Flux Maximizing Geometric Flows

Abstract

Several geometric active contour models have been proposed for segmentation in computer vision. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recent variations on this theme take into account properties of enclosed regions and allow for multiple curves or surfaces to be simultaneously represented. However, it is not clear how to apply these techniques to images of low contrast elongated structures, such as those of blood vessels. To address this problem we derive the gradient flow which maximizes the rate of increase of flux of an auxiliary vector field through a curve or surface. The calculation leads to a simple and elegant interpretation which is essentially parameter free. We illustrate its advantages with level-set based segmentations of 2D and 3D MRA images of blood vessels.