Affine transformation preserves points, straight lines, and planes.

For any asymmetric claims problem, we can always find a positive

affine transformation to transform it into a new claims problem, in which the two players' claims in the new problem are symmetric.

The fine registration using ICP algorithm aims at finding a set of

affine transformation matrixes such that the mean square error (MSE) of the distance between the corresponding nodes of the laser scan crown and the coarsely registered CT crown models achieve minimum after the

affine transformations.

Section 3 briefly repeats the

affine transformation of van der Pauw and specifies it for (100)-planes of cubic crystals, like silicon.

The

affine transformation technique is typically used to correct geometric distortions or deformations that occur owing to nonideal camera angles.

Five pairs of point are enough to calculate the parameters of

affine transformation. However, we have more feature pairs than that.

Rainbow(17, 13, 13) is computed via invoking

affine transformation, polynomial evaluation, and solving systems of linear equations in GF([([2.sup.4]).sup.2]).

We performed greedy SyN mapping driven by CC and initialized by MI with an

affine transformation. A four-level image pyramid was used to compute MI, and a five-level image pyramid was used to compute CC.

By the multithread ICP, we can calculate the transformation matrix and guide the

affine transformation. The process of applying an affine transform to a point in 3D space is shown in the following formula:

This would imply that to prove the self-similarity of a compact set X, it is necessary to evaluate all partitions of X and find in everyone of them an equivalence class which is not an

affine transformation of X.

The image augmentation contained one of several transformation techniques including

affine transformation, perspective transformation, and simple image rotations.

A range-domain mapping consists of three operations [3] sequentially on each domain block of size 2N x 2N: (1) spatial contraction of the domain block ([D.sub.j]) by downsampling or averaging the four neighboring pixels of disjoint group forming a block ([D.sub.cj]) of size N x N; (2) taking 8 geometrical transformations of each block which includes 4 rotations with 90 degrees and 4 mirror reflections; (3) for each geometrical transformed block perform contractive

affine transformation on the gray-scale values and select the parameters which give lowest MSE.

We first construct a new object function through applying directly a homogeneous

affine transformation between pre- and post-compression data.