Work

Vertex Characterization Via Second-Order Topological Derivatives

Year: 2025

Type: article

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.

Source: Journal of Mathematical Imaging and Vision

DOI: 10.1007/s10851-025-01269-3

Authors: Peter Gangl, Bochra Mejri, Otmar Scherzer

Institutions: Johann Radon Institute for Computational and Applied Mathematics, University of Vienna

Language: English

Topic: Digital Image Processing Techniques

Subfield: Computer Vision and Pattern Recognition

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090