Multi-object segmentation approach based on topological derivative and level set method

In this paper we propose a segmentation approach that applies the topological derivative as a pre-processing step. The obtained result is used for initializing a Level Set model in order to get the final result. First, the method uses a low-pass filter and the topological derivative to get a rough definition of the boundaries of interest. Then, morphological operators are applied to fill holes and discard artifacts. Next, a Level Set model is used to improve the result giving the desired approximation. We test the pipeline for cell image segmentation. Finally, we provide a full mathematical justification for the topological asymptotic expansion.