Probabilistic Solution of Ill-Posed Problems in Computational Vision

Marroquín, José L.; Mitter, Sanjoy K.; Poggio, Tommy

doi:10.2307/2289127

Cited by 395 publications

(166 citation statements)

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“…Using these samples, a Monte Carlo procedure can then estimate the requisite marginals. Unfortunately, previous MCMC approaches, which employed a histogramming strategy for density estimation [9], are ill-equipped to estimate distributions for which the sample space is large, such as P (x r∪ηr |y, θ).…”

Section: Estimating the Marginals Densitiesmentioning

confidence: 99%

“…By averaging over the functional forms P (x R |x η R , y) -instead of the samples themselves as with typical histogramming [9] -each "sample" in (3) updates P (x R |y) for all x R ∈ Λ | R| , greatly decreasing the number of samples needed for an accurate estimate. Furthermore, using multiple Markov chains (instead of the typical one [9]) improves robustness to the presence of multiple modes in P (x R ), each of which can trap the Markov chain.…”

Section: Estimating the Marginals Densitiesmentioning

confidence: 99%

“…This approach 1) employs the pseudo-likelihood [7] to simplify the EM equations without incurring any loss of generality and 2) leverages our recently presented Markov chain Monte Carlo (MCMC) method [8] to estimate the resulting complex marginal distributions. As we will discuss later, previous MCMC methods [9] are ill-equipped to perform this estimation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Image Segmentation with Implicit Color Standardization Using Spatially Constrained Expectation Maximization: Detection of Nuclei

Monaco

Hipp

Lucas

et al. 2012

Lecture Notes in Computer Science

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Abstract. Color nonstandardness -the propensity for similar objects to exhibit different color properties across images -poses a significant problem in the computerized analysis of histopathology. Though many papers propose means for improving color constancy, the vast majority assume image formation via reflective light instead of light transmission as in microscopy, and thus are inappropriate for histological analysis. Previously, we presented a novel Bayesian color segmentation algorithm for histological images that is highly robust to color nonstandardness; this algorithm employed the expectation maximization (EM) algorithm to dynamically estimate -for each individual image -the probability density functions that describe the colors of salient objects. However, our approach, like most EM-based algorithms, ignored important spatial constraints, such as those modeled by Markov random field (MRFs). Addressing this deficiency, we now present spatially-constrained EM (SCEM), a novel approach for incorporating Markov priors into the EM framework. With respect to our segmentation system, we replace EM with SCEM and then assess its improved ability to segment nuclei in H&E stained histopathology. Segmentation performance is evaluated over seven (nearly) identical sections of gastrointestinal tissue stained using different protocols (simulating severe color nonstandardness). Over this dataset, our system identifies nuclear regions with an area under the receiver operator characteristic curve (AUC) of 0.838. If we disregard spatial constraints, the AUC drops to 0.748.

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Section: Estimating the Marginals Densitiesmentioning

confidence: 99%

Section: Estimating the Marginals Densitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Image Segmentation with Implicit Color Standardization Using Spatially Constrained Expectation Maximization: Detection of Nuclei

Monaco

Hipp

Lucas

et al. 2012

Lecture Notes in Computer Science

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“…Statistical techniques have been successfully used in image processing for edge reconstruction [4,43,44,45,46]. The original image is modeled as a Markov random field (MRF) [2,3,4], and edges are reconstructed by maximum a posteriori (MAP) techniques.…”

Section: Statistical Spatial Approach: Map Estimationmentioning

confidence: 99%

Error Concealment in Encoded Video Streams

Salama

Shroff

Delp

1998

Signal Recovery Techniques for Image and Video Compression and Transmission

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When transmitting compressed video over a data network, one has to deal with how channel errors affect the decoding process. This is particularly problematic with data loss or erasures. In this paper we describe techniques to address this problem in the context of networks where channel errors or congestion can result in the loss of entire macroblocks when MPEG video is transmitted. We describe spatial and temporal techniques for the recovery of lost macroblocks. In particular, we develop estimation techniques for the reconstruction of missing macroblocks using a Markov Random Field model. We show that the widely used heuristic motion compensated error concealment technique based on averaging motion vectors is a special case of our estimation technique. We further describe a technique that can be implemented in real-time.

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“…In such a case, one can find a vast literature for solving the optimization problem stated in (3). Such techniques can be classified as combinatorial optimization approaches (the ones that try to directly estimate the c M AP ) [3,1,5,9,6] and probabilistic approaches (the ones for estimating a hidden real variable that represents the probability that c(r) takes a particular label, a PS) [8,11,4].…”

Section: Introductionmentioning

confidence: 99%

Spatial Sampling for Image Segmentation

Rivera

Dalmau

Mio

et al. 2011

The Computer Journal

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Abstract. We present a framework for image segmentation based on the ML estimator. A common hypothesis for explaining the differences among image regions is that they are generated by sampling different Likelihood Functions. We adopt last hypothesis and, additionally, we assume that such samples are i.i.d. Thus, the probability of a model generates the observed pixel value is estimated by computing the likelihood of the sample composed with the surrounding pixels.

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Probabilistic Solution of Ill-Posed Problems in Computational Vision

Cited by 395 publications

References 0 publications

Image Segmentation with Implicit Color Standardization Using Spatially Constrained Expectation Maximization: Detection of Nuclei

Image Segmentation with Implicit Color Standardization Using Spatially Constrained Expectation Maximization: Detection of Nuclei

Error Concealment in Encoded Video Streams

Spatial Sampling for Image Segmentation

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