A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching

We study the quadratic assignment problem, in computer vision also known as graph matching. Two leading solvers for this problem optimize the Lagrange decomposition duals with sub-gradient and dual ascent (also known as message passing) updates. We explore s direction further and propose several additional Lagrangean relaxations of the graph matching problem along with corresponding algorithms, which are all based on a common dual ascent framework. Our extensive empirical evaluation gives several theoretical insights and suggests a new state-of-the-art any-time solver for the considered problem. Our improvement over state-of-the-art is particularly visible on a new dataset with large-scale sparse problem instances containing more than 500 graph nodes each.Comment: Added acknowledgment

Path Planning for Cooperative Routing of Air-Ground Vehicles

We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments on several randomly generated instances

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Scalable Full Flow with Learned Binary Descriptors

We propose a method for large displacement optical flow in which local matching costs are learned by a convolutional neural network (CNN) and a smoothness prior is imposed by a conditional random field (CRF). We tackle the computation- and memory-intensive operations on the 4D cost volume by a min-projection which reduces memory complexity from quadratic to linear and binary descriptors for efficient matching. This enables evaluation of the cost on the fly and allows to perform learning and CRF inference on high resolution images without ever storing the 4D cost volume. To address the problem of learning binary descriptors we propose a new hybrid learning scheme. In contrast to current state of the art approaches for learning binary CNNs we can compute the exact non-zero gradient within our model. We compare several methods for training binary descriptors and show results on public available benchmarks.Comment: GCPR 201

On distributed scheduling in wireless networks exploiting broadcast and network coding

In this paper, we consider cross-layer optimization in wireless networks with wireless broadcast advantage, focusing on the problem of distributed scheduling of broadcast links. The wireless broadcast advantage is most useful in multicast scenarios. As such, we include network coding in our design to exploit the throughput gain brought in by network coding for multicasting. We derive a subgradient algorithm for joint rate control, network coding and scheduling, which however requires centralized link scheduling. Under the primary interference model, link scheduling problem is equivalent to a maximum weighted hypergraph matching problem that is NP-complete. To solve the scheduling problem distributedly, locally greedy and randomized approximation algorithms are proposed and shown to have bounded worst-case performance. With random network coding, we obtain a fully distributed cross-layer design. Numerical results show promising throughput gain using the proposed algorithms, and surprisingly, in some cases even with less complexity than cross-layer design without broadcast advantage