complete sets of complex zernike moment invariants and the role of the pseudoinvariants moment invariants are important shape descriptors in computer vision in this paper rules are presented to form complete sets of rotational invariants of arbitrary order given complex zernike moments the relevance of the pseudoinvariants is shown by inverting the rotational invariants to reconstruct the normalized image pattern

accurate computation of zernike moments in polar coordinates an algorithm for high precision numerical computation of zernike moments is presented the algorithm based on the introduced polar pixel tiling scheme does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on cartesian coordinates this yields a dramatic improvement of the zernike moments accuracy in terms of their reconstruction and invariance properties the introduced image tiling requires an interpolation algorithm which turns out to be of the second order importance compared to the discretization error various comparisons are made between the accuracy of the proposed method and that of commonly used techniques the results reveal the great advantage of our approach

on the inter conversion between hermite and laguerre local image expansions the nice relationship existing among the hermite gauss and the laguerre gauss image expansions whose basis functions span the same signal space is investigated as a result a novel efficient method for cartesian to polar coordinate inter conversion especially suited for dedicated hardware realization is proposed applications to local image rotation based on the simple steerability of the laguerre gauss expansion and to local image analysis based on gaussian derivatives are considered in detail a possible fixed point realization of the proposed inter conversion scheme is discussed

generalized variational inclusions and generalized resolvent equations in banach spaces in this paper we introduce and study generalized variational inclusions and generalized resolvent equations in real banach spaces it is established that generalized variational inclusion problems in uniformly smooth banach spaces are equivalent to fixed point problems we also establish a relationship between generalized variational inclusions and generalized resolvent equations by using nadler s fixed point theorem and resolvent operator technique for m accretive mappings in real banach spaces we propose an iterative algorithm for computing the approximate solutions of generalized variational inclusions the iterative algorithms for finding the approximate solutions of generalized resolvent equations are also proposed the convergence of approximate solutions of generalized variational inclusions and generalized resolvent equations obtained by the proposed iterative algorithms is also studied our results are new and represent a significant improvement of previously known results some special cases are also discussed

iterative process with errors of nonlinear equations involvingm accretive operators abstract let x be a uniformly smooth and uniformly convex banach space and t d t x x be an m accretive operator with the domain d t and the range r t for any given f x we prove that the mann and ishikawa type iterative sequences with errors converge strongly to the unique solution of the equation x tx f where t may not be lipschitz some related results deal with the convergence of mann and ishikawa type iterative sequences with errors for approximating a solution of a continuous dissipative operator equation

equivalent forms of a generalized kkm theorem and their applications in this paper we study various types of variational relation problems we establish the existence of solutions for these types of problems and point out some important particular cases and their applications we also show that some existence theorems of solution for these types of problems and some existence theorems of variational inclusion problems are equivalent to a generalized kkm theorem applying our results we obtain existence theorems of common fixed point generalized maximal element theorems a generalized coincidence theorems and a section theorem

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

systems of quasi variational relations with applications in this paper we introduce a system of quasi variational relations in short sqvr and present several examples which show that it is a very general and unified model of several problems we establish the existence of solutions of sqvp in general and several other problems in particular as an application of our results we derive maximal element theorems and a collectively fixed point theorem for a family of multivalued maps as further applications we study ky fan type inequality inclusion problem for vector valued bifunctions which includes constrained nash equilibrium problem as a special case we also present a common fixed point theorem for a family of multivalued maps the results of this paper improve and generalize several known results on system of quasi equilibrium problems system of quasi variational inclusions constrained nash equilibrium problem collectively fixed point theorem and kkm type theorems for a family of multivalued maps our results also contain several results which appeared in recent literature

iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities in this paper we study iterative algorithms for finding approximate solutions of completely generalized strongly nonlinear quasivariational inequalities which include as a special case some known results in this field our results are the extension and improvements of the results of siddiqi and ansari ding and zeng

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

auxiliary principle for generalized mixed variational like inequalities abstract in this paper we use the auxiliary principle technique to prove the existence of a solution of some new classes of variational inequalities which are called the generalized mixed variational like inequalities this technique is used to analyze an iterative algorithm several special cases which can be obtained from our main result are also discussed

a perturbed algorithm for variational inclusions a perturbed method for solving a new class of variational inclusions is presented and a convergence result which includes as a special case some known results in this field is given

ekeland type variational principle with applications to quasi variational inclusion problems abstract in this paper we study the ekeland type variational principle a caristi kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces by using these results we establish some existence results for solutions of quasi variational inclusion problems quasi optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces

maximum likelihood orientation estimation of 1 d patterns in laguerre gauss subspaces a method for measuring the orientation of linear 1 d patterns based on a local expansion with laguerre gauss circular harmonic lg ch functions is presented it lies on the property that the polar separable lg ch functions span the same space as the 2 d cartesian separable hermite gauss 2 d hg functions exploiting the simple steerability of the lg ch functions and the peculiar block linear relationship among the two expansion coefficients sets maximum likelihood ml estimates of orientation and cross section parameters of 1 d patterns are obtained projecting them in a proper subspace of the 2 d hg family it is shown in this paper that the conditional ml solution derived by elimination of the cross section parameters surprisingly yields the same asymptotic accuracy as the ml solution for known cross section parameters the accuracy of the conditional ml estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials a thorough proof of the key relationship between the lg ch and the 2 d hg expansions is also provided

mann and ishikawa type perturbed iterative algorithms for generalized quasivariational inclusions abstract in this paper we introduce a class of generalized quasivariational inclusions and show its equivalence with a class of fixed point problems by making use of the properties of proximal maps using this equivalence we develop the mann and ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions further using fixed point techniques we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms our algorithms and results improve and generalize many known corresponding algorithms and results

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

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

multiresolution circular harmonic decomposition a dictionary of complex waveforms suited for multiresolution analysis and individually steerable by multiplication by a complex factor is presented it is based on circular harmonic wavelets chw and is useful for pattern analysis under rotations the main theoretical aspects of chws are illustrated and an example of application to motion estimation is provided

the holonomy lie algebras of neutral metrics in dimension four the lie algebra isomorphism between su 1 1 su 1 1 and o 2 2 is used to obtain a list of subalgebras of the latter the resulting list of 32 subalgebras is then examined on a case by case basis to see if each can be the lie algebra of the holonomy group of a neutral metric in four dimensions the conclusions taken in conjunction with previously known results furnish a classification of such lie subalgebras of o 2 2 with only one case remaining unresolved

local orientation analysis in images by means of the hermite transform we introduce new theoretical results on how the local differential structure in images can be described processed and coded efficiently by means of the hermite transform it is shown that the hermite transform can take many alternative forms all of which have their specific advantages the various forms of the hermite transform correspond to different ways of coding the local orientation in the image and we describe a systematic theory based on well known principles from vector spaces for deriving such alternative forms one specific case called the sampled hermite transform is shown to be especially interesting for adaptive image processing and coding an application in the field of adaptive noise reduction is included by way of illustration

complex derivative filters steerable filters are a valuable tool for various low level vision tasks in this paper we argue for the use of complex analysis in the context of 2 d steerable filters in particular we recommend the use of complex partial derivatives as a computational basis complex derivatives have a major advantage in comparison to real derivatives they show a canonical rotation behavior namely a rotation affects the derivative just by a multiplication with a complex unit number so the complex derivatives can be steered in a more elegant way and above that they are less expensive to compute we present several analytical formulas for common and new filter kernels in terms of complex derivatives further we relate the complex derivatives of a gaussian with the gauss laguerre transform and show that the gauss laguerre functions provide an optimal signal representation for local and smooth images we discuss various finite difference schemes for the realization of the derivatives and use them in practice in a first experiment we use a newly introduced filter kernel for anisotropic blurring the complex formalism offers an elegant way to locally adapt the shape and orientation of the kernel second we use the proposed filters as matched filters to detect vessels in retinal images

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

spaces of complex null geodesics in complex riemannian geometry the notion of a conlplex rienlanmianl 11 mcanifold meaning a complex 1 manifold with a nondegenerate complex quadratic form on each tangent space which varies holomorphically from point to point is briefly developed it is shown that provided ii 4 every such manifold locally arises canonically as the moduli space of all quadrics of a fixed normal bundle type in an associated space of comple x liull geodesics this relationship between local geometry and global complex analysis is stable under deformations introduction the present work provides a general framework analogous to but distinct from penrose s twistor correspondence penrose 15 atiyah et al 2 for the study of real analytic pseudo riemannian geometry on manifolds whose dimension exceeds three in which points of the original manifold correspond to compact complex submanifolds quadrics in an associated complex manifold the natural intermediate step in the construction is to consider complexification of the geometry leading to the notion of a complex riemannian manifold implicitly present for instance in the work of penrose in fact it is really the conformal structure that is of fundamental importance and so having briefly introduced holomorphic metrics in chapter i we proceed to establish the fundamental facts of holomorphic conformal geometry in chapter ii finally in chapter iii we develop our generalized twistor correspondence a brief historical note is in order a special case of this correspondence where the complex riemannian manifold is complex euclidean 4 space proved to be useful for the study of yang mills fields issenberg et at 7 witten 18 several years ago in the wake of this discovery the present author first sketched his ideas on the subject in 1979 in the informal twistor newsletter of the oxford mathematical institute a more fully developed version became the author s ph d thesis lebrun 10 which forms the basis of much of the present more refined paper several results are completely new however such as the theorems in 111 4 5 in dimension four some recent results have shown these notions to be of genuine physical interest within the last year a beguiling theory of the dirac manin 13 and wave lebrun 11 operators fitting neatly within this general framework has emerged for the present however we will examine only the big picture relegating this arguably more beautiful restricted case to treatment elsewhere received by the editors march 10 1982 1980 mathematics subject classification primary 32g10 53a30 secondary 32d15 53c15 53c22 83c99 d1983 american mathematical society 0002 9947 82 00001440 06 75

reforming the theory of invariant moments for pattern recognition abstract the relationship between the algebraic invariants and the fourier mellin spectrum of an image irradiance distribution is clarified and a new approach for generating the two dimensional 2d invariant moments is proposed fifty two invariant functions of the second to the ninth order image moments are tabulated which are invariant with respect to image translation shift orientation and size changes and can be used as library functions in computer programs for automatic image identification the invariant functions derived in this study are shown useful in a numerical example concerned with a character recognition model

the studies of systems of variational inclusions problems and variational disclusions problems with applications abstract in this paper we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems from these existence results we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

de rham wu decomposition of holomorphic riemannian manifolds it is shown that a de rham wu decomposition for holomorphic riemannian manifolds is obtained easily from the underlying real geometry of holomorphic riemannian manifolds by appealing to h wu s extension to pseudo riemannian manifolds of de rham s decomposition theorem

well posedness in the generalized sense for variational inclusion and disclusion problems and well posedness for optimization problems with constraint abstract in this paper we study the well posedness in the generalized sense for variational inclusion problems and variational disclusion problems the well posedness for optimization problems with variational inclusion problems variational disclusion problems and scalar equilibrium problems as constraint

the mann and ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings abstract the purpose of this paper is to introduce and study the existence of solutions and convergence of mann and ishikawa iterative processes for a class of variational inclusions with accretive type mappings in banach spaces the results presented in this paper extend and improve the corresponding results of 1 9

advanced in plane rotation invariant correlation filters advanced correlation filter synthesis algorithms to achieve rotation invariance are described we use a specified form for the filter as the rotation invariance constraint and derive a general closed form solution for a multiclass rotation invariant filter that can recognize a number of different objects by requiring the filter to minimize the average correlation plane energy we produce a multiclass rotation invariant ri ri mace filter which controls correlation plane sidelobes and improves discrimination against false targets to improve noise performance we require the filter to minimize a weighted sum of correlation plane signal and noise energy initial test results of all filters are provided

discretization of parametrizable signal manifolds transformation invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold in particular the estimation of the distances between a transformed query signal and several transformation manifolds representing different classes provides essential information for the classification of the signal in many applications the computation of the exact distance to the manifold is costly whereas an efficient practical solution is the approximation of the manifold distance with the aid of a manifold grid in this paper we consider a setting with transformation manifolds of known parameterization we first present an algorithm for the selection of samples from a single manifold that permits to minimize the average error in the manifold distance estimation then we propose a method for the joint discretization of multiple manifolds that represent different signal classes where we optimize the transformation invariant classification accuracy yielded by the discrete manifold representation experimental results show that sampling each manifold individually by minimizing the manifold distance estimation error outperforms baseline sampling solutions with respect to registration and classification accuracy performing an additional joint optimization on all samples improves the classification performance further moreover given a fixed total number of samples to be selected from all manifolds an asymmetric distribution of samples to different manifolds depending on their geometric structures may also increase the classification accuracy in comparison with the equal distribution of samples

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

on the independence of rotation moment invariants abstract the problem of the independence and completeness of rotation moment invariants is addressed in this paper first a general method for constructing invariants of arbitrary orders by means of complex moments is described as a major contribution of the paper it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated the method how to construct such a basis and how to prove its independence and completeness is presented some practical impacts of the new results are mentioned at the end of the paper

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

perturbed algorithms and sensitivity analysis for a general class of variational inclusions in the present paper we study a perturbed iterative method for solving a general class of variational inclusions an existence result which generalizes some known results in this field a convergence result and a new iterative method are given we also prove the continuity of the perturbed solution to a parametric variational inclusion problem several special cases are discussed

the real geometry of holomorphic four metrics the real geometry of holomorphic four metrics is investigated the almost product and complex structures associated with the real eight metrics corresponding to the real and imaginary parts of the holomorphic metrics are studied it is shown that half flat holomorphic metrics and the corresponding real eight metrics are associated with integrable almost product complex and hyper kahler structures real and complex local coordinate descriptions are presented

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities

the mann process for perturbed m accretive operators in banach spaces this work was carried out while this author was visiting the university ofalabama in huntsville underthe nancial support by the lg yonam foundation 1998 and he would like to thank professor claudio h morales for his hospitality in the department of mathematics 0362 546x 01 see front matter 2001 elsevier science ltd all rights reserved pii s0362 546x 00 00115 2

simultaneous variational relation problems and related applications the aim of this paper is to present an existence result of the simultaneous variational relation problem as applications of our result we study the existence theorems of solution for the equilibrium problem variational inclusions problem common fixed points and the minimax theorem

some results on systems of quasi variational inclusion problems and systems of generalized quasi variational inclusion problems abstract in this paper we study systems of quasi variational inclusion problem and systems of quasi variational disclusion problem from the existence theorems of solution for these two types of problems we study various types of systems of quasi variational inclusion problems systems of quasi equilibrium problems systems of quasi kkm theorem abstract economics and system of kkm theorem we also show their equivalent relations we study further existence theorems of solution for generalized quasi variational inclusion problem our results are different from any existence result in the literature

the solution existence of general variational inclusion problems we propose general variational inclusion problems which are slightly different from corresponding problems considered in several recent papers in the literature and show that they are advantageous sufficient conditions for the solution existence are established as applications we derive consequences for several special cases of variational inclusion problems quasioptimization problems equilibrium problems and implicit variational inequalities and show that they improve the results of some recent existing papers

an fft based technique for translation rotation and scale invariant image registration this correspondence discusses an extension of the well known phase correlation technique to cover translation rotation and scaling fourier scaling properties and fourier rotational properties are used to find scale and rotational movement the phase correlation technique determines the translational movement this method shows excellent robustness against random noise

a detail based method for linear full reference image quality prediction in this paper a novel full reference method is proposed for image quality assessment using the combination of two separate metrics to measure the perceptually distinct impact of detail losses and of spurious details to this purpose the gradient of the impaired image is locally decomposed as a predicted version of the original gradient plus a gradient residual it is assumed that the detail attenuation identifies the detail loss whereas the gradient residuals describe the spurious details it turns out that the perceptual impact of detail losses is roughly linear with the loss of the positional fisher information while the perceptual impact of the spurious details is roughly proportional to a logarithmic measure of the signal to residual ratio the affine combination of these two metrics forms a new index strongly correlated with the empirical differential mean opinion score dmos for a significant class of image impairments as verified for three independent popular databases the method allowed alignment and merging of dmos data coming from these different databases to a common dmos scale by affine transformations unexpectedly the dmos scale setting is possible by the analysis of a single image affected by additive noise

minimum distance between pattern transformation manifolds algorithm and applications transformation invariance is an important property in pattern recognition where different observations of the same object typically receive the same label this paper focuses on a transformation invariant distance measure that represents the minimum distance between the transformation manifolds spanned by patterns of interest since these manifolds are typically nonlinear the computation of the manifold distance md becomes a nonconvex optimization problem we propose representing a pattern of interest as a linear combination of a few geometric functions extracted from a structured and redundant basis transforming the pattern results in the transformation of its constituent parts we show that when the transformation is restricted to a synthesis of translations rotations and isotropic scalings such a pattern representation results in a closed form expression of the manifold equation with respect to the transformation parameters the md computation can then be formulated as a minimization problem whose objective function is expressed as the difference of convex functions dc this interesting property permits optimally solving the optimization problem with dc programming solvers that are globally convergent we present experimental evidence which shows that our method is able to find the globally optimal solution outperforming existing methods that yield suboptimal solutions

two dimensional approach to full reference image quality assessment based on positional structural information a method for full reference visual quality assessment based on the 2 d combination of two diverse metrics is described the first metric is a measure of structural information loss based on the fisher information about the position of the structures in the observed images the second metric acts as a categorical indicator of the type of distortion that images underwent these two metrics constitute the inner state of a virtual cognitive model viewed as a system whose output is the automatic visual quality estimate the use of a 2 d metric fills the intrinsic incompleteness of methods based on a single metric while providing consistent response across different image impairment factors and blind distortion classification capability with a modest computational overhead the high accuracy and robustness of the method are demonstrated through cross validation experiments

iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo contractive mappings in banach spaces abstract in this article we prove some new convergence theorems of the ishikawa and mann iteration sequences for strongly accretive and strongly pseudo contractive mappings by using the new inequality and the new approximation methods our main results improve and extend the corresponding results of j math anal appl 151 1990 453 461 proc amer math soc 120 1994 545 551 j math appl 192 1995 502 518 j math anal appl 174 1993 441 449 acta appl math 32 1993 183 196 nonlinear anal tma 24 1995 981 987 j math anal appl 178 1993 9 21 proc amer math soc 125 6 1997 1705 1709

estimation of global motion parameters by complex linear regression global motion is very likely to occur in image sequences analysis for example it arises if the observer is moving during the sequence acquisition ego motion our aim is to get a simple method to estimate in a reliable may a set of parameters that can take into account the presence of a global motion component using only local information the novelty of our approach is in regarding spatial shift change of scale and rotation corresponding to usual camera effects such as pan and zoom as a two dimensional 2 d doppler effect the mathematical treatment is carried on in the complex plane so that the results can be easily deduced as an extension of the one dimensional 1 d case in this way we obtain simple expressions well suited for a practical realization of the estimate the method has been experimentally validated by both real pictures with a synthetic motion and real image sequences

maximum likelihood localization of 2 d patterns in the gauss laguerre transform domain theoretic framework and preliminary results usual approaches to localization i e joint estimation of position orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures which allow for position estimation independent of scale and orientation in this paper a maximum likelihood method for pattern localization working in the gauss laguerre transform glt domain is presented the glt is based on an orthogonal family of circular harmonic functions with specific radial profiles which permits optimum joint estimation of position and scale rotation parameters looking at the maxima of a gauss laguerre likelihood map the fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the cramer rao lower bound application of the ml estimation method is discussed and an example is provided