Image Models for Segmentation and Recognition

We examine image models for segmentation and classification that are based (i) on the statistical properties of natural images and (ii) on non-negative matrix or tensor codes. Regarding (i) we derive a parametric framework for variational image segmentation. Using a model for the filter response statistics of natural images we build a sound probabilistic distance measure that drives level sets toward meaningful segmentations of complex textures and natural scenes. We show that the approach can be generalized from binary image segmentation to multiple image regions and is suitable for fast greedy optimization. Regarding (ii) we use results from global deterministic optimization to obtain fast and practical algorithms for non-negative matrix and tensor factorization with sparsity constraints. Such problems were previously optimized using variations of projected gradient descent --a procedure that can be inefficient and difficult to generalize. In contrast, our approach uses highly efficient solvers from convex optimization to solve a sequence of quadratic or second-order conic programs. We show that this offers benefits in terms of efficiency and, in particular, extensibility: Our procedures are very easy to augment by additional convex constraints. We give numerous examples where such additional constraints yield improved results in image processing and recognition