matrix1) hom_mat2d_scale(Matrix1,0.5,0.5,256.0,256.0,Matrix2) hom_mat2d_rotate(Matrix2,3.14,256.0,256.0,Matrix3) hom_mat2d_translate(Matrix3,-128.0,-128.0,Matrix4) affine_trans_image(Image,TransImage,Matrix4,'constant','true') * Enlarging the part of an image in the interactively * chosen rectangular window sector: draw_rectangle2(WindowHandle,L,C,Phi,L1,L2) hom_mat2d_identity(Matrix1) get_system(width,Width) get_system(height,Height) hom_mat2d_translate(Matrix1,Height/2.0-L,Width/2.0-C,Matrix2) hom_mat2d_rotate(Matrix2,3.14-Phi,Height/2.0,Width/2.0,Matrix3) hom_mat2d_scale(Matrix3,Height/(2.0*L2),Width/(2.0*L1), \ Height/2.0,Width/2.0,Matrix4) affine_trans_image(Image,TransImage,Matrix4,'constant','true')
If the matrix HomMat2D represents an affine transformation (i.e., not a projective transformation), affine_trans_image returns 2 (H_MSG_TRUE). If the input is empty the behavior can be set via set_system(::'no_object_result',<Result>:). If necessary, an exception is raised.
hom_mat2d_identity, hom_mat2d_translate, hom_mat2d_rotate, hom_mat2d_scale, hom_mat2d_reflect
affine_trans_image_size, zoom_image_size, zoom_image_factor, mirror_image, rotate_image, affine_trans_region