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Shiftable Multiscale Transforms
, 1992
"... Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavel ..."
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Cited by 557 (36 self)
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. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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. We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads
How Iris Recognition Works
, 2003
"... Algorithms developed by the author for recognizing persons by their iris patterns have now been tested in six field and laboratory trials, producing no false matches in several million comparison tests. The recognition principle is the failure of a test of statistical independence on iris phase st ..."
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Cited by 495 (4 self)
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with extremely high confidence. The high confidence levels are important because they allow very large databases to be searched exhaustively (onetomany “identification mode”) without making any false matches, despite so many chances. Biometrics lacking this property can only survive onetoone (“verification
Factoring wavelet transforms into lifting steps
 J. Fourier Anal. Appl
, 1998
"... ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This dec ..."
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Cited by 573 (8 self)
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ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We present here a selfcontained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers. 1.
Comprehensive database for facial expression analysis
 in Proceedings of Fourth IEEE International Conference on Automatic Face and Gesture Recognition
"... Within the past decade, significant effort has occurred in developing methods of facial expression analysis. Because most investigators have used relatively limited data sets, the generalizability of these various methods remains unknown. We describe the problem space for facial expression analysis, ..."
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Cited by 590 (54 self)
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Within the past decade, significant effort has occurred in developing methods of facial expression analysis. Because most investigators have used relatively limited data sets, the generalizability of these various methods remains unknown. We describe the problem space for facial expression analysis, which includes level of description, transitions among expression, eliciting conditions, reliability and validity of training and test data, individual differences in subjects, head orientation and scene complexity, image characteristics, and relation to nonverbal behavior. We then present the CMUPittsburgh AUCoded Face Expression Image Database, which currently includes 2105 digitized image sequences from 182 adult subjects of varying ethnicity, performing multiple tokens of most primary FACS action units. This database is the most comprehensive testbed to date for comparative studies of facial expression analysis. 1.
Surface deformation due to shear and tensile faults in a halfspace
, 1985
"... A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a halfspace for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms r ..."
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Cited by 698 (1 self)
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A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a halfspace for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms representing deformations in an infinite medium, a term related to surface deformation and that is multiplied by the depth of observation point. Several practical suggestions to avoid mathematical singularities and computational instabilities are also presented. The expressions derived here represent powerful tools both for the observational and theoretical analyses of static field changes associated with earthquake and volcanic phenomena.
High confidence visual recognition of persons by a test of statistical independence
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 1993
"... Abstruct A method for rapid visual recognition of personal identity is described, based on the failure of a statistical test of independence. The most unique phenotypic feature visible in a person’s face is the detailed texture of each eye’s iris: An estimate of its statistical complexity in a samp ..."
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Cited by 596 (8 self)
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Abstruct A method for rapid visual recognition of personal identity is described, based on the failure of a statistical test of independence. The most unique phenotypic feature visible in a person’s face is the detailed texture of each eye’s iris: An estimate of its statistical complexity in a sample of the human population reveals variation corresponding to several hundred independent degreesoffreedom. Morphogenetic randomness in the texture expressed phenotypically in the iris trabecular meshwork ensures that a test of statistical independence on two coded patterns originating from different eyes is passed almost certainly, whereas the same test is failed almost certainly when the compared codes originate from the same eye. The visible texture of a person’s iris in a realtime video image is encoded into a compact sequence of multiscale quadrature 2D Gabor wavelet coefficients, whose mostsignificant bits comprise a 256byte “iris code. ” Statistical decision theory generates identification decisions from ExclusiveOR comparisons of complete iris codes at the rate of 4000 per second, including calculation of decision confidence levels. The distributions observed empirically in such comparisons imply a theoretical “crossover ” error rate of one in 131000 when a decision criterion is adopted that would equalize the false accept and false reject error rates. In the typical recognition case, given the mean observed degree of iris code agreement, the decision confidence levels correspond formally to a conditional false accept probability of one in about lo”’. Index Terms Image analysis, statistical pattern recognition, biometric identification, statistical decision theory, 2D Gabor filters, wavelets, texture analysis, morphogenesis. I.
Routing Techniques in Wireless Sensor Networks: A Survey
 IEEE Wireless Communications
, 2004
"... Wireless Sensor Networks (WSNs) consist of small nodes with sensing, computation, and wireless communications capabilities. Many routing, power management, and data dissemination protocols have been specifically designed for WSNs where energy awareness is an essential design issue. The focus, howeve ..."
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Cited by 704 (2 self)
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Wireless Sensor Networks (WSNs) consist of small nodes with sensing, computation, and wireless communications capabilities. Many routing, power management, and data dissemination protocols have been specifically designed for WSNs where energy awareness is an essential design issue. The focus, however, has been given to the routing protocols which might differ depending on the application and network architecture. In this paper, we present a survey of the stateoftheart routing techniques in WSNs. We first outline the design challenges for routing protocols in WSNs followed by a comprehensive survey of different routing techniques. Overall, the routing techniques are classified into three categories based on the underlying network structure: flat, hierarchical, and locationbased routing. Furthermore, these protocols can be classified into multipathbased, querybased, negotiationbased, QoSbased, and coherentbased depending on the protocol operation. We study the design tradeoffs between energy and communication overhead savings in every routing paradigm. We also highlight the advantages and performance issues of each routing technique. The paper concludes with possible future research areas. 1
Singularity Detection And Processing With Wavelets
 IEEE Transactions on Information Theory
, 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
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Cited by 590 (13 self)
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Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavelet transform are explained. We then prove that the local maxima of a wavelet transform detect the location of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations have a different behavior that we study separately. We show that the size of the oscillations can be measured from the wavelet transform local maxima. It has been shown that one and twodimensional signals can be reconstructed from the local maxima of their wavelet transform [14]. As an application, we develop an algorithm that removes white noises by discriminating the noise and the signal singularities through an analysis of their ...
Image denoising using a scale mixture of Gaussians in the wavelet domain
 IEEE TRANS IMAGE PROCESSING
, 2003
"... We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vecto ..."
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Cited by 514 (17 self)
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We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
Results 1  10
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