Multi-phase Volume Segmentation with Tetrahedral Mesh

In life science and material science, it is often desirable to segment a volumetric data set in such a way that multiple materials (phases) are segmented and a tetrahedral mesh representation is obtained for each segment for downstream applications. Unfortunately, obtaining a mesh, typically from CT or MRI scan, is challenging, especially in 3D. This paper proposes an novel approach for volume segmentation using a tetrahedral mesh. Our method employs a deformable model that minimizes the Mumford-Shah energy function. We apply our method to several CT data sets in order to demonstrate its advantages: multi-phase support, robustness to noise, and adaptive resolution outputs. Our method is based on the Deformable Simplicial Complex (DSC) method for tracking deformable interfaces which is designed specifically to deal with topology changes.