The iterative convolution–thresholding method (ICTM) for image segmentation. (October 2022) - Wang, Dong; Wang, Xiao-Ping
Highlights: A new method is proposed for minimizing general objective functionals for image segmentation. The method is based on the representation of segments via characteristic functions. The method simply alternates two steps: convolution and thresholding. The algorithm has the optimal complexity O(NlogN) per iteration and fast convergence. The monotone decay of the objective functional is rigorously proved. Abstract: Variational methods, which have been tremendously successful in image segmentation, work by minimizing a given objective functional. The objective functional usually consists of a fidelity term and a regularization term. Because objective functionals may vary from different types of images, developing an efficient, simple, and general numerical method to minimize them has become increasingly vital. However, many existing methods are model-based, converge relatively slowly, or involve complicated techniques. In this paper, we develop a novel iterative convolution–thresholding method (ICTM) that is simple, efficient, and applicable to a wide range of variational models for image segmentation. In ICTM, the interface between two different segment domains is implicitly represented by the characteristic functions of domains. The fidelity term is usually written into a linear functional of the characteristic functions, and the regularization term is approximated by a functional of characteristic functions in terms of heat kernel convolution. This allows us to design an iterative convolution–thresholding method to minimize the approximate energy. The method has the energy-decaying property, and thus the unconditional stability is theoretically guaranteed. Numerical experiments show that the method is simple, easy to implement, robust, and applicable to various image segmentation models.