Multi-phase image segmentation with the adaptive deformable mesh

This paper proposes a method for image segmentation using a deformable triangle mesh in the image domain. We define a piecewise constant function by labeling the mesh triangles with different phases, each representing a segment of an image. Our method finds the optimal mesh configuration and triangle labeling that minimize the piecewise constant Mumford-Shah functional. Contributions of this paper include a force model that moves mesh vertices towards the solution, and an adaptivity model that further adapts the mesh by introducing or removing vertices. The results demonstrate the advantages of our method over traditional methods like snakes and level set. Our approach supports multi-phase segmentation incurring no particular overhead. Furthermore, the use of an adaptive mesh facilitates accurate segmentation with a very compact representation. The biggest challenge of deformable meshes, changes to the topology of the segments, is handled by employing Deformable Simplical Complex (DSC), a method for explicit interface tracking.