The iterative convolution-thresholding method (ICTM) for image segmentation
This provides a more efficient and robust approach for image segmentation tasks, though it appears incremental as it builds on existing variational models.
The paper tackles the problem of minimizing variational models for image segmentation by proposing the iterative convolution-thresholding method (ICTM), which simplifies the process by representing interfaces with characteristic functions and using heat kernel convolution, resulting in a method that is simple, efficient, and energy-decaying.
In this paper, we propose a novel iterative convolution-thresholding method (ICTM) that is applicable to a range of variational models for image segmentation. A variational model usually minimizes an energy functional consisting of a fidelity term and a regularization term. In the ICTM, the interface between two different segment domains is implicitly represented by their characteristic functions. The fidelity term is then usually written as a linear functional of the characteristic functions and the regularized 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 is simple, efficient and enjoys the energy-decaying property. Numerical experiments show that the method is easy to implement, robust and applicable to various image segmentation models.