Geodesic Active Regions: A New Framework to Deal with Frame Partition Problems in Computer Vision

Abstract

This paper presents a novel variational framework for dealing with frame partition problems in computer vision by the propagation of curves. This framework integrates boundary- and region-based frame partition modules under a curve-based objective function, which aims at finding a set of minimal length curves that preserve three main properties: (i) they are regular and smooth, (ii) they are attracted by the boundary points (boundary-based information), (iii) and they create a partition that is optimal according to the expected region properties of the different hypotheses (region-based information). The defined objective function is minimized using a gradient descent method. According to the obtained motion equations, the set of initial curves is propagated toward the best partition under the influence of boundary- and region-based forces, and is constrained by a regularity force. The changes of topology are naturally handled thanks to the level set implementation. Furthermore, a coupled multiphase propagation that imposes the idea of mutually exclusive propagating curves and increases the robustness as well as the convergence rate is proposed. The proposed framework has been validated using three important applications in computer vision, the tasks of image and supervised texture segmentation in low-level vision and the task of motion estimation and tracking in motion analysis.