Laplacian Coordinates for Seeded Image Segmentation

Seed-based image segmentation methods have gained much attention lately, mainly due to their good performance in segmenting complex images with little user interaction. Such popularity leveraged the development of many new variations of seed-based image segmentation techniques, which vary greatly regarding mathematical formulation and complexity. Most existing methods in fact rely on complex mathematical formulations that typically do not guarantee unique solution for the segmentation problem while still being prone to be trapped in local minima. In this work we present a novel framework for seed-based image segmentation that is mathematically simple, easy to implement, and guaranteed to produce a unique solution. Moreover, the formulation holds an anisotropic behavior, that is, pixels sharing similar attributes are kept closer to each other while big jumps are naturally imposed on the boundary between image regions, thus ensuring better fitting on object boundaries. We show that the proposed framework outperform state-of-the-art techniques in terms of quantitative quality metrics as well as qualitative visual results.