After a brief survey on the parametric deformable models, we develop
an iterative method based on the finite difference schemes in order to obtain energy-minimizing snakes. We estimate the approximation error, the residue, and the truncature error related to the corresponding algorithm,
then we discuss its convergence, consistency, and stability. Some aspects
regarding the prosthetic sugical methods that implement the above numerical methods are also pointed out.
Abstract. This paper is devoted to give estimates involving the norm for classes of projection operators (used, for example, in the theory of deformable models) and to obtain theorems concerning the convergence or the superdense unbounded divergence corresponding to these operators.Mathematics subject classification (2000): 41A10, 41A17.
This paper is devoted to the mathematical approaches and software implementations in the domain of deformable models. Based on a general result of calculus of variations, we deduce the Euler-Lagrange-Poisson (ELP) Equation associated to the 2D deformable models, with relevant applications in medical imaging; the optimal solution of these models is found among the solutions (named extremals) of ELP Equation. Then, we perform a discretization of ELP Equation, using the method of finite differences, in order to obtain an approximation of the optimal solution for static and dynamic deformable models; this discrete solution is given by a matriceal system, which involves the so-called stiffness matrix. Finally, based on the good quality of the results obtained with this method, providing the formal definitions required by the image processing standardization, we extend the set of standard image processing operators with the "snake operator", taking into account its performances in the domain of feature extraction and object recognition in medical imaging.
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