Redistancing Dynamics for Vector-Valued Multilabel Segmentation with Costly Fidelity: Grain Identification in Polycrystal Images

A novel numerical method for multilabel segmentation of vector-valued images is presented. The algorithm seeks minimizers for a generalization of the piecewise-constant Mumford---Shah energy and is particularly appropriate for energies with a fitting (or fidelity) term that is computationally expensive to evaluate. The framework for the algorithm is the standard alternating-minimization scheme in which the update of the partition is alternated with the update of the vector-valued constants associated with each part of the segmentation. The update of the partition is based on the distance function-based diffusion-generated motion algorithms for mean curvature flow. The update of the vector-valued constants is based on an Augmented Lagrangian method. The scheme automatically chooses the appropriate number of segments in the partition. It is initialized with a partition of many more segments than are expected to be necessary. Adjacent segmentations of the partition are merged when energetically advantageous. The utility of the algorithm is demonstrated in the context of atomic-resolution polycrystalline image segmentation.