Course Description

        Probabilistic models such as Markov Random Field (MRF) and Conditional Random Field
        (CRF) have long formed a basis for solving challenging assignment problems that are
        encountered while understanding images and scenes. Computational concerns had limited
        these models to encode only unary and/or pairwise terms. Although these methods had
        produced good results, recent studies have also shown the importance of incorporating higher
        order relations between scene elements. Examples include label consistency over large regions,
        contextual information, topological constraints, connectivity in 3D and symmetry priors which are
        also shown to be formulated in MRF/CRF frameworks. The goal is to estimate properties such
        as the most probable (MAP) solutions and marginal distributions to enable learning and inference
        in these models. Arguably the most popular approaches for solving these problems are
        graph-cuts and filter-based mean-field methods. We expect to delve deep into the analysis,
        properties and comparison of these approaches.

        This tutorial will be divided in four parts. The first part will cover a general framework to
        probabilistically model the label assignment problems emphasizing different higher order
        information used to solve various problems. In the second part, we will walk through
        the filter-based mean-field and maxflow/mincut algorithms, and will extensively study and compare
        the properties of two methods. The third part will cover solving higher order MRF/CRF problems
        using these approaches. In the final part, we will provide details on ways to formulate and solve
        various problems in these frameworks, showing applications on many problems such as stereo
        reconstruction, optical flow estimation, object/attribute label assignment and intrinsic scene
        decomposition. The tutorial will be concluded by citing the pointers to various existing software
        and directions for future research works. The tutorial will be self-contained with the first and last
        parts valuable for beginners, and advanced researchers should also benefit from the other two