Convergence analysis of multidimensional parametric deformable models

摘要

Deformable models are mathematical tools, used in image processing to analyze the shape and movement of real objects due to their ability to emulate physical features such as elasticity, stiffness, mass and damping. In the original approach, parametric models are obtained from the minimization of an energy functional by means of the Euler–Lagrange equation. Finite element method is used for spatial discretization. The shape and position of the model is governed by a second-order partial differential equation system, which is obtained by applying the calculus of variations. Subsequent work propose a model formulation defined completely in the frequency domain, by translating the PDE system into the Fourier domain. This new approach offers important computational efficiency and an easier generalization to multidimensional models, since each spectral component of the model is ruled by an independent PDE. This paper reviews the frequency based formulation and analyzes the convergence and stability of these multidimensional parametric deformable models. Results show that the accuracy and speed of convergence depend on the dynamic parameters of the system and the spectrum of the data to be characterized, providing a procedure to speed-up the convergence by an appropriate choice of these parameters.