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

Article type: Research Article

Authors: Machado, D.A. | Giraldi, G.^{; *} | Novotny, A.A.

Affiliations: Laboratório Nacional de Computação Científica, Petrópolis, RJ, Brazil

Correspondence: [*] Corresponding author: Dr. G. Giraldi, National Laboratory for Scientific Computing, Petropolis, RJ, Brazil. E-mail: [email protected].

Abstract: 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.

Keywords: Image analysis, boundary extraction, topological derivative, Level Set Method

DOI: 10.3233/ICA-2011-0378

Journal: Integrated Computer-Aided Engineering, vol. 18, no. 4, pp. 301-311, 2011