Vertex characterization via second-order topological derivatives

Abstract

This paper focuses on identifying vertex characteristics in 2D images using topological asymptotic analysis. Vertex characteristics include both the location and the type of the vertex, with the latter defined by the number of lines forming it and the corresponding angles. This problem is crucial for computer vision tasks, such as distinguishing between fore- and background objects in 3D scenes. We compute the second-order topological derivative of a Mumford-Shah type functional with respect to inclusion shapes representing various vertex types. This derivative assigns a likelihood to each pixel that a particular vertex type appears there. Numerical tests demonstrate the effectiveness of the proposed approach.

References in corpus (4)

• Toplogical derivative for nonlinear magnetostatic problem
• Adjoint based methods to compute higher order topological derivatives with an application to elasticity
• Automated computation of topological derivatives with application to nonlinear elasticity and reaction-diffusion problems
• Efficient and accurate separable models for discrete material optimization: A continuous perspective