Modeling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields

Derin, Haluk; Elliott, H.

doi:10.1109/tpami.1987.4767871

Cited by 893 publications

(403 citation statements)

References 17 publications

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“…6b and c. One factor that may contribute to the error in the estimates is the lack of sufficient data for accurate estimation of conditional probabilities. Another factor may be the fact that the visible fields may be consistent with many different hidden distributions, and the ML estimation process can yield any of these distributions (Derin and Elliott, 1987).…”

Section: Results For the Markov Random Field Modelmentioning

confidence: 99%

“…MRFs have been used in computer vision and image processing for texture synthesis (Cross and Jain, 1983;Efros and Leung, 1999;Paget and Longstaff, 1998), image segmentation (Derin and Elliott, 1987), and image restoration (Geman and Geman, 1984;Li, 1995). The states of MRF texture models are all possible gray levels and directly observable.…”

Section: Related Workmentioning

confidence: 99%

“…In addition to MRFs where all states are observable, there are also hidden Markov models which contain states that are not directly observable. These hidden models are flexible and powerful when used in applications such as image restoration and segmentation (Geman and Geman, 1984;Besag, 1986;Derin and Elliott, 1987;Tonazzini et al, 2006), because many kinds of prior knowledge can be modeled. Maximum a posteriori (MAP) estimation is commonly used to restore or segment images.…”

Section: Related Workmentioning

confidence: 99%

“…For the nonhierarchical MRFs discussed thus far, exact MAP estimation is computationally expensive. Consequently, approximation methods such as iterated conditional modes (ICM) (Besag, 1986), dynamic programming (Derin and Elliott, 1987), or simulated annealing with Gibbs sampling (Geman and Geman, 1984) are used. Another difficulty with nonhierarchical MRFs is that the neighborhood systems need to be small because larger neighborhood systems dramatically increase the number of parameters and the running time of the MAP algorithms.…”

Section: Related Workmentioning

confidence: 99%

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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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Section: Results For the Markov Random Field Modelmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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

Zhang¹

2007

Bull. Math. Biol.

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“…A wide variety of texture segmentation techniques have been reported in the literature [1,2,4 -6,12,14, 15,18,21,23,26]. 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].…”

Section: Introductionmentioning

confidence: 99%