Convergence behavior of the Active Mask segmentation algorithm

We study the convergence behavior of the Active Mask (AM) framework, originally designed for segmenting punctate image patterns. AM combines the flexibility of traditional active contours, the statistical modeling power of region-growing methods, and the computational efficiency of multiscale and multiresolution methods. Additionally, it achieves experimental convergence to zero-change (fixed-point) configurations, a desirable property for segmentation algorithms. At its a core lies a voting-based distributing function which behaves as a majority cellular automaton. This paper proposes an empirical measure correlated to the convergence behavior of AM, and provides sufficient theoretical conditions on the smoothing filter operator to enforce convergence.