A class of discrete multiresolution random fields and its application to image segmentation

Wilson, Roland; Li, Chang-Tsun

doi:10.1109/tpami.2003.1159945

Cited by 75 publications

(85 citation statements)

References 35 publications

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“…p(y|x) = i∈S p(y i |x i ) (Besag, 1986) (Li, 2001) (Feng et al, 2002) (Xiao et al, 2002). However, as noted by several researchers (Bouman and Shapiro, 1994) (Pieczynski and Tebbache, 2000) (Wilson andLi, 2003)(Kumar andHebert, 2003c), this assumption is too restrictive for several natural image analysis applications. For example, consider a class that contains manmade structures (e.g.…”

Section: Noncausal Modelsmentioning

confidence: 99%

“…They further approximate the overall likelihood to be factored over the local joint distributions. Wilson and Li (Wilson and Li, 2003) assume the difference between observations from the neighboring sites to be conditionally independent given the label field. In the context of multiscale random field, Cheng and Bouman (Cheng and Bouman, 2001) make a more general assumption.…”

Section: Noncausal Modelsmentioning

confidence: 99%

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Discriminative Random Fields

Kumar

2014

Computer Vision

104

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Abstract.In this research we address the problem of classification and labeling of regions given a single static natural image. Natural images exhibit strong spatial dependencies, and modeling these dependencies in a principled manner is crucial to achieve good classification accuracy. In this work, we present Discriminative Random Fields (DRFs) to model spatial interactions in images in a discriminative framework based on the concept of Conditional Random Fields proposed by Lafferty et al (Lafferty et al., 2001). The DRFs classify image regions by incorporating neighborhood spatial interactions in the labels as well as the observed data. The DRF framework offers several advantages over the conventional Markov Random Field (MRF) framework. First, the DRFs allow to relax the strong assumption of conditional independence of the observed data generally used in the MRF framework for tractability. This assumption is too restrictive for a large number of applications in computer vision. Second, the DRFs derive their classification power by exploiting the probabilistic discriminative models instead of the generative models used for modeling observations in the MRF framework. Third, the interaction in labels in DRFs is based on the idea of pairwise discrimination of the observed data making it data-adaptive instead of being fixed a priori as in MRFs. Finally, all the parameters in the DRF model are estimated simultaneously from the training data unlike the MRF framework where the likelihood parameters are usually learned separately from the field parameters. We present preliminary experiments with man-made structure detection and binary image restoration tasks, and compare the DRF results with the MRF results.

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Section: Noncausal Modelsmentioning

confidence: 99%

Section: Noncausal Modelsmentioning

confidence: 99%

Discriminative Random Fields

Kumar

2014

Computer Vision

104

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“…To address the problems associated with nonhierarchical models, multiscale MRF models were formulated and have been extensively discussed in the image processing literature (Bouman and Shapiro, 1994;Kato et al 1996Kato et al , 1999Laferté et al, 2000;Liang and Tjahjadi, 2006;Mignotte et al, 2000;Wilson and Li, 2003). In those hierarchical MRF models, there is a series of random fields at a range of scales or resolutions, and the random field at each scale depends only on the next coarser random field above it.…”

Section: Related Workmentioning

confidence: 99%

“…In our multiscale MRF model, the value of a site at a given scale depends not only on its parent in the layer above but also on its neighbors at the same scale. In this respect, our model is closely related to the models presented in (Kato et al 1996(Kato et al , 1999Mignotte et al, 2000;Wilson and Li, 2003). However, unlike the models described by these authors, we solve the statistical inference problem by means of a sequence of related multi-resolution problems rather than as a single problem representing the entire quadtree.…”

Section: A Multiscale Mrf Modelmentioning

confidence: 99%

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Zhang¹

2007

Bull. Math. Biol.

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Cell membranes display a range of receptors that bind ligands and activate signaling pathways. Signaling is characterized by dramatic changes in membrane molecular topography, including the co-clustering of receptors with signaling molecules and the segregation of other signaling molecules away from receptors. Electron microscopy of immunogold-labeled membranes is a critical technique to generate topographical information at the 5-10 nm resolution needed to understand how signaling complexes assemble and function. However, due to experimental limitations, only two molecular species can usually be labeled at a time. A formidable challenge is to integrate experimental data across multiple experiments where there are from 10 to 100 different proteins and lipids of interest and only the positions of two species can be observed simultaneously. As a solution, we propose the use of Markov random field (MRF) modeling to reconstruct the distribution of multiple cell membrane constituents from pair-wise data sets. MRFs are a powerful mathematical formalism for modeling correlations between states associated with neighboring sites in spatial lattices. The presence or absence of a protein of a specific type at a point on the cell membrane is a state. Since only two protein types can be observed, i.e., those bound to particles, and the rest cannot be observed, the problem is one of deducing the conditional distribution of a MRF with unobservable (hidden) states. Here, we develop a multiscale MRF model and use mathematical programming techniques to infer the conditional distribution of a MRF for proteins of three types from observations showing the spatial relationships between only two types. Application to synthesized data shows that the spatial distributions of three proteins can be reliably estimated. Application to experimental data provides the first maps of the spatial relationship between groups of three different signaling molecules. The work is an important step toward a more complete understanding of membrane spatial organization and dynamics during signaling.

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“…Among those techniques, Bayesian approaches based on Markov random field (MRF) is one of the most frequently used [1,5,6,7,12,18,26]. However, despite of its local characteristic, which allows a global optimization problem to be solved locally, MRF is still a computation intensive method, especially when they are used in conjunction with stochastic relaxation scheme [25,26]. Another problem of some parametric MRF approaches is the requirement of a prior estimation of MRF parameters for each texture in the image.…”

Section: Introductionmentioning

confidence: 99%

Multiresolution genetic clustering algorithm for texture segmentation

Chiao

2003

Image and Vision Computing

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A class of discrete multiresolution random fields and its application to image segmentation

Cited by 75 publications

References 35 publications

Discriminative Random Fields

Discriminative Random Fields

Markov Random Field Modeling of the Spatial Distribution of Proteins on Cell Membranes

Multiresolution genetic clustering algorithm for texture segmentation

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