wavelet domain blur invariants for image analysis radiometric degradation is a common problem in the image acquisition part of many applications there is much research carried out in an effort to deblur such images however it has been proven that it is not always necessary to go through a burdensome process of deblurring to tackle this problem different blur invariant descriptors have been proposed so far which are either in the spatial domain or based on the properties available in the fourier domain in this paper wavelet domain blur invariants are proposed for the first time for discrete 2 d signals these descriptors which are invariant to centrally symmetric blurs inherit the advantages that this domain provides it is also proven that the spatial domain blur invariants are a special version of the proposed invariants the performance of these invariants will be demonstrated through experiments

projection operators and moment invariants to image blurring in this paper we introduce a new theory of blur invariants blur invariants are image features which preserve their values if the image is convolved by a point spread function psf of a certain class we present the invariants to convolution with an arbitrary n fold symmetric psf both in fourier and image domain we introduce a notion of a primordial image as a canonical form of all blur equivalent images it is defined in spectral domain by means of projection operators we prove that the moments of the primordial image are invariant to blur and we derive recursive formulae for their direct computation without actually constructing the primordial image we further prove they form a complete set of invariants and show how to extent their invariance also to translation rotation and scaling we illustrate by simulated and real data experiments their invariance and recognition power potential applications of this method are wherever one wants to recognize objects on blurred images

quantum symmetric kac moody pairs the present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable kac moody algebras the resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras they give rise to triangular decompositions including a quantum analog of the iwasawa decomposition and they can be written explicitly in terms of generators and relations moreover their centers and their specializations are determined the constructions follow g letzter s theory of quantum symmetric pairs for semisimple lie algebras the main additional ingredient is the classification of involutive automorphisms of the second kind of symmetrizable kac moody algebras due to kac and wang the resulting theory comprises various classes of examples which have previously appeared in the literature such as q onsager algebras and the twisted q yangians introduced by molev ragoucy and sorba

registration of images with n fold dihedral blur in this paper we extend our recent registration method designed specifically for registering blurred images the original method works for unknown blurs assuming the blurring point spread function psf exhibits an n fold rotational symmetry here we also generalize the theory to the case of dihedrally symmetric blurs which are produced by the psfs having both rotational and axial symmetries such kind of blurs are often found in unfocused images acquired by digital cameras as in out of focus shots the psf typically mimics the shape of the shutter aperture this makes our registration algorithm particularly well suited in applications where blurred image registration must be used as a preprocess step of an image fusion algorithm and where common registration methods fail due to the amount of blur we demonstrate that the proposed method leads to an improvement of the registration performance and we show its applicability to real images by providing successful examples of blurred image registration followed by depth of field extension and multichannel blind deconvolution

a blur robust descriptor with applications to face recognition understanding the effect of blur is an important problem in unconstrained visual analysis we address this problem in the context of image based recognition by a fusion of image formation models and differential geometric tools first we discuss the space spanned by blurred versions of an image and then under certain assumptions provide a differential geometric analysis of that space more specifically we create a subspace resulting from convolution of an image with a complete set of orthonormal basis functions of a prespecified maximum size that can represent an arbitrary blur kernel within that size and show that the corresponding subspaces created from a clean image and its blurred versions are equal under the ideal case of zero noise and some assumptions on the properties of blur kernels we then study the practical utility of this subspace representation for the problem of direct recognition of blurred faces by viewing the subspaces as points on the grassmann manifold and present methods to perform recognition for cases where the blur is both homogenous and spatially varying we empirically analyze the effect of noise as well as the presence of other facial variations between the gallery and probe images and provide comparisons with existing approaches on standard data sets

blur identification by the method of generalized cross validation the point spread function psf of a blurred image is often unknown a priori the blur must first be identified from the degraded image data before restoring the image generalized cross validation gcv is introduced to address the blur identification problem the gcv criterion identifies model parameters for the blur the image and the regularization parameter providing all the information necessary to restore the image experiments are presented which show that gvc is capable of yielding good identification results a comparison of the gcv criterion with maximum likelihood ml estimation shows the gcv often outperforms ml in identifying the blur and image model parameters

the revised fundamental theorem of moment invariants a revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by m k hu 1962 is presented the correction affects neither similitude scale nor rotation invariants derived using the original theorem but it does affect features invariant to general linear transformations four of the latter invariants were presented originally by hu these are revised to take the correction to the fundamental theorem into account furthermore these four invariants are combined to yield three new invariants which are additionally invariant to changes in the illumination of an image

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

the method of normalization to determine invariants the determination of invariant characteristics is an important problem in pattern recognition many invariants are known which have been obtained either by normalization or by other methods this paper shows that the method of normalization is much more general and allows one to derive a lot of sets of invariants from the second list as well to this end the normalization method is generalized and is presented in such a way that it is easy to apply thus unifying and simplifying the determination of invariants furthermore this paper discusses the advantages and disadvantages of the invariants obtained by normalization their main advantage is that the normalization process provides us with a standard position of the object because of the generality of the method also new invariants are obtained such as normalized moments more stable than known ones legendre descriptors and zernike descriptors to affine transformations two dimensional fourier descriptors and affine moment invariants obtained by combining hu s moment invariants and normalized moments

combined blur translation scale and rotation invariant image recognition by radon and pseudo fourier mellin transforms the idea of scale and rotation invariant image recognition based on radon and fourier mellin transforms has been presented recently in this paper we extend the previous work and propose a new method to construct a set of combined blur translation scale and rotation invariants using radon and pseudo fourier mellin transforms named radon and pseudo fourier mellin invariants rpfmi the proposed method is robust to additive white noise as a result of summing pixel values to generate projections in the radon transform step we also present a mathematical framework of obtaining the radon and pseudo fourier mellin transforms of blurred images and a framework of deriving the combined blur scale and rotation invariants theoretical and experimental results show the superiority of the proposed method and its robustness to additive white noise in comparison with some recent methods

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

scaling and rotation invariant analysis approach to object recognition based on radon and fourier mellin transforms various types of orthogonal moments have been widely used for object recognition and classification however these moments do not natively possess scaling invariance essential image normalization and binarization prior to moments extraction will lead to error of resampling and requantifying this paper describes a new scaling and rotation invariant analysis method for object recognition in the proposed method the radon transform is utilized to project the image onto projection space to convert the rotation of the original image to a translation of the projection in the angle variable and the scaling of the original image to a scaling of the projection in the spatial variable together with an amplitude scaling of the projection and then the fourier mellin transform is applied to the result to convert the translation in the angle variable and the scaling in the spatial variable as well as the amplitude scaling of the projection to a phase shift and an amplitude scaling respectively in order to achieve a set of completely invariant descriptors a rotation and scaling invariant function is constructed a k nearest neighbors classifier is employed to implement classification theoretical and experimental results show the high classification accuracy of this approach as a result of using the rotation and scaling invariant function instead of image binarization and normalization it is also shown that this method is relatively robust in the presence of white noise

determination of blur and affine combined invariants by normalization the determination of invariant characteristics is an important problem in pattern recognition in many situations images to be processed are usually subjected to geometric distortion and or blur degradation in this paper we introduce an approach to derive blur and affine combined invariants bai firstly we normalize the image to a standard form by using blur invariant moments as normalization constraints then we construct the blur and affine combined invariants at the standard form using the method proposed in this paper a set of blur and affine combined invariant features can be obtained easily and effectively several experimental results are presented to illustrate the performance of the invariants for simultaneously affine deformed and blur degraded images

blur invariants constructed from arbitrary moments this paper deals with moment invariants with respect to image blurring it is mainly a reaction to the works of zhang and chen recently published in these transactions we present a general method on how to construct blur invariants from arbitrary moments and show that it is no longer necessary to separately derive the invariants for each polynomial basis we show how to discard dependent terms in blur invariants definition and discuss a proper implementation of the invariants in orthogonal bases using recurrent relations an example for legendre moments is given

on the center of quantized enveloping algebras abstract letube a quasitriangular hopf algebra one may use ther matrix ofuin order to construct scalar invariants of knots analogously reshetikhin wrote down tangle invariants which take their values in the center ofu reshetikhin s expressions thus define central elements inu we prove here an identity characterizing some of these elements whenuis a quantized enveloping algebra as an application we give a proof for a statement of faddeev reshetikhin and takhtadzhyan concerning the center of a quantized enveloping algebra

image normalization by complex moments the role of moments in image normalization and invariant pattern recognition is addressed the classical idea of the principal axes is analyzed and extended to a more general definition the relationship between moment based normalization moment invariants and circular harmonics is established invariance properties of moments as opposed to their recognition properties are identified using a new class of normalization procedures the application of moment based normalization in pattern recognition is demonstrated by experiment

hyperspectral super resolution of locally low rank images from complementary multisource data remote sensing hyperspectral images hsis are quite often low rank in the sense that the data belong to a low dimensional subspace manifold this has been recently exploited for the fusion of low spatial resolution hsi with high spatial resolution multispectral images in order to obtain super resolution hsi most approaches adopt an unmixing or a matrix factorization perspective the derived methods have led to state of the art results when the spectral information lies in a low dimensional subspace manifold however if the subspace manifold dimensionality spanned by the complete data set is large i e larger than the number of multispectral bands the performance of these methods mainly decreases because the underlying sparse regression problem is severely ill posed in this paper we propose a local approach to cope with this difficulty fundamentally we exploit the fact that real world hsis are locally low rank that is pixels acquired from a given spatial neighborhood span a very low dimensional subspace manifold i e lower or equal than the number of multispectral bands thus we propose to partition the image into patches and solve the data fusion problem independently for each patch this way in each patch the subspace manifold dimensionality is low enough such that the problem is not ill posed anymore we propose two alternative approaches to define the hyperspectral super resolution through local dictionary learning using endmember induction algorithms we also explore two alternatives to define the local regions using sliding windows and binary partition trees the effectiveness of the proposed approaches is illustrated with synthetic and semi real data

blur identification using the bispectrum the authors propose inspecting the zero crossings in the central slice of the bispectrum of the observed image for blur identification this method is an extension of the classical methods for blur identification in which the power spectrum or the power cepstrum of the blurred image is applied to the bispectrum domain the proposed bispectrum based approach utilizes the ability of the bispectrum to suppress additive signal independent gaussian observation noise simulation results indicate that the method performs significantly better than the classical power spectrum based approach at low signal to noise ratios

combined blur and affine moment invariants and their use in pattern recognition abstract the paper is devoted to the recognition of objects and patterns deformed by imaging geometry as well as by unknown blurring we introduce a new class of features invariant simultaneously to blurring with a centrosymmetric psf and to affine transformation as we prove in the paper they can be constructed by combining affine moment invariants and blur invariants derived earlier combined invariants allow to recognize objects in the degraded scene without any restoration

registration of translated and rotated images using finite fourier transforms a well known method for image registration is based on a conventional correlation between phase only or whitened versions of the two images to be realigned the method covering rigid translational movements is characterized by an outstanding robustness against correlated noise and disturbances such as those encountered with nonuniform time varying illumination this correspondence discusses an extension of the method to cover both translational and rotational movements

recovering affine motion and defocus blur simultaneously motion in depth and or zooming cause defocus blur we show how the defocus blur in an image can be recovered simultaneously with affine motion we introduce the theory develop a solution method and demonstrate the validity of the theory and the solution by conducting experiments with real scenery

pattern recognition with moment invariants a comparative study and new results abstract moment invariants have been proposed as pattern sensitive features in classification and recognition applications in this paper the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data handwritten numerals and aircrafts the authors also present a detailed study of zernike and pseudo zernike moment invariants including a new procedure for deriving the moment invariants in addition the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants based on a comprehensive study with both handwritten numerals and aircraft data the authors show that the new method of deriving zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise

image features invariant with respect to blur abstract the paper is devoted to the feature based description of blurred images acquired by a linear shift invariant imaging system the proposed features are invariant with respect to blur this means with respect to the system point spread function are based on image moments and are calculated directly from the blurred image this way we are able to describe the original image without the psf identification and image restoration in many applications such as in image recognition from a database our approach is much more effective than the traditional blind restoration one the derivation of the blur invariants is the major theoretical result of the paper several experiments are presented to illustrate the efficiency of the invariants for blurred image description stability of the invariants with respect to additive random noise and boundary effect is also discussed and is shown to be sufficiently high

combined invariants to similarity transformation and to blur using orthogonal zernike moments the derivation of moment invariants has been extensively investigated in the past decades in this paper we construct a set of invariants derived from zernike moments which is simultaneously invariant to similarity transformation and to convolution with circularly symmetric point spread function psf two main contributions are provided the theoretical framework for deriving the zernike moments of a blurred image and the way to construct the combined geometric blur invariants the performance of the proposed descriptors is evaluated with various psfs and similarity transformations the comparison of the proposed method with the existing ones is also provided in terms of pattern recognition accuracy template matching and robustness to noise experimental results show that the proposed descriptors perform on the overall better

a novel sure based criterion for parametric psf estimation we propose an unbiased estimate of a filtered version of the mean squared error the blur sure stein s unbiased risk estimate as a novel criterion for estimating an unknown point spread function psf from the degraded image only the psf is obtained by minimizing this new objective functional over a family of wiener processings based on this estimated blur kernel we then perform nonblind deconvolution using our recently developed algorithm the sure based framework is exemplified with a number of parametric psf involving a scaling factor that controls the blur size a typical example of such parametrization is the gaussian kernel the experimental results demonstrate that minimizing the blur sure yields highly accurate estimates of the psf parameters which also result in a restoration quality that is very similar to the one obtained with the exact psf when plugged into our recent multi wiener sure let deconvolution algorithm the highly competitive results obtained outline the great potential of developing more powerful blind deconvolution algorithms based on sure like estimates

recognition of blurred images by the method of moments the article is devoted to the feature based recognition of blurred images acquired by a linear shift invariant imaging system against an image database the proposed approach consists of describing images by features that are invariant with respect to blur and recognizing images in the feature space the psf identification and image restoration are not required a set of symmetric blur invariants based on image moments is introduced a numerical experiment is presented to illustrate the utilization of the invariants for blurred image recognition robustness of the features is also briefly discussed

blur invariants a novel representation in the wavelet domain blur invariants in the wavelet domain are proposed for the first time in this paper wavelet domain blur invariants take advantage of several benefits that this domain provides i e different alternatives for wavelet function and analysis in different scales it is not required to model the blur system in order to extract the invariants it will be shown how the space domain blur invariants are a special case of the proposed invariants it will also be explained how the proposed invariants would not have the null space that their special case in the spatial domain have which limits their discriminative power the performance of these invariants will be demonstrated through experiments and compared to its counterpart which is defined in the spatial domain

degraded image analysis an invariant approach analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas the observed image is usually corrupted by blurring spatial degradations and random noise classical methods like blind deconvolution try to estimate the blur parameters and to restore the image we propose an alternative approach we derive the features for image representation which are invariant with respect to blur regardless of the degradation psf provided that it is centrally symmetric as we prove in the paper there exist two classes of such features the first one in the spatial domain and the second one in the frequency domain we also derive so called combined invariants which are invariant to composite geometric and blur degradations knowing these features we can recognize objects in the degraded scene without any restoration

identification and restoration of noisy blurred images using the expectation maximization algorithm a maximum likelihood approach to the blur identification problem is presented the expectation maximization algorithm is proposed to optimize the nonlinear likelihood function in an efficient way in order to improve the performance of the identification algorithm low order parametric image and blur models are incorporated into the identification method the resulting iterative technique simultaneously identifies and restores noisy blurred images

similarity transformation parameters recovery based on radon transform application in image registration and object recognition the radon transform since its introduction in the beginning of the last century has been studied deeply and applied by researchers in a great number of applications especially in the biomedical imaging fields by using the radon transform properties the issue is to recover the transformation parameters regarding the rotation scaling and translation by handling only the image projections assuming no access to the spatial domain of the image this paper proposes an algorithm using an extended version of the radon transform to recover such parameters relating to two unknown images directly from their projection data especially our approach deals with the problem of the estimation accuracy of the rotation angle and its finding in one step instead of two steps as it is reported in the literature this method may be applied in image registration as well in object recognition the results are for the first time exploited in object recognition where comparison with powerful descriptors shows the outstanding performance of the proposed paradigm moreover the influence of additive noise on registration and recognition experiments is discussed and shows the efficiency of the method to reduce the effect of the noise highlightswe define 2 based radon transform rt and motivate its use we propose an algorithm to recover rst transforms using only rt the algorithm is tested on images in real world application e g ct mri etc this rst parameter recovery method is newly applied in object recognition a new confusion matrix is designed to identify also a mislabeled class element

blur identification by residual spectral matching the estimation of the point spread function psf for blur identification often a necessary first step in the restoration of real images method is presented the psf estimate is chosen from a collection of candidate psfs which may be constructed using a parametric model or from experimental measurements the psf estimate is selected to provide the best match between the restoration residual power spectrum and its expected value derived under the assumption that the candidate psf is equal to the true psf several distance measures were studied to determine which one provides the best match the a priori knowledge required is the noise variance and the original image spectrum the estimation of these statistics is discussed and the sensitivity of the method to the estimates is examined analytically and by simulations the method successfully identified blurs in both synthetically and optically blurred images

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

single image refocusing and defocusing in this paper we present a postprocessing method to tackle the single image refocusing and defocusing problem the proposed method can accomplish the tasks of focus map estimation and image refocusing and defocusing given an image with a mixture of focused and defocused objects we first detect the edges and then estimate the focus map based on the edge blurriness which is depicted explicitly by a parametric model the image refocusing problem is addressed in a blind deconvolution framework where the image prior is modeled by using both global and local constraints in particular we correct the defocused blurry edges to sharp ones with the aid of the parametric edge model and then render this cue as a local prior to ensure the sharpness of the refocused image experimental results demonstrate that the proposed method performs well in producing visually plausible images with different focus effects from a single input

reconciling bayesian and frequentist evidence in the one sided testing problem abstract for the one sided hypothesis testing problem it is shown that it is possible to reconcile bayesian evidence against h 0 expressed in terms of the posterior probability that h 0 is true with frequentist evidence against h 0 expressed in terms of the p value in fact for many classes of prior distributions it is shown that the infimum of the bayesian posterior probability of h 0 is equal to the p value in other cases the infimum is less than the p value the results are in contrast to recent work of berger and sellke 1987 in the two sided point null case where it was found that the p value is much smaller than the bayesian infimum some comments on the point null problem are also given

gaussian blurring invariant comparison of signals and images we present a riemannian framework for analyzing signals and images in a manner that is invariant to their level of blurriness under gaussian blurring using a well known relation between gaussian blurring and the heat equation we establish an action of the blurring group on image space and define an orthogonal section of this action to represent and compare images at the same blur level this comparison is based on geodesic distances on the section manifold which in turn are computed using a path straightening algorithm the actual implementations use coefficients of images under a truncated orthonormal basis and the blurring action corresponds to exponential decays of these coefficients we demonstrate this framework using a number of experimental results involving 1d signals and 2d images as a specific application we study the effect of blurring on the recognition performance when 2d facial images are used for recognizing people

multiple depth layers and all in focus image generations by blurring and deblurring operations the depth map and all in focus generations from a single image are proposed the depth map bases on the characteristic curve of coc vs the depth characteristic curve of a camera all in focus image generation is from the estimated depth map a joint deblurring process is proposed to generate an all in focus image in this work we propose novel methods for the generation of multiple depth layers and all in focus images multiple depth layers are produced by applying a sequence of blurring and deblurring operations to determine the depth the proposed method makes no assumptions with regard to the properties of the scene in resolving depth ambiguity in complex images we also developed a method by which to generate all in focus images in which the sharpness is preserved and instabilities imposed by conventional deblurring operations largely eliminated this method involves updating outliers for which depth was over estimated while compensating for errors in the estimation of depth imposed by deblurring

symmetric pairs for quantized enveloping algebras abstract let be an involution of a semisimple lie algebra g let g denote the fixed lie subalgebra and assume the cartan subalgebra of g has been chosen in a suitable way we construct a quantum analog of u g which can be characterized as the unique subalgebra of the quantized enveloping algebra of g which is a maximal right coideal that specializes to u g

edge representation with fuzzy sets in blurred images this paper proposes a representation of edges in blurred images using the concept of fuzzy sets when the images are degraded by various asymmetric and local blurring factors the proposed representation is expressed by fuzzy membership functions and it can serve as a relative index of blur the membership function is derived from the distribution of intensity gradients and the symmetricity of gradient magnitudes and the function is calculated directly from the blurred image without identifying the point spread function or restoring image in this way the fuzzy edge representation describes edges with their degradation states by fuzzy memberships instead of the binary description of edges the index of fuzziness reflects the average amount of ambiguity presented in a fuzzy set and the moments denote an object in the image quantitatively these measures are adopted to illustrate the effectiveness of the representation in locally blurred images

hypothesis estimates and acceptability profiles for 2 2 contingency tables abstract by estimating rather than testing hypotheses regarding the degree of dependence between the factors in 2 2 tables the technical difficulties associated with small sample sizes are avoided the estimators proposed here attempt to estimate 1 when the alternative hypothesis is true and 0 when the null hypothesis is true subject to a bound on the squared error loss under the hypothesis such estimators provide guarded weights of evidence for the alternative hypothesis guarded weights of evidence based on the likelihood ratio are compared with those based on the p value or mid p value and they are shown to have lower risk functions except when the alternative is far from the hypothesis for the case of two independent binomial distributions it is shown that the conditional likelihood ratio estimator for the hypothesis of homogeneity against the two sided alternative has a smaller unconditional risk than the unconditional likelihood ratio estimator except when the binomial probabilities are f

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

blurred image recognition by legendre moment invariants processing blurred images is a key problem in many image applications existing methods to obtain blur invariants which are invariant with respect to centrally symmetric blur are based on geometric moments or complex moments in this paper we propose a new method to construct a set of blur invariants using the orthogonal legendre moments some important properties of legendre moments for the blurred image are presented and proved the performance of the proposed descriptors is evaluated with various point spread functions and different image noises the comparison of the present approach with previous methods in terms of pattern recognition accuracy is also provided the experimental results show that the proposed descriptors are more robust to noise and have better discriminative power than the methods based on geometric or complex moments

multichannel blind deconvolution of spatially misaligned images existing multichannel blind restoration techniques assume perfect spatial alignment of channels correct estimation of blur size and are prone to noise we developed an alternating minimization scheme based on a maximum a posteriori estimation with a priori distribution of blurs derived from the multichannel framework and a priori distribution of original images defined by the variational integral this stochastic approach enables us to recover the blurs and the original image from channels severely corrupted by noise we observe that the exact knowledge of the blur size is not necessary and we prove that translation misregistration up to a certain extent can be automatically removed in the restoration process

quantum flag manifolds quantum symmetric spaces and their associated universal k matrices abstract let u be a connected simply connected compact lie group with complexification g let u and g be the associated lie algebras let be the dynkin diagram of g with underlying set i and let u q u be the associated quantized universal enveloping algebra of u for some 0 q distinct from 1 let o q u be the coquasitriangular quantized function hopf algebra of u whose drinfeld double o q g r we view as the quantized function algebra of g considered as a real algebraic group we show how the datum of an involution of and a invariant function i r can be used to deform o q g r into a algebra o q id g r by a modification of the drinfeld double construction we then show how by a generalized theory of universal k matrices a specific subalgebra of o q id g r admits homomorphisms into both u q u and o q u the images being coideal subalgebras of respectively u q u and o q u we illustrate the theory by showing that two main classes of examples arise by such coideals namely quantum flag manifolds and quantum symmetric spaces except possibly for certain exceptional cases in the former case this connects to work of the first author and neshveyev while for the latter case we heavily rely on recent results of balagovic and kolb

reconstructing arbitrarily focused images from two differently focused images using linear filters we present a novel filtering method for reconstructing an all in focus image or an arbitrarily focused image from two images that are focused differently the method can arbitrarily manipulate the degree of blur of the objects using linear filters without segmentation the filters are uniquely determined from a linear imaging model in the fourier domain an effective and accurate blur estimation method is developed the simulation results show that the accuracy and computational time of the proposed method are improved compared with the previous iterative method and that the effects of blur estimation error on the quality of the reconstructed image are very small the method performs well for real images acquired without visible artifacts

image registration and object recognition using affine invariants and convex hulls this paper is concerned with the problem of feature point registration and scene recognition from images under weak perspective transformations which are well approximated by affine transformations and under possible occlusion and or appearance of new objects it presents a set of local absolute affine invariants derived from the convex hull of scattered feature points e g fiducial or marking points corner points inflection points etc extracted from the image the affine invariants are constructed from the areas of the triangles formed by connecting three vertices among a set of four consecutive vertices quadruplets of the convex hull and hence do make direct use of the area invariance property associated with the affine transformation because they are locally constructed they are very well suited to handle the occlusion and or appearance of new objects these invariants are used to establish the correspondences between the convex hull vertices of a test image with a reference image in order to undo the affine transformation between them a point matching approach for recognition follows this the time complexity for registering l feature points on the test image with n feature points of the reference image is of order o n spl times l the method has been tested on real indoor and outdoor images and performs well

recognition of images degraded by gaussian blur in this paper we propose a new theory of invariants to gaussian blur we introduce a notion of a primordial image as a canonical form of all gaussian blur equivalent images the primordial image is defined in spectral domain by means of projection operators we prove that the moments of the primordial image are invariant to gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself we show how to extend their invariance also to image rotation the application of these invariants is in blur invariant image comparison and recognition in the experimental part we perform an exhaustive comparison with two main competitors 1 the zhang distance and 2 the local phase quantization

maximum likelihood parametric blur identification based on a continuous spatial domain model a formulation for maximum likelihood ml blur identification based on parametric modeling of the blur in the continuous spatial coordinates is proposed unlike previous ml blur identification methods based on discrete spatial domain blur models this formulation makes it possible to find the ml estimate of the extent as well as other parameters of arbitrary point spread functions that admit a closed form parametric description in the continuous coordinates experimental results are presented for the cases of 1 d uniform motion blur 2 d out of focus blur and 2 d truncated gaussian blur at different signal to noise ratios

restoration of randomly blurred images via the maximum a posteriori criterion the maximum a posteriori map estimation technique is applied to the problem of restoring images distorted by noisy point spread functions and additive noise the resulting map estimator is nonlinear and is obtained by numerically maximizing a conditional probability density function the energy nonnegativity constraint is incorporated in the optimization process although the deblurring results are slightly inferior to those obtained by applying the wiener criterion the advantage of the map estimator lies in its significant suppression of noise

wavelet based affine invariant representation a tool for recognizing planar objects in 3d space a technique is developed to construct a representation of planar objects undergoing a general affine transformation the representation can be used to describe planar or nearly planar objects in a three dimensional space observed by a camera under arbitrary orientations the technique is based upon object contours parameterized by an affine invariant parameter and the dyadic wavelet transform the role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation a dissimilarity function is also developed and used to distinguish among different object representations this function makes use of the extrema on the representations thus making its computation very efficient a study of the effect of using different wavelet functions and their order or vanishing moments is also carried out experimental results show that the performance of the proposed representation is better than that of other existing methods particularly when objects are heavily corrupted with noise

invariant fitting of planar objects by primitives the determination of invariant characteristics is an important problem in pattern recognition many invariants are known which have been obtained by the method of normalization in this paper we introduce a new approach of fitting planar objects by primitives using the method of normalization e g fitting by lines triangles rectangles circles ellipses super quadrics etc objects and primitives are described by features for example by moments the main advantage is that the normalization process provides us with a canonical frame of the object and the primitive therefore the fit is invariant with respect to the transformation used by this new method an analytical fitting of non analytical objects can be achieved for example fitting by polygons furthermore the numerical effort can be reduced drastically by normalizing of the object and the primitive

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

identification of image and blur parameters for the restoration of noncausal blurs an optimal statistical parameter estimation technique is presented for the identification of unknown image and blur model parameters the development leads to an autoregressive moving average arma model identification problem where the image model coefficients define the ar part and the blur parameters define the ma part conditional maximum likelihood estimates of the unknown parameters are derived both in the absence and in the presence of observation noise the proposed algorithms constitute a generalization of previous work on blur identification in that they are able to locate the zero loci of the blurred image spectrum on the entire z 1 z 2 plane simulation results as well as photographically blurred images processed with the proposed algorithms are shown as examples

blur invariant translational image registration for n fold symmetric blurs in this paper we propose a new registration method designed particularly for registering differently blurred images such a task cannot be successfully resolved by traditional approaches our method is inspired by traditional phase correlation which is now applied to certain blur invariant descriptors instead of the original images this method works for unknown blurs assuming the blurring psf exhibits an n fold rotational symmetry it does not require any landmarks we have experimentally proven its good performance which is not dependent on the amount of blur in this paper we explicitly address only registration with respect to translation but the method can be readily generalized to rotation and scaling

pictorial recognition of objects employing affine invariance in the frequency domain describes an efficient approach to pose invariant pictorial object recognition employing spectral signatures of image patches that correspond to object surfaces which are roughly planar based on singular value decomposition svd the affine transform is decomposed into slant tilt swing scale and 2d translation unlike previous log polar representations which were not invariant to slant our log log sampling configuration in the frequency domain yields complete affine invariance the images are preprocessed by a novel model based segmentation scheme that detects and segments objects that are affine similar to members of a model set of basic geometric shapes the segmented objects are then recognized by their signatures using multidimensional indexing in a pictorial dataset represented in the frequency domain experimental results with a dataset of 26 models show 100 percent recognition rates in a wide range of 3d pose parameters and imaging degradations 0 360 spl deg swing and tilt 0 82 spl deg of slant more than three octaves in scale change window limited translation high noise levels 0 db and significantly reduced resolution 1 5

new classes of radiometric and combined radiometric geometric invariant descriptors real images can contain geometric distortions as well as photometric degradations analysis and characterization of those images without recourse to either restoration or geometric standardization is of great importance for the computer vision community as those two processes are often ill posed problems to this end it is necessary to implement image descriptors that make it possible to identify the original image in a simple way independently of the imaging system and imaging conditions ideally descriptors that capture image characteristics must be invariant to the whole range of geometric distortions and photometric degradations such as blur that may affect the image in this paper we introduce two new classes of radiometric and or geometric invariant descriptors the first class contains two types of radiometric invariant descriptors the first of these type is based on the mellin transform and the second one is based on central moments both descriptors are invariant to contrast changes and to convolution with any kernel having a symmetric form with respect to the diagonals the second class contains two subclasses of combined invariant descriptors the first subclass includes central moment based descriptors invariant simultaneously to horizontal and vertical translations to uniform and anisotropic scaling to stretching to convolution and to contrast changes the second subclass contains central complex moment based descriptors that are simultaneously invariant to similarity transformation and to contrast changes we apply these invariant descriptors to the matching of geometric transformed and or blurred images experimental results confirm both the robustness and the effectiveness of the proposed invariants

a geometric approach to shape from defocus we introduce a novel approach to shape from defocus i e the problem of inferring the three dimensional 3d geometry of a scene from a collection of defocused images typically in shape from defocus the task of extracting geometry also requires deblurring the given images a common approach to bypass this task relies on approximating the scene locally by a plane parallel to the image the so called equifocal assumption we show that this approximation is indeed not necessary as one can estimate 3d geometry while avoiding deblurring without strong assumptions on the scene solving the problem of shape from defocus requires modeling how light interacts with the optics before reaching the imaging surface this interaction is described by the so called point spread function psf when the form of the psf is known we propose an optimal method to infer 3d geometry from defocused images that involves computing orthogonal operators which are regularized via functional singular value decomposition when the form of the psf is unknown we propose a simple and efficient method that first learns a set of projection operators from blurred images and then uses these operators to estimate the 3d geometry of the scene from novel blurred images our experiments on both real and synthetic images show that the performance of the algorithm is relatively insensitive to the form of the psf our general approach is to minimize the euclidean norm of the difference between the estimated images and the observed images the method is geometric in that we reduce the minimization to performing projections onto linear subspaces by using inner product structures on both infinite and finite dimensional hilbert spaces both proposed algorithms involve only simple matrix vector multiplications which can be implemented in real time

moment forms invariant to rotation and blur in arbitrary number of dimensions we present the construction of combined blur and rotation moment invariants in arbitrary number of dimensions moment invariants to convolution with an arbitrary centrosymmetric filter are derived first and then their rotationally invariant forms are found by means of group representation theory to achieve the desired combined invariance several examples of the invariants are calculated explicitly to illustrate the proposed procedure their invariance robustness and capability of using in template matching and in image registration are demonstrated on 3d mri data and 2d indoor images

local phase quantization plus a principled method for embedding local phase quantization into fisher vector for blurred image recognition abstract advances in computer vision and image processing technology have led to great success in image recognition when the images are clear however in real world applications images are often blurred due to factors such as atmospheric turbulence object camera relative motion and focus this imposes a great challenge on practical image recognition tasks to improve the performance of burred image recognition one main approach is to extract blur insensitive visual descriptors a well established blur insensitive texture feature local phase quantization lpq can achieve promising results with a trade off between effectiveness and efficiency however for complicated visual recognition tasks its performance is still not satisfactory to leverage the discriminative power of lpq we propose local phase quantization plus lpq which embeds lpq into fisher vector fv to acquire mid level blurred image representation under the bag of words bow model to better fit fv instead of using real and imaginary parts as in lpq lpq directly quantizes the local phases of the short term fourier transform stft directly this results in lower dimensionality features but stronger local pattern characterization power lpq is densely sampled for blurred image representation a sliding window screens the image with vertical and horizontal strides lpq s are then acquired from all resulting local regions to better maintain spatial structure characteristics the sliding window is divided into finer cells after being fv encoded local lpq s are aggregated through sum pooling to generate the image signature a wide range of experiments on 5 challenging datasets of different types textures faces scenes clouds and flower demonstrate that lpq significantly outperforms lpq and other well established visual features in discriminative power

geometric invariant features in the radon transform domain for near duplicate image detection radon transform has been widely used in content based image representation due to its excellent geometric properties in this paper we propose a family of geometric invariant features based on radon transform for near duplicate image detection according to the theoretical analysis between geometric operations translation scaling and rotation and radon transform we present a geometric invariant feature model based on the feature model we developed four kinds of geometric invariant features in addition a uniform sampling technique is introduced to combine different features the comprehensive performance of the combined feature is better than that of a single one extensive experiments show that the proposed features are robust not only to rotation and scaling but also to other operations such as compression noise contamination blurring illumination modification cropping etc and achieve strong competitive performance compared with the state of the art image features