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15
Global Stereo Reconstruction under Second Order Smoothness Priors
"... Second-order priors on the smoothness of 3D surfaces are a better model of typical scenes than first-order priors. However, stereo reconstruction using global inference algorithms, such as graph-cuts, has not been able to incorporate second-order priors because the triple cliques needed to express t ..."
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Cited by 127 (8 self)
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Second-order priors on the smoothness of 3D surfaces are a better model of typical scenes than first-order priors. However, stereo reconstruction using global inference algorithms, such as graph-cuts, has not been able to incorporate second-order priors because the triple cliques needed to express them yield intractable (non-submodular) optimization problems. This paper shows that inference with triple cliques can be effectively optimized. Our optimization strategy is a development of recent extensions to α-expansion, based on the “QPBO ” algorithm [5, 14, 26]. The strategy is to repeatedly merge proposal depth maps using a novel extension of QPBO. Proposal depth maps can come from any source, for example fronto-parallel planes as in α-expansion, or indeed any existing stereo algorithm, with arbitrary parameter settings. Experimental results demonstrate the usefulness of the second-order prior and the efficacy of our optimization framework. An implementation of our stereo framework is available online [34].
Efficient Belief Propagation for Higher-Order Cliques Using Linear Constraint Nodes
- COMPUTER VISION AND IMAGE UNDERSTANDING
, 2008
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Segmenting video into classes of algorithm-suitability
- in CVPR
, 2010
"... Given a set of algorithms, which one(s) should you apply to, i) compute optical flow, or ii) perform feature matching? Would looking at the sequence in question help you decide? It is unclear if even a person with intimate knowledge of all the different algorithms and access to the sequence itself c ..."
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Cited by 22 (4 self)
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Given a set of algorithms, which one(s) should you apply to, i) compute optical flow, or ii) perform feature matching? Would looking at the sequence in question help you decide? It is unclear if even a person with intimate knowledge of all the different algorithms and access to the sequence itself could predict which one to apply. Our hypothesis is that the most suitable algorithm can be chosen for each video automatically, through supervised training of a classifier. The classifier treats the different algorithms as black-box alternative “classes, ” and predicts when each is best because of their respective performances on training examples where ground truth flow was available. Our experiments show that a simple Random Forest classifier is predictive of algorithm-suitability. The automatic
Efficient new view synthesis using pairwise dictionary priors
- In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition
, 2007
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Toward global minimum through combined local minima
- In ECCV
, 2008
"... Abstract. There are many local and greedy algorithms for energy minimization over Markov Random Field (MRF) such as iterated condition mode (ICM) and various gradient descent methods. Local minima solutions can be obtained with simple implementations and usually require smaller computational time th ..."
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Cited by 9 (3 self)
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Abstract. There are many local and greedy algorithms for energy minimization over Markov Random Field (MRF) such as iterated condition mode (ICM) and various gradient descent methods. Local minima solutions can be obtained with simple implementations and usually require smaller computational time than global algorithms. Also, methods such as ICM can be readily implemented in a various difficult problems that may involve larger than pairwise clique MRFs. However, their short comings are evident in comparison to newer methods such as graph cut and belief propagation. The local minimum depends largely on the initial state, which is the fundamental problem of its kind. In this paper, disadvantages of local minima techniques are addressed by proposing ways to combine multiple local solutions. First, multiple ICM solutions are obtained using different initial states. The solutions are combined with random partitioning based greedy algorithm called Combined Local Minima (CLM). There are numerous MRF problems that cannot be efficiently implemented with graph cut and belief propagation, and so by introducing ways to effectively combine local solutions, we present a method to dramatically improve many of the pre-existing local minima algorithms. The proposed approach is shown to be effective on pairwise stereo MRF compared with graph cut and sequential tree re-weighted belief propagation (TRW-S). Additionally, we tested our algorithm against belief propagation (BP) over randomly generated 30×30 MRF with 2×2 clique potentials, and we experimentally illustrate CLM’s advantage over message passing algorithms in computation complexity and performance. 1
Learning generative texture models with extended Fields-of-Experts
, 2009
"... We evaluate the ability of the popular Field-of-Experts (FoE) to model structure in images. As a test case we focus on modeling synthetic and natural textures. We find that even for modeling single textures, the FoE provides insufficient flexibility to learn good generative models – it does not perf ..."
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Cited by 9 (4 self)
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We evaluate the ability of the popular Field-of-Experts (FoE) to model structure in images. As a test case we focus on modeling synthetic and natural textures. We find that even for modeling single textures, the FoE provides insufficient flexibility to learn good generative models – it does not perform any better than the much simpler Gaussian FoE. We propose an extended version of the FoE (allowing for bimodal potentials) and demonstrate that this novel formulation, when trained with a better approximation of the likelihood gradient, gives rise to a more powerful generative model of specific visual structure that produces significantly better results for the texture task.
Efficient Belief Propagation for Higher Order Cliques Using Linear Constraint Nodes
, 2008
"... Belief propagation over pairwise connected Markov Random Fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higher-order intera ..."
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Cited by 8 (2 self)
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Belief propagation over pairwise connected Markov Random Fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higher-order interactions are sometimes required. Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique. In this paper, we introduce a new technique to compute belief propagation messages in time linear with respect to clique size for a large class of potential functions over real-valued variables. We discuss how this technique can be generalized to still wider classes of potential functions at varying levels of efficiency. Also, we develop a form of nonparametric belief representation specifically designed to address issues common to networks with higher-order cliques and also to the use of guaranteed-convergent forms of belief propagation. To illustrate these techniques, we perform efficient inference in graphical models where the spatial prior of natural images is captured by 2×2 cliques. This approach shows significant improvement over the commonly used pairwise-connected models, and may benefit a variety of applications using belief propagation to infer images or range images, including stereo, shape-from-shading, image-based rendering, segmentation, and matting.
Estimating Markov random field potentials for natural images
- IN INT. CONF. ON INDEPENDENT COMPONENT ANALYSIS AND BLIND SOURCE SEPARATION
, 2009
"... Markov Random Field (MRF) models with potentials learned from the data have recently received attention for learning the low-level structure of natural images. A MRF provides a principled model for whole images, unlike ICA, which can in practice be estimated for small patches only. However, learni ..."
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Cited by 7 (3 self)
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Markov Random Field (MRF) models with potentials learned from the data have recently received attention for learning the low-level structure of natural images. A MRF provides a principled model for whole images, unlike ICA, which can in practice be estimated for small patches only. However, learning the filters in an MRF paradigm has been problematic in the past since it required computationally expensive Monte Carlo methods. Here, we show how MRF potentials can be estimated using Score Matching (SM). With this estimation method we can learn filters of size 12×12 pixels, considerably larger than traditional ”hand-crafted ” MRF potentials. We analyze the tuning properties of the filters in comparison to ICA filters, and show that the optimal MRF potentials are similar to the filters from an overcomplete ICA model.
A Tiered Move-making Algorithm for General Pairwise MRFs
"... A large number of problems in computer vision can be modeled as energy minimization problems in a markov random field (MRF) framework. Many methods have been developed over the years for efficient inference, especially in pairwise MRFs. In general there is a trade-off between the complexity/efficien ..."
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Cited by 2 (0 self)
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A large number of problems in computer vision can be modeled as energy minimization problems in a markov random field (MRF) framework. Many methods have been developed over the years for efficient inference, especially in pairwise MRFs. In general there is a trade-off between the complexity/efficiency of the algorithm and its convergence properties, with certain problems requiring more complex inference to handle general pairwise potentials. Graphcuts based α-expansion performs well on certain classes of energies, and sequential tree reweighted message passing (TRWS) and loopy belief propagation (LBP) can be used for non-submodular cases. These methods though suffer from poor convergence and often oscillate between solutions. In this paper, we propose a tiered move making algorithm which is an iterative method. Each move to the next configuration is based on the current labeling and an optimal tiered move, where each tiered move requires one application of the dynamic programming based tiered labeling method introduced in Felzenszwalb et. al. [2]. The algorithm converges to a local minimum for any general pairwise potential, and we give a theoretical analysis of the properties of the algorithm, characterizing the situations in which we can expect good performance. We evaluate the algorithm on many benchmark labeling problems such as stereo, image segmentation, image stitching and image denoising, as well as random energy minimization. Our method consistently gets better energy values than α-expansion, LBP, quadratic pseudo-boolean optimization (QPBO), and is competitive with TRWS. 1.
Efficient Statistical Methods for 3D Shape Inference
, 2008
"... Visual inference is a complex and ambiguous problem, and these properties have presented a significant obstacle to developing effective algorithms for many visual tasks. In this thesis, I begin by developing a methodology for statistical inference that is particularly suited for the complex tasks of ..."
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Cited by 1 (0 self)
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Visual inference is a complex and ambiguous problem, and these properties have presented a significant obstacle to developing effective algorithms for many visual tasks. In this thesis, I begin by developing a methodology for statistical inference that is particularly suited for the complex tasks of visual perception. The approach is based on Belief Propagation, a highly successful inference technique that has lead to notable progress in a number of statistical inference applications. Unfortunately, the computational complexity of belief propagation allows it to be applied to only fairly simple statistical distributions, thus excluding many of the rich statistical problems encountered in computer vision. In this thesis, I introduce a new technique to reduce the computational complexity of belief propagation from exponential to linear in the clique size of the underlying graphical model. These advancements allow us to efficiently solve inference problems that were previously intractable. I then apply this methodology to several visual tasks. In one example, I develop a statistical approach to the problem of estimating 3D shape from
