Bounded Labeling Function for Global Segmentation of Multi-part Objects with Geometric Constraints

The inclusion of shape and appearance priors have proven useful for obtaining more accurate and plausible segmentations, especially for complex objects with multiple parts. In this paper, we augment the popular Mum ford-Shah model to incorporate two important geometrical constraints, termed containment and detachment, between different regions with a specified minimum distance between their boundaries. Our method is able to handle multiple instances of multi-part objects defined by these geometrical constraints using a single labeling function while maintaining global optimality. We demonstrate the utility and advantages of these two constraints and show that the proposed convex continuous method is superior to other state-of-the-art methods, including its discrete counterpart, in terms of memory usage, and metrication errors.