A Gradient Projection Algorithm for Relaxation Methods

Mohammed, John L.; Hummel, Robert A.; Zucker, Steven W.

doi:10.1109/tpami.1983.4767394

Cited by 32 publications

(7 citation statements)

References 2 publications

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“…The above iteration equation is only one of many choices. A detailed implementation of such a projection operator used in is described in (Mohammed et al 1983). GP is an extended steepest descent procedure for solving programming problems under linear constraints.…”

Section: Maxirnization Forrnulationmentioning

confidence: 99%

Markov Random Field Modeling in Computer Vision

1995

Computer Science Workbench

984

779

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Section: Maxirnization Forrnulationmentioning

confidence: 99%

Markov Random Field Modeling in Computer Vision

1995

Computer Science Workbench

984

779

View full text Add to dashboard Cite

“…It implies that except for the boundary of K K, the gradient ascent procedure stays always inside the space and thus requires no projection. In other words, the projection operation Å K K , which otherwise may become much more complicated [33], reduces to…”

Section: A Relaxation Network For Texture Flowmentioning

confidence: 99%

The perceptual organization of texture flow: a contextual inference approach

Ben-Shahar

Zucker

2003

IEEE Trans. Pattern Anal. Machine Intell.

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Locally parallel dense patterns-sometimes called texture flows-define a perceptually coherent structure of particular significance to perceptual organization. We argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation, texture flows deserve attention equal to edge segment grouping and curve completion. This paper develops the notion of texture flow from a geometrical point of view to argue that local measurements of such structures must incorporate two curvatures. We show how basic theoretical considerations lead to a unique model for the local behavior of the flow and to a notion of texture flow "good continuation." This, in turn, translates to a specification of consistency constraints between nearby flow measurements which we use for the computation of globally (piecewise) coherent structure through the contextual framework of relaxation labeling. We demonstrate the results on synthetic and natural images.

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“…To overcome this problem, Rosenfeld et al (1976) formulated probabilistic relaxation. Much of the work involving consistent labelling has adopted Hummel and Zucker's optimization paradigm Faugeras and Berthod, 1981;Lloyd, 1983;Mohammed et al, 1983;Wilson and Hancock, 1997). The problem is to nd a set of label assignments that optimizes some global consistency measure.…”

Section: Consistent Labellingmentioning

confidence: 99%

“…the update operator is required to monotonically increase the quality of the solution: this was the approach used by Hummel and Zucker (1983) and others (Hancock and Kittler, 1990a;Faugeras and Berthod, 1981;Lloyd, 1983;Mohammed et al, 1983;Wilson and Hancock, 1997). Gradient ascent is appropriate when an initial guess can be made, which is close to the nal solution in the sense that there are no intervening local optima.…”

Section: Consistent Labellingmentioning

confidence: 99%

Empirical Modelling of Genetic Algorithms

Myers

Hancock

2001

Evolutionary Computation

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This paper addresses the problem of reliably setting genetic algorithm parameters for consistent labelling problems. Genetic algorithm parameters are notoriously difficult to determine. This paper proposes a robust empirical framework, based on the analysis of factorial experiments. The use of a graeco-latin square permits an initial study of a wide range of parameter settings. This is followed by fully crossed factorial experiments with narrower ranges, which allow detailed analysis by logistic regression. The empirical models derived can be used to determine optimal algorithm parameters and to shed light on interactions between the parameters and their relative importance. Re-fined models are produced, which are shown to be robust under extrapolation to up to triple the problem size.

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A Gradient Projection Algorithm for Relaxation Methods

Cited by 32 publications

References 2 publications

Markov Random Field Modeling in Computer Vision

Markov Random Field Modeling in Computer Vision

The perceptual organization of texture flow: a contextual inference approach

Empirical Modelling of Genetic Algorithms

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