coherent multiscale image processing using dual tree quaternion wavelets the dual tree quaternion wavelet transform qwt is a new multiscale analysis tool for geometric image features the qwt is a near shift invariant tight frame representation whose coefficients sport a magnitude and three phases two phases encode local image shifts while the third contains image texture information the qwt is based on an alternative theory for the 2d hilbert transform and can be computed using a dual tree filter bank with linear computational complexity to demonstrate the properties of the qwt s coherent magnitude phase representation we develop an efficient and accurate procedure for estimating the local geometrical structure of an image we also develop a new multiscale algorithm for estimating the disparity between a pair of images that is promising for image registration and flow estimation applications the algorithm features multiscale phase unwrapping linear complexity and sub pixel estimation accuracy

image analysis by bessel fourier moments in this paper we proposed a new set of moments based on the bessel function of the first kind named bessel fourier moments bfms which are more suitable than orthogonal fourier mellin and zernike moments for image analysis and rotation invariant pattern recognition compared with orthogonal fourier mellin and zernike polynomials of the same degree the new orthogonal radial polynomials have more zeros and these zeros are more evenly distributed the bessel fourier moments can be thought of as generalized orthogonalized complex moments theoretical and experimental results show that the bessel fourier moments perform better than the orthogonal fourier mellin and zernike moments ofmms and zms in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions

embedding formulae in diffraction theory embedding formulae are remarkable as they allow one to decompose scattering problems apparently dependent upon several angular variables angles of incidence and observation into those dependent upon fewer angular variables in terms of facilitating rapid computations across considerable parameter regimes this is a considerable advantage our aim is to derive embedding formulae for scattering and diffraction problems in acoustics electromagnetism and elasticity here we construct a general approach to formulating and using embedding formulae we do this using complementary approaches overly singular states and a physical interpretation in terms of sources the crucial point we identify is the form of the auxiliary state used in the reciprocal theorem this is unphysically singular at the edge and is reminiscent of weight function methods used in fracture mechanics illustrative implementations of our approach are given using wiener hopf techniques for semi infinite model problems in both elasticity and acoustics we also demonstrate our approach using a numerical example from acoustics and we make connections with high frequency asymptotic methods

orthogonal moments based on exponent functions exponent fourier moments abstract in this paper we propose a new set of orthogonal moments based on exponent functions named exponent fourier moments efms which are suitable for image analysis and rotation invariant pattern recognition compared with zernike polynomials of the same degree the new radial functions have more zeros and these zeros are evenly distributed this property make efms have strong ability in describing image unlike zernike moments the kernel of computation of efms is extremely simple theoretical and experimental results show that exponent fourier moments perform very well in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions the exponent fourier moments can be thought of as generalized orthogonal complex moments

quadratic algebra associated with rational calogero moser models classical calogero moser models with rational potential are known to be superintegrable that is on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom they possess an additional set of r 1 algebraically and functionally independent globally defined conserved quantities at the quantum level kuznetsov uncovered the existence of a quadratic algebrastructure as an underlying key for superintegrability for the models based on a type root systems here we demonstrate in a universal way the quadratic algebrastructure for quantum rational calogero moser models based on any root systems

quaternion polar harmonic fourier moments for color images abstract this paper proposes quaternion polar harmonic fourier moments qphfm for color image processing and analyzes the properties of qphfm after extending chebyshev fourier moments chfm to quaternion chebyshev fourier moments qchfm comparison experiments including image reconstruction and color image object recognition on the performance of qphfm and quaternion zernike moments qzm quaternion pseudo zernike moments qpzm quaternion orthogonal fourier mellin moments qofmm qchfm and quaternion radial harmonic fourier moments qrhfm are carried out experimental results show qphfm can achieve an ideal performance in image reconstruction and invariant object recognition in noise free and noisy conditions in addition this paper discusses the importance of phase information of quaternion orthogonal moments in image reconstruction

two dimensional polar harmonic transforms for invariant image representation this paper introduces a set of 2d transforms based on a set of orthogonal projection bases to generate a set of features which are invariant to rotation we call these transforms polar harmonic transforms phts unlike the well known zernike and pseudo zernike moments the kernel computation of phts is extremely simple and has no numerical stability issue whatsoever this implies that phts encompass the orthogonality and invariance advantages of zernike and pseudo zernike moments but are free from their inherent limitations this also means that phts are well suited for application where maximal discriminant information is needed furthermore phts make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application

quantum versus classical integrability in calogero moser systems calogero moser systems are classical and quantum integrable multiparticle dynamics defined for any root system the quantum calogero systems having 1 q2 potential and a confining q2 potential and the sutherland systems with 1 sin2q potentials have integer energy spectra characterized by the root system various quantities of the corresponding classical systems e g minimum energy frequencies of small oscillations the eigenvalues of the classical lax pair matrices etc at the equilibrium point of the potential are investigated analytically as well as numerically for all root systems to our surprise most of these classical data are also integers or they appear to be quantized to be more precise these quantities are polynomials of the coupling constant s with integer coefficients the close relationship between quantum and classical integrability in calogero moser systems deserves fuller analytical treatment which would lead to better understanding of these systems and of integrable systems in general

recognitive aspects of moment invariants moment invariants are evaluated as a feature space for pattern recognition in terms of discrimination power and noise tolerance the notion of complex moments is introduced as a simple and straightforward way to derive moment invariants through this relation properties of complex moments are used to characterize moment invariants aspects of information loss suppression and redundancy encountered in moment invariants are investigated and significant results are derived the behavior of moment invariants in the presence of additive noise is also described

image analysis by tchebichef moments this paper introduces a new set of orthogonal moment functions based on the discrete tchebichef polynomials the tchebichef moments can be effectively used as pattern features in the analysis of two dimensional images the implementation of the moments proposed in this paper does not involve any numerical approximation since the basis set is orthogonal in the discrete domain of the image coordinate space this property makes tchebichef moments superior to the conventional orthogonal moments such as legendre moments and zernike moments in terms of preserving the analytical properties needed to ensure information redundancy in a moment set the paper also details the various computational aspects of tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction

image analysis by krawtchouk moments a new set of orthogonal moments based on the discrete classical krawtchouk polynomials is introduced the krawtchouk polynomials are scaled to ensure numerical stability thus creating a set of weighted krawtchouk polynomials the set of proposed krawtchouk moments is then derived from the weighted krawtchouk polynomials the orthogonality of the proposed moments ensures minimal information redundancy no numerical approximation is involved in deriving the moments since the weighted krawtchouk polynomials are discrete these properties make the krawtchouk moments well suited as pattern features in the analysis of two dimensional images it is shown that the krawtchouk moments can be employed to extract local features of an image unlike other orthogonal moments which generally capture the global features the computational aspects of the moments using the recursive and symmetry properties are discussed the theoretical framework is validated by an experiment on image reconstruction using krawtchouk moments and the results are compared to that of zernike pseudo zernike legendre and tchebyscheff moments krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants an object recognition experiment shows krawtchouk moment invariants perform significantly better than hu s moment invariants in both noise free and noisy conditions

quaternion polar complex exponential transform for invariant color image description moments and moment invariants have been widely used as a basic feature descriptors in image analysis pattern recognition and image retrieval however they are mainly used to deal with the binary or gray scale images which lose some significant color information recently quaternion techniques were introduced to conventional image moments including fourier mellin moments zernike pseudo zernike moments and bessel fourier moments etc for describing color images and some quaternion moment and moment invariants were developed but the conventional image moments usually cannot effectively capture the image information especially the edges besides the kernel computation of them involves computation of a number of factorial terms which inevitably cause the numerical stability of these moments based on effective polar complex exponential transform pcet and algebra of quaternions we introduced the quaternion polar complex exponential transform qpcet for describing color images in this paper which can be seen as the generalization of pcet for gray level images it is shown that the qpcets can be obtained from the pcet of each color channel we derived and analyzed the rotation scaling and translation rst invariant property of qpcet we also discussed the problem of color image retrieval using qpcet experimental results are provided to illustrate the efficiency of the proposed color image descriptors

embedding formulae for diffraction by rational wedge and angular geometries embedding is the process of taking the far field directivity from a diffraction problem or problems involving line sources or multipoles placed at a sharp edge and then constructing the far field for the same geometry for more general incidence using only this canonical problem s thus far embedding has been limited to planar parallel scattering surfaces for instance collections of parallel cracks or slits it appeared that there was a fundamental limitation to embedding disallowing its use for angular structures in this article we overcome this limitation and demonstrate the use of embedding upon wedge diffraction problems and upon a simple polygonal shape a limitation is that the final formulae are for rational wedge angles

efficient implementation of quaternion fourier transform convolution and correlation by 2 d complex fft the concepts of quaternion fourier transform qft quaternion convolution qcv and quaternion correlation which are based on quaternion algebra have been found to be useful for color image processing however the necessary computational algorithms and their complexity still need some attention we develop efficient algorithms for qft qcv and quaternion correlation the conventional complex two dimensional 2 d fourier transform ft is used to implement these quaternion operations very efficiently with these algorithms we only need two complex 2 d fts to implement a qft six complex 2 d fts to implement a one side qcv or a quaternion correlation and 12 complex 2 d fts to implement a two side qcv and the efficiency of these quaternion operations is much improved meanwhile we also discuss two additional topics the first one is about how to use qft and qcv for quaternion linear time invariant qlti system analysis this topic is important for quaternion filter design and color image processing besides we also develop the spectrum product qcv it is an improvement of the conventional form of qcv for any arbitrary input functions it always corresponds to the product operation in the frequency domain it is very useful for quaternion filter design

fast algorithm for point pattern matching invariant to translations rotations and scale changes abstract based on 2 d cluster approach a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters scaling s and rotation on a two parameter space s experiments are conducted both on real and synthetic data the experimental results show that the proposed matching algorithm can handle translation rotation and scaling differences under noisy or distorted condition the computational time is just about 0 5 s for 50 to 50 point matching on sun 4 workstation

weinstein s diffraction problem embedding formula and spectral equation in parabolic approximation a short wave problem of reflection and radiation by an open end of a two dimensional planar waveguide is studied the incident mode is assumed to have frequency close to the cut off the problem is studied in the parabolic approximation a recently developed approach based on the embedding formula and the spectral equation for the directivity of an edge green s function is applied to the problem

hypercomplex fourier transforms of color images fourier transforms are a fundamental tool in signal and image processing yet until recently there was no definition of a fourier transform applicable to color images in a holistic manner in this paper hypercomplex numbers specifically quaternions are used to define a fourier transform applicable to color images the properties of the transform are developed and it is shown that the transform may be computed using two standard complex fast fourier transforms the resulting spectrum is explained in terms of familiar phase and modulus concepts and a new concept of hypercomplex axis a method for visualizing the spectrum using color graphics is also presented finally a convolution operational formula in the spectral domain is discussed

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

diffraction of elastic waves by a penny shaped crack analytical and numerical results the diffraction of time harmonic stress waves by a penny shaped crack in an infinite elastic solid is an important problem in fracture mechanics and in the theory of the ultrasonic inspection of materials martin proc r soc lond a 378 263 1981 has proved that the corresponding linear boundary value problem has precisely one solution and that this solution can be constructed by solving a two dimensional fredholm integral equation of the second kind however this integral equation has a complicated matrix kernel and the components of its vector solution are coupled the main purpose of the present paper is to show how martin s integral equation can be explicitly solved in terms of a sequence of functions each of which satisfies a very simple scalar integral equation of the second kind this simplification may be made for any incident wave for an incident plane wave further simplifications are possible we show that the solution at an arbitrary angle of incidence can be derived from the solution at a particular angle of incidence namely grazing incidence the resulting computational procedure is especially attractive if only the stressintensity factors or the far field displacements are required finally we present some numerical results for the scattering of a p wave at normal incidence and an sv wave at oblique incidence and compare these with those of other authors

scattering by cracks beneath fluid solid interfaces abstract the scattering of incident plane elastic or fluid body waves and interfacial waves by an arbitrarily orientated subsurface crack is considered the crack lies in an infinite elastic half space that is coupled to an overlying fluid half space material parameters relevant for water metal and water rock combinations are taken and far field scattering patterns are given these demonstrate beam formation along critical angles for light or moderate fluid coupling it is shown that the beams form along different critical angles depending upon the magnitude of the coupling in addition reciprocity relations relating the far field scattering coefficients viewed along an angle and generated by one type of plane wave incident along to the scattering coefficient viewed along generated by another plane wave incident along are found reciprocity relations involving interfacial waves are also given power flow theorems are derived these relate the time averaged scattered power to a combination of far field scattering coefficients this is used to determine the proportion of scattered power converted into the different types of scattered wave the reciprocity and power flow theorems provide a powerful consistency check upon the numerical accuracy of the results the boundary value problem is recast as a system of coupled integro differential equations for the unknown jump in displacement across the crack faces these integral equations are solved in an efficient and fast numerical manner by performing the integrations over the crack faces analytically thus reducing the computational effort substantially

quaternion moment and its invariants for color object classification moment invariants are important shape descriptors in computer vision in this study we propose new sets of quatemion moment descriptors for color image they are constructed in the quaternion framework and are an extension of complex moment invariants for grayscale images this is a useful tool in color image processing and color object recognition tasks that require the similarity invariance the advantage of the proposed quatemion moment invariants is that they can not only process color image in a holistic manner but also grayscale one in addition the computational complexity of the proposed method is much lower than the quaternion zernike moments defined in the polar coordinates an example of using the quaternion moment invariants as pattern features for a color object classification application is given theoretical and experimental results show that the proposed descriptors perform better than the other competing moment based methods c 2014 elsevier inc all rights reserved

quaternion bessel fourier moments and their invariant descriptors for object reconstruction and recognition in this paper the quaternion bessel fourier moments are introduced the significance of phase information in quaternion bessel fourier moments is investigated and an accurate estimation method for rotation angle is described furthermore a new set of invariant descriptors based on the magnitude and the phase information of quaternion bessel fourier moments is derived experimental results show that quaternion bessel fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion zernike moments quaternion pseudo zernike moments and quaternion orthogonal fourier mellin moments in addition the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments the proposed invariant descriptors show also better robustness to geometric and photometric transformations quaternion bessel fourier moments for color image reconstruction and recognition an accurate estimation method for rotation angle throughout quaternion moments the invariant descriptor using the moment magnitudes and phase coefficients

algebraic linearization of dynamics of calogero type for any coxeter group calogero moser systems can be generalized for any root system including the noncrystallographic cases the algebraic linearization of the generalized calogero moser systems and of their quadratic respectively quartic perturbations are discussed

explicit solutions of the classical calogero and sutherland systems for any root system explicit solutions of the classical calogero rational with without harmonic confining potential and sutherland trigonometric potential systems is obtained by diagonalization of certain matrices of simple time evolution the method works for calogero sutherland systems based on any root system it generalizes the well known results by olshanetsky and perelomov for the a type root systems explicit solutions of the rational and trigonometric higher hamiltonian flows of the integrable hierarchy can be readily obtained in a similar way for those based on the classical root systems

quaternion fourier mellin moments for color images the quaternion fourier mellin moments for describing color images are introduced which can be seen as the generalization of traditional fourier mellin moments for gray level images then the quaternion fourier mellin moment invariants are derived which could be a useful tool in color object recognition tasks that require the similarity invariance in addition the problem of color image registration using quaternion fourier mellin moments is discussed the registration method can match color images differing in rotation and scaling the advantage of our method is that it can process color image directly without losing color information experimental results validate the effectiveness of the method we proposed