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,

This simplification will reduce necessary number of corresponding points used in stitching images together, and this simplified image transformation is called

affine transformation. In

affine transformation, parallel lines are remaining parallel after it is transformed to new coordinate.

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.