13 research outputs found
OpenGM: A C++ Library for Discrete Graphical Models
OpenGM is a C++ template library for defining discrete graphical models and performing inference on these models, using a wide range of state-of-the-art algorithms. No restrictions are imposed on the factor graph to allow for higher-order factors and arbitrary neighborhood structures. Large models with repetitive structure are handled efficiently because (i) functions that occur repeatedly need to be stored only once, and (ii) distinct functions can be implemented differently, using different encodings alongside each other in the same model. Several parametric functions (e.g. metrics), sparse and dense value tables are provided and so is an interface for custom C++ code. Algorithms are separated by design from the representation of graphical models and are easily exchangeable. OpenGM, its algorithms, HDF5 file format and command line tools are modular and extendible
Efficient SDP Inference for Fully-connected CRFs Based on Low-rank Decomposition
Conditional Random Fields (CRF) have been widely used in a variety of
computer vision tasks. Conventional CRFs typically define edges on neighboring
image pixels, resulting in a sparse graph such that efficient inference can be
performed. However, these CRFs fail to model long-range contextual
relationships. Fully-connected CRFs have thus been proposed. While there are
efficient approximate inference methods for such CRFs, usually they are
sensitive to initialization and make strong assumptions. In this work, we
develop an efficient, yet general algorithm for inference on fully-connected
CRFs. The algorithm is based on a scalable SDP algorithm and the low- rank
approximation of the similarity/kernel matrix. The core of the proposed
algorithm is a tailored quasi-Newton method that takes advantage of the
low-rank matrix approximation when solving the specialized SDP dual problem.
Experiments demonstrate that our method can be applied on fully-connected CRFs
that cannot be solved previously, such as pixel-level image co-segmentation.Comment: 15 pages. A conference version of this work appears in Proc. IEEE
Conference on Computer Vision and Pattern Recognition, 201
Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study
This paper proposes a method for construction of approximate feasible primal
solutions from dual ones for large-scale optimization problems possessing
certain separability properties. Whereas infeasible primal estimates can
typically be produced from (sub-)gradients of the dual function, it is often
not easy to project them to the primal feasible set, since the projection
itself has a complexity comparable to the complexity of the initial problem. We
propose an alternative efficient method to obtain feasibility and show that its
properties influencing the convergence to the optimum are similar to the
properties of the Euclidean projection. We apply our method to the local
polytope relaxation of inference problems for Markov Random Fields and
demonstrate its superiority over existing methods.Comment: 20 page, 4 figure
A discriminative view of MRF pre-processing algorithms
While Markov Random Fields (MRFs) are widely used in computer vision, they
present a quite challenging inference problem. MRF inference can be accelerated
by pre-processing techniques like Dead End Elimination (DEE) or QPBO-based
approaches which compute the optimal labeling of a subset of variables. These
techniques are guaranteed to never wrongly label a variable but they often
leave a large number of variables unlabeled. We address this shortcoming by
interpreting pre-processing as a classification problem, which allows us to
trade off false positives (i.e., giving a variable an incorrect label) versus
false negatives (i.e., failing to label a variable). We describe an efficient
discriminative rule that finds optimal solutions for a subset of variables. Our
technique provides both per-instance and worst-case guarantees concerning the
quality of the solution. Empirical studies were conducted over several
benchmark datasets. We obtain a speedup factor of 2 to 12 over expansion moves
without preprocessing, and on difficult non-submodular energy functions produce
slightly lower energy.Comment: ICCV 201
Submodular relaxation for inference in Markov random fields
In this paper we address the problem of finding the most probable state of a
discrete Markov random field (MRF), also known as the MRF energy minimization
problem. The task is known to be NP-hard in general and its practical
importance motivates numerous approximate algorithms. We propose a submodular
relaxation approach (SMR) based on a Lagrangian relaxation of the initial
problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR
does not decompose the graph structure of the initial problem but constructs a
submodular energy that is minimized within the Lagrangian relaxation. Our
approach is applicable to both pairwise and high-order MRFs and allows to take
into account global potentials of certain types. We study theoretical
properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on
Pattern Analysis and Machine Intelligenc
Automatically Selecting Inference Algorithms for Discrete Energy Minimisation
Minimisation of discrete energies defined over factors is an important
problem in computer vision, and a vast number of MAP inference algorithms have
been proposed. Different inference algorithms perform better on factor graph
models (GMs) from different underlying problem classes, and in general it is
difficult to know which algorithm will yield the lowest energy for a given GM.
To mitigate this difficulty, survey papers advise the practitioner on what
algorithms perform well on what classes of models. We take the next step
forward, and present a technique to automatically select the best inference
algorithm for an input GM. We validate our method experimentally on an extended
version of the OpenGM2 benchmark, containing a diverse set of vision problems.
On average, our method selects an inference algorithm yielding labellings with
96% of variables the same as the best available algorithm