# affine transformation

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 Noun 1 affine transformation - (mathematics) a transformation that is a combination of single transformations such as translation or rotation or reflection on an axismath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementtransformation - (mathematics) a function that changes the position or direction of the axes of a coordinate system
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For analysis, head motion correction is done, the functional images are co-registered to structural images using a six-parameter rigid-body transformation and a 12-parameter affine transformation (8).
Rotation is a case of an affine transformation, and it is widely used in image processing (for example image registration).
* Scale Invariance: If T:[R.sup.2] [right arrow] [R.sup.2] represents a positive affine transformation, that is, T(x, y) = ([r.sub.1]x + [s.sub.1], [r.sub.2]y + [s.sub.2]) for some positive constant [r.sub.i] and some constant [s.sub.i], then we have g([c.sub.1]; [c.sub.2], E, T([u.sub.1], [u.sub.2])) = g([c.sub.1], [c.sub.2], E, [u.sub.1], [u.sub.2]) for any ([c.sub.1], [c.sub.2], E, [u.sub.1], [u.sub.2]) [member of] C.
The aim of coarse registration is to find an affine transformation matrix such that the two body-fitted coordinate systems can be aligned after the affine transformation.
Thereby we use the affine transformation of van der Pauw [8] in order to replace the original device having anisotropic resistivity by an equivalent device having isotropic conductivity.
The procedure used for the preprocessing comprised the following steps: (1) conversion of RGB images to grayscale, (2) affine transformation, (3) extraction of the region of interest (ROI), and (4) histogram equalization.
As an affine transformation is a nonsingular linear transformation followed by a translation, we regard the mapping relationship between two images as an affine transformation.
The construction of Rainbow includes affine transformation [L.sub.1], central map transformation F, and affine transformation [L.sub.2]; that is,
In the first step, reference image and target image were globally aligned using affine transformation. Region of interest was selected and a mesh of control points was initialized over the region using the affine transformation.
Thus, the affine transformation is optimized with respect to translation, rotation, scaling, and shearing with a mixture of 12 parameters.
Generally, ICP could be adopted on the input feature point clouds to calculate the parameters of an affine transformation matrix.

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