An efficient iterative thresholding method for image segmentation
This work addresses image segmentation for computer vision applications, but it appears incremental as it builds on existing Mumford-Shah functional approaches with a new iterative optimization method.
The authors tackled the problem of multi-phase image segmentation by proposing an efficient iterative thresholding method that minimizes a piecewise constant Mumford-Shah functional, achieving optimal complexity of O(N log N) per iteration and demonstrating energy decay properties.
We proposed an efficient iterative thresholding method for multi-phase image segmentation. The algorithm is based on minimizing piecewise constant Mumford-Shah functional in which the contour length (or perimeter) is approximated by a non-local multi-phase energy. The minimization problem is solved by an iterative method. Each iteration consists of computing simple convolutions followed by a thresholding step. The algorithm is easy to implement and has the optimal complexity $O(N \log N)$ per iteration. We also show that the iterative algorithm has the total energy decaying property. We present some numerical results to show the efficiency of our method.