Hyper Graphs Inference Through Convex Relaxations And Move Making Algorithms

(Hyper)-graphs Inference Through Convex Relaxations and Move Making Algorithms

Computational visual perception seeks to reproduce human vision through the combination of visual sensors, artificial intelligence and computing. To this end, computer vision tasks are often reformulated as mathematical inference problems where the objective is to determine the set of parameters corresponding to the lowest potential of a task-specific objective function. Graphical models have been the most popular formulation in the field over the past two decades where the problem is viewed as a discrete assignment labeling one. Modularity, scalability and portability are the main strengths of these methods which once combined with efficient inference algorithms they could lead to state of the art results. In this tutorial we focus on the inference component of the problem and in particular we discuss in a systematic manner the most commonly used optimization principles in the context of graphical models. Our study concerns inference over low rank models (interactions between variables are constrained to pairs) as well as higher order ones (arbitrary set of variables determine hyper-cliques on which constraints are introduced) and seeks a concise, self-contained presentation of prior art as well as the presentation of the current state of the art methods in the field.

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. - Covers contemporary developments relating to the analysis and learning of images, shapes and forms - Presents mathematical models and quick computational techniques relating to the topic - Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods

Stanford Bulletin