Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming

Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming1

We introduce a novel optimization method, semidefinite programming, to the field of computer vision and apply it to the combinatorial problem of minimizing quadratic functionals in binary decision variables subject to linear constraints. The approach is (tuning) parameter free and computes high-quality combinatorial solutions using interior-point methods (convex programming) and a randomized hy...

Image Labeling and Grouping by Minimizing Linear Functionals over Cones

We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization pointof-view. Rather than trying to compute the global minimum a goal we consider as elusive in these cases we wish to design opt...

Convex Relaxations for Binary Image Partitioning and Perceptual Grouping

Guest Editors' Introduction to the Special Section on Energy Minimization Methods in Computer Vision and Pattern Recognition

ENERGY minimization techniques are central to many methods in computer vision and pattern recognition. Stated simply, if a task can be posed as the minimization of an energy measure, which may, for instance, be the negative logarithm of a probability or an entropy, then a variety of optimization methods may be applied to locate the solution. The solution may be a vector of parameters representi...

Grouping with Bias

We present a graph partitioning method to integrate prior knowledge in data grouping. We consider priors represented by three types of constraints: unitary constraints on labelling of groups, partial a priori grouping information, external in uence on binary constraints. They are modelled as biases in the grouping process. We incorporate these biases into graph partitioning criteria. Computatio...