Digital Image Segmentation as an Optimization Problem

Abstract

Segmentation is one of the most important tasks in image processing. It consist in classify the pixels in two or more groups depending on their intensity levels and a threshold value. The quality of the segmentation depends on the method applied to select the threshold. The use of the classical implementations for multilevel thresholding is computationally expensive since they exhaustively search the best values to optimize the objective function. Under such conditions, the use of optimization evolutionary approaches has been extended. In this chapter, a multilevel thresholding (MT) algorithm based on the EMO is introduced. The approach combines the good search capabilities of EMO algorithm with objective functions proposed by three popular MT methods: Otsu, Kapur and Tsallis. The algorithm takes random samples from a feasible search space inside the image histogram. Such samples build each particle in the EMO context whereas its quality is evaluated considering the objective function employed by the Otsu’s, Kapur’s or Tsallis method. Guided by these objective values the set of candidate solutions are evolved using the EMO operators until an optimal solution is found. The approach generates a multilevel segmentation algorithm which can effectively identify the threshold values of a digital image in a reduced number of iterations.