3D Flux Maximizing Flows

A number of geometric active contour and surface models have been proposed for shape segmentation in the literature. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) so that it clings to the features of interest in an intensity image. Several of these models have been derived, using a variational formulation, as gradient flows which minimize or maximize a particular energy functional. However, in practice these models often fail on images of low contrast or narrow structures. To address this problem we have recently proposed the idea of maximizing the rate of increase of flux of an auxiliary vector field through a curve. This has lead to an interpretation as a 2D gradient flow, which is essentially parameter free. In this paper we extend the analysis to 3D and prove that the form of the gradient flow does not change. We illustrate its potential with level-set based segmentations of blood vessels in a large 3D computed rotational angiography (CRA) data set.