Reconstruction of Probability Density Functions from Channel Representations

Felsberg, Michael

doi:10.1007/11499145_50

Cited by 8 publications

(14 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• From the measured coefficients in the nonparametric density representation, a continuous density is to be estimated under the assumption of minimum information (maximum entropy) [15].…”

Section: Fig 1 Illustration Of Distribution Fields: the Image (Top) mentioning

confidence: 99%

“…This section makes use of notation and derivations according to [15]. The channel representation is built by channel encoding samples x (m) from a distribution with density p, resulting in the channel vector…”

Section: Encodingmentioning

confidence: 99%

“…In contrast to previous work on maximum entropy reconstruction [15], we will use cos 2 -kernels instead of quadratic B-splines…”

Section: Encodingmentioning

confidence: 99%

“…In contrast to the decoding as suggested above, which just estimates the mode of the distribution, maximum entropy decoding [15] attempts to extract the whole distribution. The idea is to find the simplest, i.e., the least informative, distribution, which fits the channel coefficients, by maximizing its differential entropy…”

Section: Maximum Entropy Reconstructionmentioning

confidence: 99%

“…To the best of our knowledge, the explicit solution of λ n cannot be calculated, and it has been suggested to apply a Newton method using numerical evaluations of the integrals on a very fine grid [15]. Obviously, this comes with an enormous efficiency penalty and is thus only interesting for single simulations.…”

Section: Maximum Entropy Reconstructionmentioning

confidence: 99%

See 4 more Smart Citations

Approximative Coding Methods for Channel Representations

Öfjäll

Felsberg

2017

J Math Imaging Vis

Self Cite

View full text Add to dashboard Cite

Most methods that address computer vision problems require powerful visual features. Many successful approaches apply techniques motivated from nonparametric statistics. The channel representation provides a framework for nonparametric distribution representation. Although early work has focused on a signal processing view of the representation, the channel representation can be interpreted in probabilistic terms, e.g., representing the distribution of local image orientation. In this paper, a variety of approximative channel-based algorithms for probabilistic problems are presented: a novel efficient algorithm for density reconstruction, a novel and efficient scheme for nonlinear gridding of densities, and finally a novel method for estimating Copula densities. The experimental results provide evidence that by relaxing the requirements for exact solutions, efficient algorithms are obtained.

show abstract

“…• From the measured coefficients in the nonparametric density representation, a continuous density is to be estimated under the assumption of minimum information (maximum entropy) [15].…”

Section: Fig 1 Illustration Of Distribution Fields: the Image (Top) mentioning

confidence: 99%

Section: Encodingmentioning

confidence: 99%

“…In contrast to previous work on maximum entropy reconstruction [15], we will use cos 2 -kernels instead of quadratic B-splines…”

Section: Encodingmentioning

confidence: 99%

Section: Maximum Entropy Reconstructionmentioning

confidence: 99%

Section: Maximum Entropy Reconstructionmentioning

confidence: 99%

See 3 more Smart Citations

Approximative Coding Methods for Channel Representations

Öfjäll

Felsberg

2017

J Math Imaging Vis

Self Cite

View full text Add to dashboard Cite

show abstract

Mathematical Methods for Signal and Image Analysis and Representation

Florack¹,

Duits²,

Jongbloed³

et al. 2011

Computational Imaging and Vision

View full text Add to dashboard Cite

This comprehensive book series embraces state-of-the-art expository works and advanced research monographs on any aspect of this interdisciplinary field.Topics covered by the series fall in the following four main categories:• Imaging Systems and Image Processing • Computer Vision and Image Understanding • Visualization •Applications of Imaging TechnologiesOnly monographs or multi-authored books that have a distinct subject area, that is where each chapter has been invited in order to fulfill this purpose, will be considered for the series. Volume 41 For further volumes: www.springer.com/series/5754 Luc Florack r Remco Duits r Geurt Jongbloed r Marie-Colette van Lieshout r Laurie Davies Editors

show abstract

Adaptive Filtering Using Channel Representations

Felsberg

2011

Computational Imaging and Vision

Self Cite

View full text Add to dashboard Cite

This review article gives an overview on adaptive filtering methods based on channel representations. The framework of channel representations and its relation to density estimation is introduced. The fast and accurate scheme of virtual shift decoding is introduced and applied in several variants of channel smoothing:• channel smoothing with alpha-synthesis for improving stability of edge-enhancing filtering • orientation adaptive channel smoothing with applications to coherence-enhancing filtering • channel smoothing using graph-cuts for improving filtering results at corners • channel-coded feature maps (CCFMs) which lead to a significant speed-up of channel averaging • CCFM-based smoothing based on optimal parameters derived from a novel uncertainty relationFor each method, an algorithmic description and some examples of results are provided, together with discussions and references of the original papers. Cross connections to other articles in this volume are given where appropriate.

show abstract

Reconstruction of Probability Density Functions from Channel Representations

Cited by 8 publications

References 9 publications

Approximative Coding Methods for Channel Representations

Approximative Coding Methods for Channel Representations

Mathematical Methods for Signal and Image Analysis and Representation

Adaptive Filtering Using Channel Representations

Contact Info

Product

Resources

About