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
ImageAffineTrans. The affine
transformation is described by the homogeneous transformation matrix
HomMat2D, which can be created using the operators
hom_mat2d_translate, etc., or be
the result of operators like
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 output image.
Generally, transformed points will lie between pixel coordinates.
Therefore, an appropriate interpolation scheme must 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
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).
Bicubic interpolation. The gray value is determined from the nearest pixels through bicubic interpolation. If the affine transformation contains a scaling with a scale factor < 1, no smoothing is performed, which may cause severe aliasing effects (high quality for enlargements, slow).
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 (high 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. When using fixed point arithmetic, the domain of
resulting images can differ as well.
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
of this border of undefined gray values can be
estimated as , 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: If set to 'true', the size will be
adapted so that no clipping occurs at the right or lower edge. If
set to 'false', the target image has the same size as the
input image. Note that, independent of
image is always clipped at the left and upper edge, i.e., all image
parts that have negative coordinates after the transformation are
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
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
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
before using it in
For an explanation of the different 2D coordinate systems used in HALCON, see the introduction of chapter Transformations / 2D Transformations.
→object (byte / int2 / uint2 / real)
→object (byte / int2 / uint2 / real)
Input transformation matrix.
Type of interpolation.
Default value: 'constant'
List of values: 'bicubic', '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: read_image (Image, 'ic0') 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: dev_get_window (WindowHandle) 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),
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.