Sampling the Affine Rectangle

The definition for sampling an affine rectangle within an image includes both the definition of an affine rectangle and the number of affine pixels into which it is divided. The number of affine pixels is determined by the number of divisions along the Po-Px and Po-Py axes applied to the rectangle.

The figure below shows each of the affine rectangles shown in Affine rectangles, with the number of x-axis and y-axis divisions.

Affine rectangles and affine pixels

Affine rectangles which represent aligned orthogonal transformations of the input image client coordinate system can be used to create affine samples without the need to perform complicated processing. If the affine rectangle does not, some kind of sampling must be applied to produce a sampled image. The figure below illustrates this problem.

Orthogonal and non-orthogonal affine sampling rectangles

The problem of determining the pixel values when sampling an affine rectangle that is not aligned to the pixel grid of the input image is solved by sampling the pixel grid to produce the sampled image. The Affine Rectangle Sampling tool supports three types of sampling: uninterpolated sampling, bilinear interpolation, and high-precision interpolation.