Multiresolution Markov models for signal and image processing

Willsky, Alan S.

doi:10.1109/jproc.2002.800717

Cited by 248 publications

(229 citation statements)

References 282 publications

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“…Objects at different depths exhibit very different behaviors at different resolutions, and using multiscale features allows us to capture these variations (Willsky 2002). For example, blue sky may appear similar at different scales, but textured grass would not.…”

Section: Features For Absolute Depthmentioning

confidence: 99%

3-D Depth Reconstruction from a Single Still Image

2007

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We consider the task of 3-d depth estimation from a single still image. We take a supervised learning approach to this problem, in which we begin by collecting a training set of monocular images (of unstructured indoor and outdoor environments which include forests, sidewalks, trees, buildings, etc.) and their corresponding ground-truth depthmaps. Then, we apply supervised learning to predict the value of the depthmap as a function of the image. Depth estimation is a challenging problem, since local features alone are insufficient to estimate depth at a point, and one needs to consider the global context of the image. Our model uses a hierarchical, multiscale Markov Random Field (MRF) that incorporates multiscale local-and global-image features, and models the depths and the relation between depths at different points in the image. We show that, even on unstructured scenes, our algorithm is frequently able to recover fairly accurate depthmaps. We further propose a model that incorporates both monocular cues and stereo (triangulation) cues, to obtain significantly more accurate depth estimates than is possible using either monocular or stereo cues alone.

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Section: Features For Absolute Depthmentioning

confidence: 99%

3-D Depth Reconstruction from a Single Still Image

2007

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“…Multiresolution signal and image analysis and multiscale algorithms are of interest in many fields [13], [14]. In particular, efficient restoration algorithms in statistical models defined on Hidden Markov trees (HMT) have been developed (see e.g.…”

Section: A Introductionmentioning

confidence: 99%

Exact Bayesian Prediction in a Class of Markov-switching Models

Bardel

Desbouvries

2010

Methodol Comput Appl Probab

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Jump-Markov state-space systems (JMSS) are widely used in statistical signal processing. However as is well known Bayesian restoration in JMSS is an NP-hard problem, so in practice all inference algorithms need to resort to some approximations. In this paper we focus on the computation of the conditional expectation of the hidden variable of interest given the available observations, which is optimal from the Bayesian quadratic risk viewpoint. We show that in some stochastic systems, namely the Partially Pairwise Markov-switching Chains (PPMSC) and Trees (PPMST), no approximation scheme is actually needed since the conditional expectation of interest (be it either in a filtering or prediction problem) can be computed exactly and in a number of operations linear in the number of observations. Index TermsBayesian restoration, Jump-Markov state-space systems, Partially Pairwise Markov switching models, NP-hard problems.

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“…The method is based on an algorithm [28] inspired by image processing research. The degree of freedom to choose a certain tree and to set up the parameters for the update of the ensemble makes the method very appealing.…”

Section: Introductionmentioning

confidence: 99%

Multiscale ensemble filtering for reservoir engineering applications

et al. 2008

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Reservoir management requires periodic updates of the simulation models using the production data available over time. Traditionally, validation of reservoir models with production data is done using a history matching process. Uncertainties in the data, as well as in the model, lead to a nonunique history matching inverse problem. It has been shown that the ensemble Kalman filter (EnKF) is an adequate method for predicting the dynamics of the reservoir. The EnKF is a sequential Monte-Carlo approach that uses an ensemble of reservoir models. For realistic, large-scale applications, the ensemble size needs to be kept small due to computational inefficiency. Consequently, the error space is not well covered (poor cross-correlation matrix approximations) and the updated parameter field becomes scattered and loses important geological features (for example, the contact between high-and low-permeability values). The prior geological knowledge present in the initial time is not found anymore in the final updated parameter. We propose a new approach to overcome some of the EnKF limitations. This paper shows the specifications and results of the ensemble multiscale filter (EnMSF) for automatic history matching. EnMSF replaces, at each update time, the prior sample covariance with a multiscale tree. The global dependence is preserved via the parent-child relation in the tree (nodes at the adjacent scales). After constructing the tree, the Kalman update is performed. The properties of the EnMSF are presented here with a 2D, two-phase (oil and water) small twin experiment, and the results are compared to the EnKF. The advantages of using EnMSF are localization in space and scale, adaptability to prior information, and efficiency in case many measurements are available. These advantages make the EnMSF a practical tool for many data assimilation problems.

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Multiresolution Markov models for signal and image processing

Cited by 248 publications

References 282 publications

3-D Depth Reconstruction from a Single Still Image

3-D Depth Reconstruction from a Single Still Image

Exact Bayesian Prediction in a Class of Markov-switching Models

Multiscale ensemble filtering for reservoir engineering applications

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