Level set framework with transcendental constraint for robust and fast image segmentation

Though image segmentation models are plentiful and have many applications nowadays, it can be difficult to segment images with complex boundaries and serious intensity inhomogeneity. To some extent, the region-scalable fitting energy model can segment images suffering from intensity inhomogeneity since it considers image intensity as a function, but it relies on initial conditions dramatically. Nowadays, prior knowledge has been widely applied in image segmentation models, which can integrate automatic method and experts experience in one robust and fast segmentation model. In this paper we present a new model that can segment various images accurately by taking the advantages of the region-scalable fitting energy model and the advanced transcendental constraint from artificial experience. The proposed energy functional consists of a smooth length term, a target image data term and a transcendental constraint term. The transcendental constraint term plays a key role in the proposed model, which not only gives the accurate segmentation results but also provides us the chance to carry out the parallel computation. In the proposed-parallel model, the efficiency is improved a lot and the results become more precise compared with other methods. The split Bregman method is applied to minimize the energy functional. Furthermore, we present the convergence analysis and the time complexity analysis of our algorithm. Multiple experimental results and comparisons including parameters sensitivity discussion are shown to demonstrate the superiority of the proposed model such as high accuracy, robustness and efficiency.