Topological Derivative as a Tool for Image Processing Part I: Image Segmentation
Ignacio Larrabide, Antônio André Novotny, Mohamed Masmoudi, A. Feij · 2006
The introduction to medicine of techniques coming from Computational Modeling among other areas, made the use of imaging data such us Computed Tomography (CT), Magnetic Resonance Imaging (MRI), Single Photon Emission Tomography (SPECT), Positron Emission Tomography (PET) and Ultrasound (US) mandatory in order to apply these techniques to patient specific data. The process of identifying different tissues and organs, called segmentation, is a major concern in this analysis. Our aim in this paper is to present a novel image segmentation method based on the topological asymptotic expansion of a cost functional endowed to quantify the cost associated to a specific segmentation of the image data. This expansion leads to the so-called Topological Derivative, which allows us to quantify the sensitivity of a problem when the domain is perturbed by the introduction of an heterogeneity (hole, inclusion, source term, etc.). In particular, we use the Topological Derivative as a descent direction to minimize the associated cost function, leading to a new image segmentation algorithm. Finally, some experimental results are presented in order to show the robustness of this methodology even in the presence of very large noise in the image data.