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]).
In this case, 2D affine transformation
can be used to get the transformation parameters between two neighboring images.
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
Assuming that v(w - l) = u(w - l) and v(w) = u(w) by using a suitable positive affine transformation
, we may uniquely select [zeta] [member of] (w - l, w) that serves as a benchmark value for agent u's current consumption (see Figure 1).
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  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.