research-article

Probabilistic Analysis of Regularization

Authors:

M. WermanAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 15, Issue 10

Pages 982 - 995

https://doi.org/10.1109/34.254057

Published: 01 October 1993 Publication History

Abstract

In order to use interpolated data wisely, it is important to have reliability and confidence measures associated with it. A method for computing the reliability at each point of any linear functional of a surface reconstructed using regularization is presented. The proposed method is to define a probability structure on the class of possible objects and compute the variance of the corresponding random variable. This variance is a natural measure for uncertainty, and experiments have shown it to correlate well with reality. The probability distribution used is based on the Boltzmann distribution. The theoretical part of the work utilizes tools from classical analysis, functional analysis, and measure theory on function spaces. The theory was tested and applied to real depth images. It was also applied to formalize a paradigm of optimal sampling, which was successfully tested on real depth images.

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Lanza AMorigi SSgallari F(2016)Constrained TV$$_p$$p-$$\ell _2$$ℓ2 Model for Image RestorationJournal of Scientific Computing10.1007/s10915-015-0129-x68:1(64-91)Online publication date: 1-Jul-2016
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Nikolova M(2004)A Variational Approach to Remove Outliers and Impulse NoiseJournal of Mathematical Imaging and Vision10.1023/B:JMIV.0000011920.58935.9c20:1-2(99-120)Online publication date: 1-Jan-2004
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Index Terms

Probabilistic Analysis of Regularization
1. Mathematics of computing
  1. Probability and statistics

Index terms have been assigned to the content through auto-classification.

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cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 15, Issue 10

October 1993

129 pages

ISSN:0162-8828

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Copyright © Copyright © 1993 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 October 1993

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Cited By

Lanza AMorigi SSciacchitano FSgallari F(2018)Whiteness Constraints in a Unified Variational Framework for Image RestorationJournal of Mathematical Imaging and Vision10.5555/3288649.328872860:9(1503-1526)Online publication date: 1-Nov-2018
https://dl.acm.org/doi/10.5555/3288649.3288728
Lanza AMorigi SSgallari F(2016)Constrained TV$$_p$$p-$$\ell _2$$ℓ2 Model for Image RestorationJournal of Scientific Computing10.1007/s10915-015-0129-x68:1(64-91)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1007/s10915-015-0129-x
Nikolova M(2004)A Variational Approach to Remove Outliers and Impulse NoiseJournal of Mathematical Imaging and Vision10.1023/B:JMIV.0000011920.58935.9c20:1-2(99-120)Online publication date: 1-Jan-2004
https://dl.acm.org/doi/10.1023/B%3AJMIV.0000011920.58935.9c
Keren D(2003)Recognizing image "style" and activities in video using local features and naive BayesPattern Recognition Letters10.1016/S0167-8655(03)00152-124:16(2913-2922)Online publication date: 1-Dec-2003
https://dl.acm.org/doi/10.1016/S0167-8655%2803%2900152-1
Keren DOsadchy MGotsman C(2001)AntifacesIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/34.93584823:7(747-761)Online publication date: 1-Jul-2001
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https://dl.acm.org/doi/10.1109/34.922710
Keren DWerman M(1999)A Full Bayesian Approach to Curve and Surface ReconstructionJournal of Mathematical Imaging and Vision10.1023/A:100831721057611:1(27-43)Online publication date: 1-Sep-1999
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Keren DGotlib A(1998)Denoising Color Images Using Regularization and “Correlation Terms”Journal of Visual Communication and Image Representation10.1006/jvci.1998.03929:4(352-365)Online publication date: 1-Dec-1998
https://dl.acm.org/doi/10.1006/jvci.1998.0392
Fieguth PKarl WWillsky A(1998)Efficient Multiresolution Counterparts to Variational Methods for Surface ReconstructionComputer Vision and Image Understanding10.1006/cviu.1997.063070:2(157-176)Online publication date: 1-May-1998
https://dl.acm.org/doi/10.1006/cviu.1997.0630

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