Comparison of Concave Point Detection Methods for Overlapping Convex Objects Segmentation

Segmentation of overlapping convex objects has gained a lot of attention in numerous biomedical and industrial applications. A partial overlap between two or more convex shape objects leads to a shape with concave edge points that correspond to the intersections of the object boundaries. Therefore, it is a common practice to utilize these concave points to segment the contours of overlapping objects. Although a concave point has a clear mathematical definition, the task of concave point detection (CPD) from noisy digital images with limited resolution is far from trivial. This work provides the first comprehensive comparison of CPD methods with both synthetic and real world data. We further propose a modification to an earlier CPD method and show that it outperforms the other methods. Finally, we demonstrate that by using the enhanced concave points we obtain segmentation results that outperform the state-of-the-art in the task of partially overlapping convex object segmentation.