A Dirichlet Energy Criterion for Graph-Based Image Segmentation

We consider a graph-based approach for image segmentation. We introduce several novel graph construction models which are based on graph-based segmentation criteria extending beyond -- and bridging the gap between -- segmentation approaches based on edges and homogeneous regions alone. The resulting graph is partitioned using a criterion based on the sum of the minimal Dirichlet energies of partition components. We propose an efficient primal-dual method for computing the Dirichlet energy ground state of partition components and a rearrangement algorithm is used to improve graph partitions. The method is applied to a number of example segmentation problems. We demonstrate the graph partitioning method on the five-moons toy problem, and illustrate the various image-based graph constructions, before successfully running a variety of region-, edge-, hybrid, and texture-based image segmentation experiments. Our method seamlessly generalizes region-and edge-based image segmentation to the multi-phase case and can intrinsically deal with image bias as well as more interesting image features such as texture descriptors.