Ground truth energies for hierarchies of segmentations

International audienceIn evaluating a hierarchy of segmentations H of an image by ground truth G, which can be partitions of the space or sets, we look for the optimal partition in H that " fits" G best. Two energies on partial partitions express the proximity from H to G, and G to H. They derive from a local version of the Hausdor distance. Then the problem amounts to nding the cut of the hierarchy which minimizes the said energy. This cuts provide global similarity measures of precision and recall. This allows to contrast two input hierarchies with respect to the G, and also to describe how to compose energies from di erent ground truths. Results are demonstrated over the Berkeley database

Image Segmentation with Joint Regularization and Histogram Separation

In this thesis optimization methods for image segmentation are studied. The common theme of all the methods is that we have a histogram model for appearance terms that we optimize jointly with smoothness. Recently it has been shown that if one assumes a histogram model for appearance, it is possible to optimize an approximation of the energy using only one graph cut, by ignoring the non-submodular volumetric penalty term. We show how to include the volumetric term using the Fast trust region framework. Fast trust region is a recently proposed method that is able to handle a large class of non-submodular energies by solving a sequence of graph cut problems. A comparison of these methods shows that Fast trust region typically obtains a lower energy value and higher segmentation quality, at the cost of requiring multiple graph cuts. Furthermore, we extend the simple histogram term to the multi-class setting and show that it is possible to optimize it with alpha-expansions. This is applied to the problems of stereo depth estimation and geometric model fitting

Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications

In computer vision, many problems such as image segmentation, pixel labelling, and scene parsing can be formulated as binary quadratic programs (BQPs). For submodular problems, cuts based methods can be employed to efficiently solve large-scale problems. However, general nonsubmodular problems are significantly more challenging to solve. Finding a solution when the problem is of large size to be of practical interest, however, typically requires relaxation. Two standard relaxation methods are widely used for solving general BQPs--spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high, especially for large scale problems. In this work, we present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton methods, for the dual problem. Both of them are significantly more efficiently than standard interior-point methods. In practice, the smoothing Newton solver is faster than the quasi-Newton solver for dense or medium-sized problems, while the quasi-Newton solver is preferable for large sparse/structured problems. Our experiments on a few computer vision applications including clustering, image segmentation, co-segmentation and registration show the potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern Analysis and Machine Intelligenc