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60
A Survey of Image Registration Techniques
 ACM Computing Surveys
, 1992
"... Registration is a fundamental task in image processing used to match two or more pictures taken, for example, at different times, from different sensors or from different viewpoints. Over the years, a broad range of techniques have been developed for the various types of data and problems. These ..."
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Cited by 964 (2 self)
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Registration is a fundamental task in image processing used to match two or more pictures taken, for example, at different times, from different sensors or from different viewpoints. Over the years, a broad range of techniques have been developed for the various types of data and problems. These techniques have been independently studied for several different applications resulting in a large body of research. This paper organizes this material by establishing the relationship between the distortions in the image and the type of registration techniques which are most suitable. Two major types of distortions are distinguished. The first type are those which are the source of misregistration, i.e., they are the cause of the misalignment between the two images. Distortions which are the source of misregistration determine the transformation class which will optimally align the two images. The transformation class in turn influences the general technique that should be taken....
A Review of Medical Image Registration
 Interactive imageguided neurosurgery
, 1993
"... Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergist ..."
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Cited by 32 (0 self)
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Introduction The ever expanding gamut of medical imaging techniques provides the clinician an increasingly multifaceted view of brain function and anatomy. The information provided by the various imaging modalities is often complementary (i.e. provides separate but useful information) and synergistic (i.e. the combination of information provides useful extra information). For example, Xray computed tomography (CT) and magnetic resonance (MR) imaging exquisitely demonstrate brain anatomy but provide little functional information. Positron emission tomography (PET) and single photon emission computed tomography (SPECT) scans display aspects of brain function and allow metabolic measurements but poorly delineate anatomy. Furthermore, CT and MR images describe complementary morphologic features. For example, bone and calcifications are best seen on CT images, while softtissue structures are better differentiated by MR imaging. Clinical diagnosis and therapy planning and evaluatio
On the Weyl Representation of Metaplectic Operators
, 2005
"... We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no nontrivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslovtype indices; these indices intervene in a cru ..."
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Cited by 20 (11 self)
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We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no nontrivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslovtype indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder.
Linear TimeFrequency Filters: Online Algorithms and Applications
, 2002
"... This chapter discusses practical discretetime methods for the timefrequency (TF) design of linear timevariant (LTV) filters. The filters are specified via a prescribed TF weight function (timevarying transfer function). We consider both explicit TF filter designs where a TF representation of the ..."
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Cited by 18 (3 self)
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This chapter discusses practical discretetime methods for the timefrequency (TF) design of linear timevariant (LTV) filters. The filters are specified via a prescribed TF weight function (timevarying transfer function). We consider both explicit TF filter designs where a TF representation of the LTV filter is matched to the specified TF weight function, and implicit TF filter designs that use an analysisweightingsynthesis procedure involving a linear TF signal representation. All filter designs allow for efficient online implementations and are thus suited to realtime applications. Our theoretical development is complemented by detailed descriptions of online algorithms, discussions of the choice of design parameters, and estimates of computational complexity and memory requirements. The performance and selected applications of the various TF filters are illustrated via numerical simulations.
Integral Operators, Pseudodifferential Operators, and Gabor Frames
, 2003
"... This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that ..."
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Cited by 16 (4 self)
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This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is traceclass. This result significantly improves a sufficient condition due to Daubechies and Hörmander.
Nonstationary spectral analysis based on timefrequency operator symbols and underspread approximations
 IEEE TRANS. INF. THEORY
, 2006
"... We present a unified framework for timevarying or time–frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all m ..."
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Cited by 14 (6 self)
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We present a unified framework for timevarying or time–frequency (TF) spectra of nonstationary random processes in terms of TF operator symbols. We provide axiomatic definitions and TF operator symbol formulations for two broad classes of TF spectra, one of which is new. These classes contain all major existing TF spectra such as the Wigner–Ville, evolutionary, instantaneous power, and physical spectrum. Our subsequent analysis focuses on the practically important case of nonstationary processes with negligible highlag TF correlations (socalled underspread processes). We demonstrate that for underspread processes all TF spectra yield effectively identical results and satisfy several desirable properties at least approximately. We also show that Gabor frames provide approximate Karhunen–Loève (KL) functions of underspread processes and TF spectra provide a corresponding approximate KL spectrum. Finally, we formulate simple approximate input–output relations for the TF spectra of underspread processes that are passed through underspread linear timevarying systems. All approximations are substantiated mathematically by upper bounds on the associated approximation errors. Our results establish a TF calculus for the secondorder analysis and timevarying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes.
On the recovery of a function on a circular domain
 IEEE Trans. Inform. Theory
, 2002
"... Abstract—We consider the problem of estimating a function ( ) on the unit disk (): 2 + 2 1, given a discrete and noisy data recorded on a regular square grid. An estimate of ( ) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distin ..."
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Cited by 14 (4 self)
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Abstract—We consider the problem of estimating a function ( ) on the unit disk (): 2 + 2 1, given a discrete and noisy data recorded on a regular square grid. An estimate of ( ) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the origin of coordinates yielding therefore a rotationally invariant estimate. For radial functions, the orthogonal set has a particularly simple form being related to the classical Legendre polynomials. We give the statistical accuracy analysis of the proposed estimate of ( ) in the sense of the 2 metric. It is found that there is an inherent limitation in the precision of the estimate due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to the celebrated problem in the analytic number theory called the lattice points of a circle. In fact, the obtained bounds for the mean integrated squared error are determined by the best known result so far on the problem of lattice points within the circular domain. Index Terms—Accuracy, circle orthogonal polynomials, circle problem, circular domain, lattice points, nonparametric estimate, radial functions, rotational invariance, twodimensional (2D) functions, Zernike functions. I.
Symplectically Covariant Schrödinger Equation in Phase
, 2005
"... A classical theorem of Stone and von Neumann states that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of squareintegrable functions on configuration space. Using the Wigner–Moyal transform, we constr ..."
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Cited by 12 (4 self)
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A classical theorem of Stone and von Neumann states that the Schrödinger representation is, up to unitary equivalences, the only irreducible representation of the Heisenberg group on the Hilbert space of squareintegrable functions on configuration space. Using the Wigner–Moyal transform, we construct an irreducible representation of the Heisenberg group on a certain Hilbert space of squareintegrable functions defined on phase space. This allows us to extend the usual Weyl calculus into a phasespace calculus and leads us to a quantum mechanics in phase space, equivalent to standard quantum mechanics. We also briefly discuss the extension of metaplectic operators to phase space and the probabilistic interpretation of the solutions of the phasespace Schrödinger equation. PACS numbers: 02.40.Vh, 03.65.−w 1. Introduction and
Class of Algorithms for Realtime Subpixel Registration
 Proceedings of SPIE, Vol
"... In 1972, Barnea and Silverman presented a new approach to the wide field of template matching, the SSDalgorithm. Further work has been done to adapt the method to gain subpixel accuracy. Intense investigation of the proposed algorithms led to our new approach: by interpolating the template instead ..."
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Cited by 10 (0 self)
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In 1972, Barnea and Silverman presented a new approach to the wide field of template matching, the SSDalgorithm. Further work has been done to adapt the method to gain subpixel accuracy. Intense investigation of the proposed algorithms led to our new approach: by interpolating the template instead of the reference image, and by applying sort of an errorcorrection to the resulting subpixelvalue, both computation time and accuracy can be improved. Exhaustive experiments with a CCDcamera and various kinds of reference images showed that a maximum error of 10% of the pixel period can be expected. Depending on the kind of image, mean square errors range from 0.4% to 4%. INTRODUCTION In 1972, Barnea and Silverman presented the SSDalgorithm, a fast way to solve the problem of image registration [1]. Extending it to subpixel accuracy ([2],[3]), nevertheless, increased the computational cost to an amount where realtime applications seemed almost impossible. In this paper we presen...
A new approach to the ⋆genvalue equation
, 2008
"... We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our method makes use of a Weyltype representation of the starproduct and of the properties of the crossWigner tran ..."
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Cited by 6 (3 self)
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We show that the eigenvalues and eigenfunctions of the stargenvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our method makes use of a Weyltype representation of the starproduct and of the properties of the crossWigner transform, which appears as an intertwining operator. MSC (2000): 47G30, 81S10