A Variational Approach to the Evolution of Radial Basis Functions for Image Segmentation

In this paper we derive differential equations for evolving radial basis functions (RBFs) to solve segmentation problems. The differential equations result from applying variational calculus to energy functionals designed for image segmentation. Our methodology supports evolution of all parameters of each RBF, including its position, weight, orientation, and anisotropy, if present. Our framework is general and can be applied to numerous RBF interpolants. The resulting approach retains some of the ideal features of implicit active contours, like topological adaptivity, while requiring low storage overhead due to the sparsity of our representation, which is an unstructured list of RBFs. We present the theory behind our technique and demonstrate its usefulness for image segmentation.