Abstract

The Mumford-Shah (MS) model has been studied in details in this thesis. It is found that the piecewise constant approximation MS model can not be used for images with large variation in the intensities. Therefore a linear approximation MS model is introduced. We have found that the linear approximation MS model provides better segmentation results than the piecewise constant MS model. The level set methods are used in the numerical computations. We have explicitly proved that the MS energy decreases with time (iterations) for all cases. The o and p dependence of the MS model is also studied. It is found that when o becomes large, the piecewise constant model is recovered. On the other hand, if o tends to zero, detailed structure of the input image can be obtained by the MS segmentation model. The MS and the Rudin-Osher-Fatemi (ROF) like models are generalized to include high order derivative terms. It is found that this kind of model can be used for edges with low contrast. The MS model is also generalized to a new model which can be used to detect roof edges which are difficult to detect by other models. Verification of the proposed models is done based on experimental results