Transformation Of Images By Radial Basis Functions With Varying Centre Point

In this paper we modify radial basis functions enabling mapping of images by preserving a specific segment on the transforming space and aligning given surfaces on images. Our mapping functions are derived from the concept of the classical radial basis functions overcoming some of their shortcomings. Unlike the classical functions which are restricted to point set of landmarks only, our functions are able to handle surface, contour, and point landmarks. The criterion for our functions is that they must be continuous and provide one-to-one mapping. We align the given landmarks with our functions by shifting points along rays normal to the given specific surface. This approach allows transforming brain images preserving positions of the anterior and posterior commissures (AC-PC) as well as the midsagittal plane. The proposed method can be useful in brain warping for analysis of volumetric and two-dimensional scans