Segmentação de Imagens via Análise de Sensibilidade

Abstract

Segmentation is the phase of the image processing where the input image is divided into constituent parts or objects. In general, the automatic segmentation is one of the most difficult tasks in digital image processing. In this work we used the topological sensitivity analysis as segmentation technique. The idea of segmentation of images via topological sensitivity analysis is to consider the class switching as an infinitesimal non-smooth perturbation of a pixel and calculate the sensitivity to this perturbation by a functional form associated with this disorder. In fact, the algorithms in the literature using the above approach are based on the Mumford-Shah functional whose minimum value is associated with the segmented image. The topological derivative is a scalar field that provides a first order approximation of the functional disorder associated with each pixel for each class of segmentation. Thus, in pixels where the topological derivative takes its most negative values ??will decrease the cost function and the corresponding change will result in better targeting than the previous. This work aims to present a comparative analysis of four segmentation algorithms based on topological derivative, three of them taken from the literature: Top-Shape 1, Shape 2 and Top-Sdt-Discrete, and the last top-Shape3, a new algorithm. The construction of the last algorithm is motivated by the analysis of the previous algorithms and limiting characteristics found, and derived results with higher quality and performance