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**1 - 1**of**1**### Convex Optimization for Image Segmentation

"... Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar ..."

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Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar motion). Segmentation is a highly ambiguous task, and usually requires some prior knowledge. This can either be obtained by interactive user input in an supervised manner, or completely unsupervised using strong prior knowledge. In this thesis we use continuous energy minimization to tackle all of these problems. Continuous energy minimization provides an elegant way to model a problem like image segmentation. If the problem is convex, there are powerful optimization algorithms available. Additionally, we are guaranteed to find the globally optimal solution. We give an extensive introduction to convex optimization methods in computer vision. A great part of this thesis is devoted to basic image segmentation. We investigate the continuous maximum flow model for the two label segmentation, as well as optimization problems for multi-label segmentation. To obtain good segmentation results in a reasonable time, it is important that the energy,