The majority of standard segmentation methods use linear appearance models summing unary potentials (e.g. intensity log-likelihoods) inside each segment. Implicitly, this corresponds to i.i.d. assumption about intensities within each segment. This obvious over-simplification often leads to non-robustness and artifacts. We discuss more general non-linear constraints on segment appearance and some recent optimization methods for such models (some guarantee global optimality or approximation bounds). We focus on several types of generic constraints: MDL-based complexity of appearance, geometric constraints on relations between segment subparts (e.g. inclusion/exclusion, relative position, etc. useful in bio-medical applications due to anatomy). We will also discuss other non-linear constraints on intensity appearance, volume, and shape using trust region approach.
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