Efficient Belief Propagation for Vision Using Linear Constraint Nodes

Potetz, Brian

doi:10.1109/cvpr.2007.383094

Cited by 58 publications

(84 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These constraints are compatible with many simple models of spatial priors for images [14]. However, many real-world applications require potential functions that violate these constraints, such as the Lambertian constraint in shape-from-shading [9], hard linear constraints of the type discussed in section 3.3, or the spatial priors of 3D shape, which include planar surfaces [15]. Graph cuts was originally designed for inference of binary random variables, but was extended to multivariate distributions…”

Section: Methods Of Statistical Inferencementioning

confidence: 85%

“…Belief propagation has been used with great success in a variety of applications [16,17,[2][3][4]. Point estimates obtained using belief propagation typically outperform gradient descent significantly, and belief propagation can succeed in cases where gradient descent is overwhelmed by local suboptimal extrema [9] Perhaps the most serious difficulty with using belief propagation is that it is slow for factors with many variables. Specifically, belief propagation requires computing messages from each factor node to each of its neighbors in the factor graph; each of these messages requires computation that is exponential in the number of neighbors of the factor node (this is also known as the clique size, equal to the number of variables in x i ).…”

Section: Methods Of Statistical Inferencementioning

confidence: 99%

“…In a previous paper by one of the authors [9], this technique was used for an application that infers 3D shape from a shaded image. The approach described here made it possible to to combine a hard linear constraint that enforced the integrability of the surface:…”

Section: Embedding Additional Potentialsmentioning

confidence: 99%

“…This relationship between p and q could be implemented as a pairwise clique in an overcomplete factor graph with the integrability constraint enforced using hard linear constraint nodes of clique-size four [9]. Alternatively, the Lambertian relationship could be enforced using cliques of size three in a complete factor graph whose variable 11 nodes represent depth at each pixel:…”

Section: Hard Linear Constraint Nodesmentioning

confidence: 99%

“…In section 8, we show that a prior model of natural images using 2 × 2 MRF cliques strongly outperforms pairwise-connected models. The ability to use more accurate models of image or range image priors has the potential to significantly aid the performance of several computer vision applications, including stereo [3], photometric stereo [4], shape-from-shading [9], image-based rendering [10], segmentation, and matting [7].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient belief propagation for higher-order cliques using linear constraint nodes

Potetz

Lee

2008

Computer Vision and Image Understanding

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Methods Of Statistical Inferencementioning

confidence: 85%

Section: Methods Of Statistical Inferencementioning

confidence: 99%

Section: Embedding Additional Potentialsmentioning

confidence: 99%

Section: Hard Linear Constraint Nodesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient belief propagation for higher-order cliques using linear constraint nodes

Potetz

Lee

2008

Computer Vision and Image Understanding

Self Cite

View full text Add to dashboard Cite

show abstract

Non-parametric Higher-Order Random Fields for Image Segmentation

Márquez-Neila

Kohli

Rother

et al. 2014

Computer Vision – ECCV 2014

View full text Add to dashboard Cite

Abstract. Models defined using higher-order potentials are becoming increasingly popular in computer vision. However, the exact representation of a general higher-order potential defined over many variables is computationally unfeasible. This has led prior works to adopt parametric 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 segmentations. 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.

show abstract