On Graph-Structured Discrete Labelling Problems in Computer Vision: Learning, Inference and Applications

A number of problems in computer vision (e.g., image segmentation, gender classification of faces, etc) can be formulated as graph-structured discrete labelling problems, where the goal is to predict labels (e.g. foreground/background, male/female) for a set of variables (e.g. pixels, faces in an image, etc) that have some known underlying structure (e.g., neighbouring pixels in an image often have related labels). This task of inferring optimal labels of structured variables is typically posed as the minimization of a discrete energy function over a graph, and is NP-hard for general graphs. This thesis is composed of three parts. In the first part, we present algorithms for learning the parameters of these energy functions from fully-labelled and partially-labelled training data. In the second part, we present a new approximate inference algorithm called Outer-Planar Decomposition (OPD). OPD decomposes the given intractable energy-minimization problem over a graph into tractable subproblems over outerplanar subgraphs and then employs message passing over these subgraphs to get an approximate global solution for the original graph. OPD outperforms current state-of-art inference methods on hard synthetic problems and is competitive on real computer-vision applications. Finally, in the third part, we demonstrate our work and apply this structured prediction paradigm to interactive co-segmentation of groups of related images and interactive 3D reconstruction of objects and scenes.