| Image segmentation is a process of partitioning an image into sub-regions. Each sub-region has a consistent trait throughout that is different from other sub-regions in the image. Such traits can be intensity, color, or texture of the image. The region-based piecewise constant Mumford-Shah model has gained great popularity in solving image segmentation problems. It, without utilizing the gradient of the image, can segment and smooth images simultaneously. What's more, in this model, the initial curve can be put at anywhere within the image domain. Even through the piecewise constant Mumford-Shah model is very promising, it still has some drawbacks: first, it is unable to deal with images with intensity inhomogeneity. Second, it is not robust enough to segment images with high noise.In this thesis, first, we proposed a new numerical method for solving the piecewise constant Mumford-Shah model. In our method, the analysis domain is sampled by unstructured point cloud, which means the analysis domain is gridless or meshless. These sampling points are adaptively distributed according the local information of an image, hence allows extremely convenient enhancement/ reduction the precision of computation by simply putting more or less points on the computation domain. Later, we applied the numerical method in solving the multi-channel piecewise constant Mumford-Shah model, which is used for texture segmentation, and multiple Gabor transforms of the original image are used to discriminate textures.Second, we proposed a novel region-based geometric active contour model framework employing neighboring information constraints. The fundamental power of this strategy makes use of the image information at the support domain around each point of interest, thus effectively enlarges the capture range of each point to have a better regional understanding of the information with its local neighborhood. Our model is able to robustly segment images with intensity inhomogeneous or high noise. |
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