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39
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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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
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.
Window annealing over square lattice markov random field
"... Abstract. Monte Carlo methods and their subsequent simulated annealing are able to minimize general energy functions. However, the slow convergence of simulated annealing compared with more recent deterministic algorithms such as graph cuts and belief propagation hinders its popularity over the larg ..."
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Abstract. Monte Carlo methods and their subsequent simulated annealing are able to minimize general energy functions. However, the slow convergence of simulated annealing compared with more recent deterministic algorithms such as graph cuts and belief propagation hinders its popularity over the large dimensional Markov Random Field (MRF). In this paper, we propose a new efficient sampling-based optimization algorithm called WA (Window Annealing) over squared lattice MRF, in which cluster sampling and annealing concepts are combined together. Unlike the conventional annealing process in which only the temperature variable is scheduled, we design a series of artificial ”guiding ” (auxiliary) probability distributions based on the general sequential Monte Carlo framework. These auxiliary distributions lead to the maximum a posteriori (MAP) state by scheduling both the temperature and the proposed maximum size of the windows (rectangular cluster) variable. This new annealing scheme greatly enhances the mixing rate and consequently reduces convergence time. Moreover, by adopting the integral image technique for computation of the proposal probability of a sampled window, we can achieve a dramatic reduction in overall computations. The proposed WA is compared with several existing Monte Carlo based optimization techniques as well as state-of-the-art deterministic methods including Graph Cut (GC) and sequential tree re-weighted belief propagation (TRW-S) in the pairwise MRF stereo problem. The experimental results demonstrate that the proposed WA method is comparable with GC in both speed and obtained energy level. 1
Combining Shape-from-Shading and Stereo using Gaussian-Markov Random Fields
"... In this paper we present a method of combining stereo and shape-from-shading information, taking account of the local reliability of each shape estimate. Local estimates of disparity and orientation are modelled using Gaussian distributions. A Gaussian-Markov random field is used to represent the di ..."
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In this paper we present a method of combining stereo and shape-from-shading information, taking account of the local reliability of each shape estimate. Local estimates of disparity and orientation are modelled using Gaussian distributions. A Gaussian-Markov random field is used to represent the disparity-map, taking into account interactions between disparity measurements and surface orientation, and the MAP estimate found using belief propagation. Local estimates of the precision of disparities and surface normals are found and used to control the process so that the most accurate data source is used in each region. We assess the performance of our approach using both synthetic and real stereo pairs, and compare against ground truth.
Non-parametric Higher-order Random Fields for Image Segmentation
"... Abstract. Models defined using higher-order potentials are becoming increasingly popular in computer vision. However, the exact representa-tion of a general higher-order potential defined over many variables is computationally unfeasible. This has led prior works to adopt paramet-ric potentials that ..."
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Abstract. Models defined using higher-order potentials are becoming increasingly popular in computer vision. However, the exact representa-tion of a general higher-order potential defined over many variables is computationally unfeasible. This has led prior works to adopt paramet-ric potentials that can be compactly represented. This paper proposes a non-parametric higher-order model for image labeling problems that uses a patch-based representation of its potentials. We use the transformation scheme of [11, 25] to convert the higher-order potentials to a pair-wise form that can be handled using traditional inference algorithms. This representation is able to capture structure, geometrical and topological information of labels from training data and to provide more precise seg-mentations. Other tasks such as image denoising and reconstruction are also possible. We evaluate our method on denoising and segmentation problems with synthetic and real images.
Ray Markov Random Fields for Image-Based 3D Modeling: Model and Efficient Inference
"... In this paper, we present an approach to multi-view image-based 3D reconstruction by statistically inversing the ray-tracing based image generation process. The proposed algorithm is fast, accurate and does not need any initialization. The geometric representation is a discrete volume divided into v ..."
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In this paper, we present an approach to multi-view image-based 3D reconstruction by statistically inversing the ray-tracing based image generation process. The proposed algorithm is fast, accurate and does not need any initialization. The geometric representation is a discrete volume divided into voxels, with each voxel associated with two properties: opacity (shape) and color (appearance). The problem is then formulated as inferring each voxel’s most probable opacity and color through MAP estimation of the developed Ray Markov Random Fields (RayMRF). RayMRF is constructed with three kinds of cliques: the usual unary and pairwise cliques favoring connected voxel regions, and most importantly ray-cliques modelling the ray-tracing based image generation process. Each ray-clique connects the voxels that the viewing ray passes through. It provides a principled way of modeling the occlusion without approximation. The inference problem involved in the MAP estimation is handled by an optimized belief propagation algorithm. One unusual structure of the proposed MRF is that each ray-clique usually involves hundreds/thousands of random variables, which seems to make the inference computationally formidable. Thanks to the special property of the ray-clique functional form, we investigate the deep factorization property of ray-clique energy and get a highly efficient algorithm based on the general loopy belief propagation, which has reduced the computational complexity from exponential to linear. Both of the efficient inference algorithm and the overall system concept are new. Combining these results in an algorithm that can reverse the image generation process very fast. 3D surface reconstruction in a 100x100x100, i.e., 10 6 voxel space with 10 images requires roughly 3 minutes on a 3.0 GHz single-core CPU. The running time grows linearly with respect to the number of voxels and the number of images. And the speed could be further improved with a hierarchical sparse representation of the volume, like octree. Experiments on several standard datasets show the quality and speed of the proposed models and algorithms. 1.
An improved belief propagation method for dynamic collage. The Visual Computer
, 2009
"... An improved belief propagation method for dynamic collage ..."
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An improved belief propagation method for dynamic collage
Estimating the Bayes Point Using Linear Knapsack Problems
"... A Bayes Point machine is a binary classifier that approximates the Bayes-optimal classifier by estimating the mean of the posterior distribution of classifier parameters. Past Bayes Point machines have overcome the intractability of this goal by using message passing techniques that approximate the ..."
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A Bayes Point machine is a binary classifier that approximates the Bayes-optimal classifier by estimating the mean of the posterior distribution of classifier parameters. Past Bayes Point machines have overcome the intractability of this goal by using message passing techniques that approximate the posterior of the classifier parameters as a Gaussian distribution. In this paper, we investigate alternative message passing approaches that do not rely on Gaussian approximation. To make this possible, we introduce a new computational shortcut based on linear multiplechoice knapsack problems that reduces the complexity of approximating Bayes Point belief propagation messages from exponential to linear in the number of data features. Empirical tests of our approach show significant improvement in linear classification over both soft-margin SVMs and Expectation Propagation Bayes Point machines for several realworld UCI datasets. 1.
Higher-Order Clique Reduction Without Auxiliary Variables
"... We introduce a method to reduce most higher-order terms of Markov Random Fields with binary labels into lower-order ones without introducing any new variables, while keeping the minimizer of the energy unchanged. While the method does not reduce all terms, it can be used with existing techniques tha ..."
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We introduce a method to reduce most higher-order terms of Markov Random Fields with binary labels into lower-order ones without introducing any new variables, while keeping the minimizer of the energy unchanged. While the method does not reduce all terms, it can be used with existing techniques that transforms arbitrary terms (by introducing auxiliary variables) and improve the speed. The method eliminates a higher-order term in the polynomial representation of the energy by finding the value assignment to the variables involved that cannot be part of a global minimizer and increasing the potential value only when that particular combination occurs by the exact amount that makes the potential of lower order. We also introduce a faster approximation that forego the guarantee of exact equivalence of minimizer in favor of speed. With experi-ments on the same field of experts dataset used in previous work, we show that the roof-dual algorithm after the re-duction labels significantly more variables and the energy converges more rapidly. 1.
A hybrid approach for MRF optimization problems: Combination of stochastic sampling and . . .
- COMPUTER VISION AND IMAGE UNDERSTANDING 115 (2011) 1623–1637
, 2011
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