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

Parsimonious Segmentation of Time Series' by Potts Models

Typical problems in the analysis of data sets like time-series or images crucially rely on the extraction of primitive features based on segmentation. Variational approaches are a popular and convenient framework in which such problems can be studied. We focus on Potts models as simple nontrivial instances. The discussion proceeds along two data sets from brain mapping and functional genomics

A Multi-cut Formulation for Joint Segmentation and Tracking of Multiple Objects

Recently, Minimum Cost Multicut Formulations have been proposed and proven to be successful in both motion trajectory segmentation and multi-target tracking scenarios. Both tasks benefit from decomposing a graphical model into an optimal number of connected components based on attractive and repulsive pairwise terms. The two tasks are formulated on different levels of granularity and, accordingly, leverage mostly local information for motion segmentation and mostly high-level information for multi-target tracking. In this paper we argue that point trajectories and their local relationships can contribute to the high-level task of multi-target tracking and also argue that high-level cues from object detection and tracking are helpful to solve motion segmentation. We propose a joint graphical model for point trajectories and object detections whose Multicuts are solutions to motion segmentation {\it and} multi-target tracking problems at once. Results on the FBMS59 motion segmentation benchmark as well as on pedestrian tracking sequences from the 2D MOT 2015 benchmark demonstrate the promise of this joint approach

VQS: Linking Segmentations to Questions and Answers for Supervised Attention in VQA and Question-Focused Semantic Segmentation

Rich and dense human labeled datasets are among the main enabling factors for the recent advance on vision-language understanding. Many seemingly distant annotations (e.g., semantic segmentation and visual question answering (VQA)) are inherently connected in that they reveal different levels and perspectives of human understandings about the same visual scenes --- and even the same set of images (e.g., of COCO). The popularity of COCO correlates those annotations and tasks. Explicitly linking them up may significantly benefit both individual tasks and the unified vision and language modeling. We present the preliminary work of linking the instance segmentations provided by COCO to the questions and answers (QAs) in the VQA dataset, and name the collected links visual questions and segmentation answers (VQS). They transfer human supervision between the previously separate tasks, offer more effective leverage to existing problems, and also open the door for new research problems and models. We study two applications of the VQS data in this paper: supervised attention for VQA and a novel question-focused semantic segmentation task. For the former, we obtain state-of-the-art results on the VQA real multiple-choice task by simply augmenting the multilayer perceptrons with some attention features that are learned using the segmentation-QA links as explicit supervision. To put the latter in perspective, we study two plausible methods and compare them to an oracle method assuming that the instance segmentations are given at the test stage.Comment: To appear on ICCV 201