Algebraic Topology-Based Image Deformation: A Unified Model

Abstract

In this paper, a new method for image deformation is presented. It is based upon decomposition of the deformation problem into basic physical laws. Unlike other methods that solve a differential or an energetic formulation of the physical laws involved, we encode the basic laws using computational algebraic topology. Conservative laws are translated into exact global values and constitutive laws are judiciously approximated. In order to illustrate the effectiveness of our model, we deal with both small- and large-scale deformation, utilizing elasticity theory and the viscous fluid model, respectively. The proposed approach is validated through a series of tests on optical flow estimation and image registration.