Tree Shape Priors with Connectivity Constraints Using Convex Relaxation on General Graphs

Abstract

In this work we propose a novel method to include a connectivity prior into image segmentation that is based on a binary labeling of a directed graph, in this case a geodesic shortest path tree. Specifically we make two contributions: First, we construct a geodesic shortest path tree with a distance measure that is related to the image data and the bending energy of each path in the tree. Second, we include a connectivity prior in our segmentation model, that allows to segment not only a single elongated structure, but instead a whole connected branching tree. Because both our segmentation model and the connectivity constraint are convex a global optimal solution can be found. To this end, we generalize a recent primal-dual algorithm for continuous convex optimization to an arbitrary graph structure. To validate our method we present results on data from medical imaging in angiography and retinal blood vessel segmentation.

Additional details