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We give necessary and sufficient conditions for uniqueness of the support vector solution for the problems of pattern recognition and regression estimation, for a general class of cost functions. We show that if the solution is not unique, all support vectors are necessarily at bound, and we give some simple examples of non-unique solutions. We note that(More)
One of the more successful approaches to image segmentation involves formulating the problem as the minimisation of a Mumford-Shah functional and then applying region merging algorithms to approximate the minimiser. Moreover, it can be proved mathematically that such segmentations have desirable properties, and further, fast implementations are available.(More)