PALMS Image Partitioning - A New Parallel Algorithm for the Piecewise Affine-Linear Mumford-Shah Model

Abstract

We present a method for computing approximate solutions of the piecewise affine-linear Mumford-Shah model - PALMS Image Partitioning. The piecewise affine-linear Mumford-Shah model is a variational approach to image partitioning. The underlying algorithm is based on a splitting approach using ADMM. The emerging subproblems are solved exactly and efficiently. We detail the solver for these subproblems which is based on dynamic programming and incorporates an acceleration strategy. The subproblems are solved in parallel in our implementation to provide an efficient overall algorithm. We conduct extended studies on the effects of the algorithmic parameters. Thereby, the implemented algorithm is further optimized w.r.t. runtime and efficiency. Finally, we underpin the efficiency of the algorithm by a comparison with the state-of-the-art which shows that the presented algorithm has lower computation times and yields lower mean functional values.