Image Processing Using Calculus of Variations and PDEs Tools

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Bozorgmanesh, Hassan | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46308 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi, Morteza
Abstract:
The aim of this thesis is to investigate recent methods for Image Processing(Any signal process which it’s input is an image and it’s ouput is an image or a set of Image parameters) using Calculus of variation tools. Methods which are to be investigated has been divided into two well known parts of Image Processing : Image Restoration and Image Segmentation.Image Processing Chapter includes two sections: one calculus of variations methods(energy method), other methods based on PDEs(heat equation and Malik-Perona equation). In studing each of this methods, It has been tried to include experimental results and negative and positive points of them.In Image Segmentation Chapter, first Mumford-Shah functional which is one of the most important functionals in the Image Processing, has been studied. In this direction there are explainations about existence and uniqueness of Mumford-Shah functional, it’s boundaries and different numerical methods for solving it. In the continue, active countours and level sets methods has been studied.In the last chapter one of the most recent methods for Image segmentation which tries to improve classical methods, has been fully investigated
Keywords:
Image Processing ; Partial Differential Equations ; Image Reconstruction ; Image Segmentation