Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation

Zhang, Jun; Modestino, J.W.; Langan, David A.

doi:10.1109/83.298395

Cited by 153 publications

(96 citation statements)

References 16 publications

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“…A major difficulty in applying the EM algorithm to MRFs is in the calculation of the conditional expectation, which is generally intractable because it requires summing over all possible configurations. Therefore, approximation techniques such as the mean field approximation (Celeux et al, 2003;Tonazzini et al, 2006;Zhang, 1992) and pseudo-likelihood method (Chalmond, 1989;Zhang et al, 1994) are used. The EM algorithm has been extended for parameter estimation on a quadtree (Bouman and Shapiro, 1994;Laferté et al, 2000).…”

Section: Related Workmentioning

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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Section: Related Workmentioning

confidence: 99%

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

Zhang¹

2007

Bull. Math. Biol.

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“…As in [22], implicit in the E-step is the computation of the conditional expectation of Zk given Yk and U(P). This is equivalent to computing the probabilities of each of the individual measurements belonging to each of the target classes.…”

Section: Skmentioning

confidence: 99%

“…Taking the approach used in [22], the approximate techniques of Besag [34] are used instead of the Monte-Carlo method of [32]. In particular, the pseudo-likelihood approximation of P(zklcIk) is used in the form…”

Section: Calculation Of E-stepmentioning

confidence: 99%

“…The more complex stochastic models pose a problem in that the analytical expression for the conditional expectation required in the E-Step can only be found for rather simple models. However, approximate techniques are shown to be effective [22] in overcoming these difficulties. Recently, iteration of the expectation step is shown to result in a self-consistent mean-field approximation [23] of the state process [24,25,26,27,28] and offers significant performance advantages in complex stochastic models.…”

Section: Introductionmentioning

confidence: 99%

“…Another application in which the EM algorithm has been used is the area of image segmentation [20,21,15,22]. In the unsupervised segmentation problem, training data is not available and feature values which characterize different classes of regions must be estimated from the data directly.…”

Section: Introductionmentioning

confidence: 99%

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Application of the EM algorithm for the multitarget/multisensor tracking problem

Molnar

Modestino

1998

IEEE Trans. Signal Process.

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An important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies. A number of approaches have been proposed for this multitarget/multisensor tracking problem ranging from reasonably simple, though ad-hoc, schemes to fairly complex, but theoretically optimum, approaches. In this paper we describe a new iterative procedure for multitarget/multisensor tracking based upon use of the expectation-maximization (EM) algorithm. More specifically, we pose the multitarget/multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data while the target-associated sensor outputs constitute the complete data. This formulation then allows a straightforward application of the EM algorithm which provides an iterative solution to the simultaneous maximum-likelihood (ML) and/or maximum a posteriori (MAP) estimate of the target states, under the assumption of appropriate motion models, based upon the outputs of disparate sensors. The advantage of this EM-based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum, but computationally infeasible, simultaneous ML estimator. We provide selected results illustrating the performance/complexity characteristics of this EM-based approach compared to competing schemes.This work supported in part by DAAH04-95-1-0103

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2‐D Linear Stochastic Modeling

Alata¹,

Cariou²

2008

Two‐Dimensional Signal Analysis

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Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation

Cited by 153 publications

References 16 publications

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

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

Application of the EM algorithm for the multitarget/multisensor tracking problem

2‐D Linear Stochastic Modeling

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