Image segmentation based on variational techniques

Altınoklu, Metin Burak
In this thesis, the image segmentation methods based on the MumfordShah variational approach have been studied. By obtaining an optimum point of the Mumford-Shah functional which is a piecewise smooth approximate image and a set of edge curves, an image can be decomposed into regions. This piecewise smooth approximate image is smooth inside of regions, but it is allowed to be discontinuous region wise. Unfortunately, because of the irregularity of the Mumford Shah functional, it cannot be directly used for image segmentation. On the other hand, there are several approaches to approximate the Mumford-Shah functional. In the first approach, suggested by Ambrosio-Tortorelli, it is regularized in a special way. The regularized functional (Ambrosio-Tortorelli functional) is supposed to be gamma-convergent to the Mumford-Shah functional. In the second approach, the Mumford-Shah functional is minimized in two steps. In the first minimization step, the edge set is held constant and the resultant functional is minimized. The second minimization step is about updating the edge set by using level set methods. The second approximation to the Mumford-Shah functional is known as the Chan-Vese method. In both approaches, resultant PDE equations (Euler-Lagrange equations of associated functionals) are solved by finite difference methods. In this study, both approaches are implemented in a MATLAB environment. The overall performance of the algorithms has been investigated based on computer simulations over a series of images from simple to complicated.


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Citation Formats
M. B. Altınoklu, “Image segmentation based on variational techniques,” M.S. - Master of Science, Middle East Technical University, 2009.