The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Paul M. Baggenstoss - One of the best experts on this subject based on the ideXlab platform.
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on the equivalence of hanning weighted and overlapped analysis windows using different window sizes
IEEE Signal Processing Letters, 2012Co-Authors: Paul M. BaggenstossAbstract:This letter is concerned with time-series analysis using overlapped processing windows shaded using the Hanning window function, such as is used in short-time Fourier transform (STFT) analysis. We present a special case where different analysis window sizes produce equivalent outputs where equivalence is defined by the existence of an orthonormal linear transformation relating the two analyses. We apply the concept to the problem of detecting pulses of unknown duration in Gaussian noise. We also demonstrate how the method can be used to apply the PDF Projection Theorem to shaded overlapped processing windows.
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FUSION 2008 Tutorial Proposal: F undamentals of the Class-Specific Method
2008Co-Authors: Paul M. BaggenstossAbstract:The class-specific method (CSM) is an approach for constructing classifiers with class-dependent features that blends signal processing with classifcation theory. CSM is based on the mathematical identity called the probability density function (PDF) Projection Theorem that extends classical Bayesian theory. In contrast to conventional classifiers, feature extraction is an integral part of the theory. Because CSM does not need a common feature space, the dimensionality curse can be avoided. The tutorial covers fundamentals including generative and discriminative classiifers, the PDF Projection Theorem, classspecific modules and the chain rule. Many intuitive examples are providded. Some advanced examples are also covered.
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IbPRIA - A new optimal classifier architecture to aviod the dimensionality curse
Pattern Recognition and Image Analysis, 2003Co-Authors: Paul M. BaggenstossAbstract:In paper we present the theoretical foundation for optimal classification using class-specific features and provide examples of its use. A new PDF Projection Theorem makes it possible to project probability density functions from a low-dimensional feature space back to the raw data space. An M-ary classifier is constructed by estimating the PDFs of class-specific features, then transforming each PDF back to the raw data space where they can be fairly compared. Although statistical sufficiency is not a requirement, the classifier thus constructed will become equivalent to the optimal Bayes classifier if the features meet sufficiency requirements individually for each class. This classifier is completely modular and avoids the dimensionality curse associated with large complex problems. By recursive application of the Projection Theorem, it is possible to analyze complex signal processing chains. It is possible to automate the feature and model selection process by direct comparison of log-likelihood values on the common raw data domain. Pre-tested modules are available for a wide range of features including linear functions of independent random variables, cepstrum, and MEL cepstrum.
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The PDF Projection Theorem and the class-specific method
IEEE Transactions on Signal Processing, 2003Co-Authors: Paul M. BaggenstossAbstract:We present the theoretical foundation for optimal classification using class-specific features and provide examples of its use. A new probability density function (PDF) Projection Theorem makes it possible to project probability density functions from a low-dimensional feature space back to the raw data space. An M-ary classifier is constructed by estimating the PDFs of class-specific features, then transforming each PDF back to the raw data space where they can be fairly compared. Although statistical sufficiency is not a requirement, the classifier thus constructed becomes equivalent to the optimal Bayes classifier if the features meet sufficiency requirements individually for each class. This classifier is completely modular and avoids the dimensionality curse associated with large complex problems. By recursive application of the Projection Theorem, it is possible to analyze complex signal processing chains. We apply the method to feature sets, including linear functions of independent random variables, cepstrum, and Mel cepstrum. In addition, we demonstrate how it is possible to automate the feature and model selection process by direct comparison of log-likelihood values on the common raw data domain.
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ICPR (1) - The chain-rule processor: optimal classification through signal processing
Object recognition supported by user interaction for service robots, 2002Co-Authors: Paul M. BaggenstossAbstract:The chain-rule processor is a method of constructing an optimal Bayes classifier from a bank of processors. Each processor is a feature extractor designed to separate the given class from a class-dependent reference hypothesis, thereby avoiding the curse of dimensionality. This work builds upon prior work in optimal classifier design using class-specific features. The chain-rule processor is an improvement that recursively applies the PDF Projection Theorem.
Roberto Cipolla - One of the best experts on this subject based on the ideXlab platform.
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likelihood models for template matching using the pdf Projection Theorem
British Machine Vision Conference, 2004Co-Authors: Arasanathan Thayananthan, Ramanan Navaratnam, Philip H S Torr, Roberto CipollaAbstract:Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.
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BMVC - Likelihood models for template matching using the PDF Projection Theorem
Procedings of the British Machine Vision Conference 2004, 2004Co-Authors: Arasanathan Thayananthan, Ramanan Navaratnam, Philip H S Torr, Roberto CipollaAbstract:Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.
Arasanathan Thayananthan - One of the best experts on this subject based on the ideXlab platform.
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likelihood models for template matching using the pdf Projection Theorem
British Machine Vision Conference, 2004Co-Authors: Arasanathan Thayananthan, Ramanan Navaratnam, Philip H S Torr, Roberto CipollaAbstract:Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.
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BMVC - Likelihood models for template matching using the PDF Projection Theorem
Procedings of the British Machine Vision Conference 2004, 2004Co-Authors: Arasanathan Thayananthan, Ramanan Navaratnam, Philip H S Torr, Roberto CipollaAbstract:Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.
Antoine Derighetti - One of the best experts on this subject based on the ideXlab platform.
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SETS OF p-UNIQUENESS ON NONCOMMUTATIVE LOCALLY COMPACT GROUPS
Colloquium Mathematicum, 2017Co-Authors: Antoine DerighettiAbstract:We prove that a closed subgroup H of a locally compact group G is a set of p-uniqueness (1 < p < infinity) if and only if H is locally negligible. We also obtain the inverse Projection Theorem for sets of p-uniqueness.
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On Herz's Projection Theorem
Illinois Journal of Mathematics, 2004Co-Authors: Antoine DerighettiAbstract:Keywords: convolution operator ; contractive Projection ; amenable group ; Fo lner's condition Reference CAHRU-ARTICLE-2004-001View record in Web of Science Record created on 2008-12-10, modified on 2016-08-08
Philip H S Torr - One of the best experts on this subject based on the ideXlab platform.
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likelihood models for template matching using the pdf Projection Theorem
British Machine Vision Conference, 2004Co-Authors: Arasanathan Thayananthan, Ramanan Navaratnam, Philip H S Torr, Roberto CipollaAbstract:Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.
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BMVC - Likelihood models for template matching using the PDF Projection Theorem
Procedings of the British Machine Vision Conference 2004, 2004Co-Authors: Arasanathan Thayananthan, Ramanan Navaratnam, Philip H S Torr, Roberto CipollaAbstract:Template matching techniques are widely used in many computer vision tasks. Generally, a likelihood value is calculated from similarity measures, however the relation between these measures and the data likelihood is often incorrectly stated. It is clear that accurate likelihood estimation will improve the efficiency of the matching algorithms. This paper introduces a novel method for estimating the likelihood PDFS accurately based on the PDF Projection Theorem, which provides the correct relation between the feature likelihood and the data likelihood, permitting the use of different types of features for different types of objects and still estimating consistent likelihoods. The proposed method removes the normalization and bias problems that are usually associated with the likelihood calculations. We demonstrate that it significantly improves template matching in pose estimation problems. Qualitative and quantitative results are compared against traditional likelihood estimation schemes.
