Bandwidth reducing Parameterization

A method for parameterization of closed 2 dimensional contours is presented in this report. The introduced method reduces the dimensionality of the parameter space taking care of the nature of the shape curvature. The description parameters are evaluated using a fast optimization algorithm. Three different optimization methods were implemented, but only a Gauss-Newton method was fast enough for practical use. Some simple objects were parameterized and the results show that the parameter space is in fact concentrated in the part of larger curvature. Introduction A frequently encountered problem in medical imaging is that of finding a transformation which maps the shape resp. boundary of an object onto an other. In general two shapes represent different examples from the same class of object (e.g. two corpus callosi) and the mapping function is a non-rigid transformation. There are numerous techniques proposed in the literature to solve such correspondence problems. The methods can be intuitively split up into three main classes described in the next few sections. 1. Pairwise Correspondence The classical or intuitive idea of correspondence is the direct comparison of two shapes. A correspondence is found by optimizing a goalfunction that measures the similarity between a pair of shapes. For measuring similarity different features can be used: e.g. landmarks,