Ten Lectures on Statistical and Structural Pattern Recognition

Schlesinger, Matthew; Hlaváč, Václav

doi:10.1007/978-94-017-3217-8

Cited by 164 publications

(135 citation statements)

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“…The name '2D grammars' was later assigned a different meaning in the book [SH02] by Schlesinger and Hlaváč. In their original meaning, they largely coincide with MRF.…”

Section: Approach By Schlesinger Et Almentioning

confidence: 99%

A Linear Programming Approach to Max-Sum Problem: A Review

Werner

2007

IEEE Trans. Pattern Anal. Machine Intell.

276

356

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The max-sum labeling problem, defined as maximizing a sum of functions of pairs of discrete variables, is a general optimization problem with numerous applications, e.g., computing MAP assignments of a Markov random field. We review a not widely known approach to the problem based on linear programming relaxation, developed by . We also show how this old approach contributes to more recent results, most importantly by Wainwright et al. In particular, we review Schlesinger's upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to constraint satisfaction problem, how it can be understood as a linear programming relaxation, and three kinds of consistency necessary for optimality of the upper bound. As special cases, we revisit problems with two labels and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application to structural image analysis.

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“…The name '2D grammars' was later assigned a different meaning in the book [SH02] by Schlesinger and Hlaváč. In their original meaning, they largely coincide with MRF.…”

Section: Approach By Schlesinger Et Almentioning

confidence: 99%

A Linear Programming Approach to Max-Sum Problem: A Review

Werner

2007

IEEE Trans. Pattern Anal. Machine Intell.

276

356

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“…Considerations closely similar to those in [10] show this process converges to a local log-likelihood maximum. Let the log-likelihood of Eq.…”

Section: Intensity Model Of Pc-mra Imagesmentioning

confidence: 54%

“…Sequential EM-based initialization forms an LCDG-approximation of a given empirical marginal gray level distribution using the conventional EM-algorithm [10] …”

Section: Intensity Model Of Pc-mra Imagesmentioning

confidence: 99%

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A Novel 3D Joint Markov-Gibbs Model for Extracting Blood Vessels from PC–MRA Images

El-Baz

Gimel’farb

Falk

et al. 2009

Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009

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Abstract. New techniques for more accurate segmentation of a 3D cerebrovascular system from phase contrast (PC) magnetic resonance angiography (MRA) data are proposed. In this paper, we describe PC-MRA images and desired maps of regions by a joint Markov-Gibbs random field model (MGRF) of independent image signals and interdependent region labels but focus on most accurate model identification. To better specify region borders, each empirical distribution of signals is precisely approximated by a Linear Combination of Discrete Gaussians (LCDG) with positive and negative components. We modified the conventional Expectation-Maximization (EM) algorithm to deal with the LCDG. The initial segmentation based on the LCDG-models is then iteratively refined using a MGRF model with analytically estimated potentials. Experiments with both the phantoms and real data sets confirm high accuracy of the proposed approach.

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“…In order to be able to do that, we have to use a coordinate transform such that if we fit the linear decision boundary in the transformed space, we can transform it back and get a quadratic function. This process is sometimes referred to as the basis expansion [6] or feature space straightening [12].…”

Section: Quadratic Mappingmentioning

confidence: 99%

Estimation of fitness landscape contours in EAs

Pošík

2007

Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation

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Evolutionary algorithms applied in real domain should profit from information about the local fitness function curvature. This paper presents an initial study of an evolutionary strategy with a novel approach for learning the covariance matrix of a Gaussian distribution. The learning method is based on estimation of the fitness landscape contour line between the selected and discarded individuals. The distribution learned this way is then used to generate new population members. The algorithm presented here is the first attempt to construct the Gaussian distribution this way and should be considered only a proof of concept; nevertheless, the empirical comparison on low-dimensional quadratic functions shows that our approach is viable and with respect to the number of evaluations needed to find a solution of certain quality, it is comparable to the state-of-the-art CMA-ES in case of sphere function and outperforms the CMA-ES in case of elliptical function.

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Ten Lectures on Statistical and Structural Pattern Recognition

Cited by 164 publications

References 0 publications

A Linear Programming Approach to Max-Sum Problem: A Review

A Linear Programming Approach to Max-Sum Problem: A Review

A Novel 3D Joint Markov-Gibbs Model for Extracting Blood Vessels from PC–MRA Images

Estimation of fitness landscape contours in EAs

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