683 research outputs found
Efficient Semidefinite Branch-and-Cut for MAP-MRF Inference
We propose a Branch-and-Cut (B&C) method for solving general MAP-MRF
inference problems. The core of our method is a very efficient bounding
procedure, which combines scalable semidefinite programming (SDP) and a
cutting-plane method for seeking violated constraints. In order to further
speed up the computation, several strategies have been exploited, including
model reduction, warm start and removal of inactive constraints.
We analyze the performance of the proposed method under different settings,
and demonstrate that our method either outperforms or performs on par with
state-of-the-art approaches. Especially when the connectivities are dense or
when the relative magnitudes of the unary costs are low, we achieve the best
reported results. Experiments show that the proposed algorithm achieves better
approximation than the state-of-the-art methods within a variety of time
budgets on challenging non-submodular MAP-MRF inference problems.Comment: 21 page
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
MAP inference via Block-Coordinate Frank-Wolfe Algorithm
We present a new proximal bundle method for Maximum-A-Posteriori (MAP)
inference in structured energy minimization problems. The method optimizes a
Lagrangean relaxation of the original energy minimization problem using a multi
plane block-coordinate Frank-Wolfe method that takes advantage of the specific
structure of the Lagrangean decomposition. We show empirically that our method
outperforms state-of-the-art Lagrangean decomposition based algorithms on some
challenging Markov Random Field, multi-label discrete tomography and graph
matching problems
An ILP Solver for Multi-label MRFs with Connectivity Constraints
Integer Linear Programming (ILP) formulations of Markov random fields (MRFs)
models with global connectivity priors were investigated previously in computer
vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear
Programing (LP) relaxations \cite{globalinter,globalconn} or simplified
versions \cite{graphcutbase} of the problem were solved. This paper
investigates the ILP of multi-label MRF with exact connectivity priors via a
branch-and-cut method, which provably finds globally optimal solutions. The
method enforces connectivity priors iteratively by a cutting plane method, and
provides feasible solutions with a guarantee on sub-optimality even if we
terminate it earlier. The proposed ILP can be applied as a post-processing
method on top of any existing multi-label segmentation approach. As it provides
globally optimal solution, it can be used off-line to generate ground-truth
labeling, which serves as quality check for any fast on-line algorithm.
Furthermore, it can be used to generate ground-truth proposals for weakly
supervised segmentation. We demonstrate the power and usefulness of our model
by several experiments on the BSDS500 and PASCAL image dataset, as well as on
medical images with trained probability maps.Comment: 19 page
Discrete-Continuous ADMM for Transductive Inference in Higher-Order MRFs
This paper introduces a novel algorithm for transductive inference in
higher-order MRFs, where the unary energies are parameterized by a variable
classifier. The considered task is posed as a joint optimization problem in the
continuous classifier parameters and the discrete label variables. In contrast
to prior approaches such as convex relaxations, we propose an advantageous
decoupling of the objective function into discrete and continuous subproblems
and a novel, efficient optimization method related to ADMM. This approach
preserves integrality of the discrete label variables and guarantees global
convergence to a critical point. We demonstrate the advantages of our approach
in several experiments including video object segmentation on the DAVIS data
set and interactive image segmentation
Discrete Visual Perception
International audienceComputational vision and biomedical image have made tremendous progress of the past decade. This is mostly due the development of efficient learning and inference algorithms which allow better, faster and richer modeling of visual perception tasks. Graph-based representations are among the most prominent tools to address such perception through the casting of perception as a graph optimization problem. In this paper, we briefly introduce the interest of such representations, discuss their strength and limitations and present their application to address a variety of problems in computer vision and biomedical image analysis
A Multiscale Framework for Challenging Discrete Optimization
Current state-of-the-art discrete optimization methods struggle behind when
it comes to challenging contrast-enhancing discrete energies (i.e., favoring
different labels for neighboring variables). This work suggests a multiscale
approach for these challenging problems. Deriving an algebraic representation
allows us to coarsen any pair-wise energy using any interpolation in a
principled algebraic manner. Furthermore, we propose an energy-aware
interpolation operator that efficiently exposes the multiscale landscape of the
energy yielding an effective coarse-to-fine optimization scheme. Results on
challenging contrast-enhancing energies show significant improvement over
state-of-the-art methods.Comment: 5 pages, 1 figure, To appear in NIPS Workshop on Optimization for
Machine Learning (December 2012). Camera-ready version. Fixed typos,
acknowledgements adde
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