The Influence of Object Shape on the Convergence of Active Contour Models for Image Segmentation

In this article, we investigate the relationship between the range of optimal parameters of active contour models and the shape of the target object. We focus on the weights of the internal and external energy terms of the snakes functional. Our contributions are 3-fold. First, we propose a normalization step that brings the search space for optimal parameters into a bounded range. Secondly, we perform a systematic study of the behaviour of active contour models for all possible settings of their parameters and on a large set of synthetic geometric shapes. We introduce the concept of stability diagrams as a novel approach for assessing the stability of active contour models given a range of parameter values. Finally, we show that over a series of evolving shapes the region of the parameter domain that corresponds to suitable coefficients for segmentation, hereinafter referred to as feasible solution region, follows a predictable trend. Using shape diagrams as a metric for characterizing shapes quantitatively, we are able to correlate the shape of the objects to segment with the location and extent of the feasible solution region in the parameter domain.