Edge Potential Functions (EPF) and Genetic Algorithms (GA) for Edge-Based Matching of Visual Objects

Edges are known to be a semantically rich representation of the contents of a digital image. Nevertheless, their use in practical applications is sometimes limited by computation and complexity constraints. In this paper, a new approach is presented that addresses the problem of matching visual objects in digital images by combining the concept of Edge Potential Functions (EPF) with a powerful matching tool based on Genetic Algorithms (GA). EPFs can be easily calculated starting from an edge map and provide a kind of attractive pattern for a matching contour, which is conveniently exploited by GAs. Several tests were performed in the framework of different image matching applications. The results achieved clearly outline the potential of the proposed method as compared to state of the art methodologies. (c) 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

Uniform ball property and existence of optimal shapes for a wide class of geometric functionals

In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the exist ence of a $C^{1,1}$-regular minimizer for general geometric functionals and cons traints involving the first- and second-order properties of surfaces, such as in $\mathbb{R}^{3}$ problems of the form: $$\inf \int_{\partial \Omega} j_0 [ \mathbf{x},\mathbf{n}(\mathbf{x}) ] dA (\mathbf{x}) + \int_{\partial \Omega} j_1 [ \mathbf{x},\mathbf{n}(\mathbf{x}),H(\mathbf{x}) ] dA (\mathbf{x}) + \int_{\partial \Omega} j_2 [\mathbf{x},\mathbf{n}(\mathbf{x}),K(\mathbf{x})] dA (\mathbf{x}),$$ where $\mathbf{n}$, $H$, and $K$ respectively denotes the normal, the scalar mea n curvature and the Gaussian curvature. We gives some various applications in th e modelling of red blood cells such as the Canham-Helfrich energy and the Willmo re functional