discrete laguerre gaussian transforms and their applications laguerre gaussian functions serve as a complete and orthonormal basis for a variety of physical problems such as 2d isotropic quantum harmonic oscillators and circularly symmetric laser modes in this paper we propose discrete laguerre gaussian functions which are defined such that some elegant physical properties are preserved and a fast computation algorithm of complexity o n log n is available discrete laguerre gaussian transforms as introduced in this paper inherit nice properties from discrete laguerre gaussian functions and admit signal analysis over circularly symmetric patterns it is demonstrated through examples that discrete laguerre gaussian transforms find applications in circular pattern keypoints selection object detection image compression rotational invariance feature for pattern recognition and rotational angle estimation

design of steerable wavelets to detect multifold junctions we propose a framework for the detection of junctions in images although the detection of edges and key points is a well examined and described area the multiscale detection of junction centers especially for odd orders poses a challenge in pattern analysis the goal of this paper is to build optimal junction detectors based on 2d steerable wavelets that are polar separable in the fourier domain the approaches we develop are general and can be used for the detection of arbitrary symmetric and asymmetric junctions the backbone of our construction is a multiscale pyramid with a radial wavelet function where the directional components are represented by circular harmonics and encoded in a shaping matrix we are able to detect m fold junctions in different scales and orientations we provide experimental results on both simulated and real data to demonstrate the effectiveness of the algorithm

circular harmonic analysis of psf s corresponding to separable polar coordinate frequency responses with emphasis on fan filtering a method based on radius dependent angular fourier coefficients circular harmonics is used to analyze the point spread function psf of any 2 d filter whose frequency response is separable in the polar coordinate variables the approach relies on the ability to express the psf as the angular cyclic convolution of two functions related to the angular and radial characteristics of the frequency response respectively a general theory is developed and is subsequently specialized to the ideal but important case of fan filtering in the general case the exponential and gaussian radial profiles are considered in detail both because of their mathematical tractability and because of their usefulness for discussing fan filtering uniform radial profile through limiting arguments besides providing insight into the structure of the psf for separable and fan filters the theory leads to a synthesis procedure via fft s which is demonstrated in situations of interest

structural similarity quality metrics in a coding context exploring the space of realistic distortions perceptual image quality metrics have explicitly accounted for human visual system hvs sensitivity to subband noise by estimating just noticeable distortion jnd thresholds a recently proposed class of quality metrics known as structural similarity metrics ssim models perception implicitly by taking into account the fact that the hvs is adapted for extracting structural information from images we evaluate ssim metrics and compare their performance to traditional approaches in the context of realistic distortions that arise from compression and error concealment in video compression transmission applications in order to better explore this space of distortions we propose models for simulating typical distortions encountered in such applications we compare specific ssim implementations both in the image space and the wavelet domain these include the complex wavelet ssim cwssim a translation insensitive ssim implementation we also propose a perceptually weighted multiscale variant of cwssim which introduces a viewing distance dependence and provides a natural way to unify the structural similarity approach with the traditional jnd based perceptual approaches

complex wavelet structural similarity a new image similarity index we introduce a new measure of image similarity called the complex wavelet structural similarity cw ssim index and show its applicability as a general purpose image similarity index the key idea behind cw ssim is that certain image distortions lead to consistent phase changes in the local wavelet coefficients and that a consistent phase shift of the coefficients does not change the structural content of the image by conducting four case studies we have demonstrated the superiority of the cw ssim index against other indices e g dice hausdorff distance commonly used for assessing the similarity of a given pair of images in addition we show that the cw ssim index has a number of advantages it is robust to small rotations and translations it provides useful comparisons even without a preprocessing image registration step which is essential for other indices moreover it is computationally less expensive

vsnr a wavelet based visual signal to noise ratio for natural images this paper presents an efficient metric for quantifying the visual fidelity of natural images based on near threshold and suprathreshold properties of human vision the proposed metric the visual signal to noise ratio vsnr operates via a two stage approach in the first stage contrast thresholds for detection of distortions in the presence of natural images are computed via wavelet based models of visual masking and visual summation in order to determine whether the distortions in the distorted image are visible if the distortions are below the threshold of detection the distorted image is deemed to be of perfect visual fidelity vsnr infin and no further analysis is required if the distortions are suprathreshold a second stage is applied which operates based on the low level visual property of perceived contrast and the mid level visual property of global precedence these two properties are modeled as euclidean distances in distortion contrast space of a multiscale wavelet decomposition and vsnr is computed based on a simple linear sum of these distances the proposed vsnr metric is generally competitive with current metrics of visual fidelity it is efficient both in terms of its low computational complexity and in terms of its low memory requirements and it operates based on physical luminances and visual angle rather than on digital pixel values and pixel based dimensions to accommodate different viewing conditions

invariant solutions to the strominger system on complex lie groups and their quotients using canonical 1 parameter family of hermitian connections on the tangent bundle we provide invariant solutions to the strominger system on certain complex lie groups and their quotients both flat and non flat cases are discussed in detail this paper answers a question proposed by andreas and garcia fernandez in comm math phys 332 3 1381 1383 2014

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

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

multichannel blind image deconvolution using the bussgang algorithm spatial and multiresolution approaches this work extends the bussgang blind equalization algorithm to the multichannel case with application to image deconvolution problems we address the restoration of images with poor spatial correlation as well as strongly correlated natural images the spatial nonlinearity employed in the final estimation step of the bussgang algorithm is developed according to the minimum mean square error criterion in the case of spatially uncorrelated images for spatially correlated images the nonlinearity design is rather conducted using a particular wavelet decomposition that detecting lines edges and higher order structures carries out a task analogous to those of the preattentive stage of the human visual system experimental results pertaining to restoration of motion blurred text images out of focus spiky images and blurred natural images are reported

lie groups with flat gauduchon connections we pursue the research line proposed in yang and zheng acta math sinica english series 34 8 1259 1268 2018 about the classification of hermitian manifolds whose s gauduchon connection nabla s 1 frac s 2 nabla c frac s 2 nabla b is flat where s in mathbb r and nabla c and nabla b are the chern and the bismut connections respectively we focus on lie groups equipped with a left invariant hermitian structure such spaces provide an important class of hermitian manifolds in various contexts and are often a valuable vehicle for testing new phenomena in complex and hermitian geometry more precisely we consider a connected 2n dimensional lie group g equipped with a left invariant complex structure j and a left invariant compatible metric g and we assume that its connection nabla s is flat our main result states that if either n 2 or there exits a nabla s parallel left invariant frame on g then g must be kahler this result demonstrates rigidity properties of some complete hermitian manifolds with nabla s flat hermitian metrics

on causal and semicausal codes for joint information embedding and source coding a source of random message bits is to be embedded into a covertext modeled as a discrete memoryless source dms resulting in a stegotext from which the embedded bits should be recoverable a causal code for such a scenario consists of an encoder that generates the stegotext as a causal function of the message bits and the covertext and a decoder that reproduces the message bits as a causal function of the stegotext a semicausal code on the other hand has an encoder that is causal only with respect to the covertext and not necessarily with respect to the message and has a possibly noncausal decoder we analyze the possible tradeoffs among a the distortion between the stegotext and the covertext b the compressibility of the stegotext and c the rate at which random bits are embedded that are achievable with causal and semicausal codes with and without attacks on the stegotext we also study causal and semicausal codes for the private version of the above scenario in which the decoder has access to the covertext connections are made with the causal rate distortion function of neuhoff and gilbert as well as the problem of channel coding with causal side information at the transmitter analyzed by shannon

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

new families of fourier eigenfunctions for steerable filtering a new diadic family of eigenfunctions of the 2 d fourier transform has been discovered specifically new wavelets are derived by steering the elongated hermite gauss filters with respect to rotations thus obtaining a natural generalization of the laguerre gauss harmonics interestingly these functions are also proportional to their 2 d fourier transform their analytical expression is provided in a compact and treatable form by means of a new ad hoc matrix notation in which the cases of even and odd orders of the hermite polynomials are unified moreover these functions can be efficiently implemented by means of a recursive formula that is derived in this paper the proposed filters are applied to the problem of gradient estimation to improve the theoretical canny tradeoff of position accuracy versus noise rejection that occurs in edge detection experimental results show considerable improvements in using the new wavelets over both isotropic gaussian derivatives and other elongated steerable filters more recently introduced finally being the proposed wavelets a set of fourier eigenfunctions they can be of interest in other fields of science such as optics and quantum mechanics

a local index theorem for non kahler manifolds on considere des conditions suffisantes pour qu un theoreme d indice local soit vrai pour un operateur de dirac associe a une connexion qui ne coincide pas necessairement avec la connexion de levi civita l

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

on joint information embedding and lossy compression in the presence of a stationary memoryless attack channel we consider the problem of optimum joint public information embedding and lossy compression with respect to a fidelity criterion the decompressed composite sequence stegotext is distorted by a stationary memoryless attack resulting in a forgery which in turn is fed into the decoder whose task is to retrieve the embedded information the goal of this paper is to characterize the maximum achievable embedding rate r sub e the embedding capacity c sub e as a function of the compression composite rate r sub c and the allowed average distortion level spl delta such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length we characterize the embedding capacity and demonstrate how it can be approached in principle we also provide a single letter expression of the minimum achievable composite rate as a function of r sub e and spl delta below which there exists no reliable embedding scheme

on random coding error exponents of watermarking systems watermarking codes are analyzed from an information theoretic viewpoint as a game between an information hider and an active attacker while the information hider embeds a secret message watermark in a covertext message typically text image sound or video stream within a certain distortion level the attacker processes the resulting watermarked message within limited additional distortion in attempt to invalidate the watermark for the case where the covertext source is memoryless or more generally where there exists some transformation that makes it memoryless we provide a single letter characterization of the maximin game of the random coding error exponent associated with the average probability of erroneously decoding the watermark this single letter characterization is in effect because if the information hider utilizes a memoryless channel to generate random codewords for every covertext message the causal attacker will maximize the damage by implementing a memoryless channel as well partial results for the dual minimax game and the conditions for the existence of a saddle point are also presented

a multiresolution approach for texture synthesis using the circular harmonic functions in this paper an unsupervised model based texture reproduction technique is described in accordance with the julesz s 1962 conjecture the statistical properties of the prototype up to the second order are copied in order to generate a synthetic texture perceptually indistinguishable from the given sample however this task is accomplished using a hybrid approach which operates partially in the spatial domain and partially in a multiresolution domain the latter employed is the circular harmonic function chf domain since it has been proven to be well suited for mimicking the behavior of the human visual system hvs this approach allows for a wide range of textures typologies obtaining synthetic textures that better match the prototype with respect to the ones obtained using techniques based on the julesz s conjecture operating only in the spatial domain and to dramatically reduce the computational complexity of similar methods operating only in the multiresolution domain

on joint information embedding and lossy compression we consider the problem of optimum joint information embedding and lossy compression with respect to a fidelity criterion the goal is to find the minimum achievable compression composite rate r sub c as a function of the embedding rate r sub e and the average distortion level spl delta allowed such that the average probability of error in decoding of the embedded message can be made arbitrarily small for sufficiently large block length we characterize the minimum achievable composite rate for both the public and the private versions of the problem and demonstrate how this minimum can be approached in principle we also provide an alternative single letter expression of the maximum achievable embedding rate embedding capacity as a function of r sub c and spl delta above which there exist no reliable embedding schemes

steerable wavelet machines swm learning moving frames for texture classification we present texture operators encoding class specific local organizations of image directions loids in a rotation invariant fashion the loids are key for visual understanding and are at the origin of the success of the popular approaches such as local binary patterns lbps and the scale invariant feature transform sift whereas lbps and sift yield hand crafted image representations we propose to learn data specific representations of the loids in a rotation invariant fashion the image operators are based on steerable circular harmonic wavelets chws offering a rich and yet compact initial representation for characterizing natural textures the joint location and orientation required to encode the loids is preserved by using moving frames mfs texture representations built from locally steered image gradients that are invariant to rigid motions in a second step we use support vector machines to learn a multi class shaping matrix for the initial chw representation yielding data driven mfs called steerable wavelet machines swms the swm forward function is composed of linear operations i e convolution and weighted combinations interleaved with non linear steermax operations we experimentally demonstrate the effectiveness of the proposed operators for classifying natural textures our scheme outperforms recent approaches on several test suites of the outex and the curet databases

rotation invariant hog descriptors using fourier analysis in polar and spherical coordinates the histogram of oriented gradients hog is widely used for image description and proves to be very effective in many vision problems rotation invariant analysis is necessary or preferred popular solutions are mainly based on pose normalization or learning neglecting some intrinsic properties of rotations this paper presents a method to build rotation invariant hog descriptors using fourier analysis in polar spherical coordinates which are closely related to the irreducible representation of the 2d 3d rotation groups this is achieved by considering a gradient histogram as a continuous angular signal which can be well represented by the fourier basis 2d or spherical harmonics 3d as rotation invariance is established in an analytical way we can avoid discretization artifacts and create a continuous mapping from the image to the feature space in the experiments we first show that our method outperforms the state of the art in a public dataset for a car detection task in aerial images we further use the princeton shape benchmark and the shrec 2009 generic shape benchmark to demonstrate the high performance of our method for similarity measures of 3d shapes finally we show an application on microscopic volumetric data

shiftable multiscale transforms one of the major drawbacks of orthogonal wavelet transforms is their lack of translation invariance the content of wavelet subbands is unstable under translations of the input signal wavelet transforms are also unstable with respect to dilations of the input signal and in two dimensions rotations of the input signal the authors formalize these problems by defining a type of translation invariance called shiftability in the spatial domain shiftability corresponds to a lack of aliasing thus the conditions under which the property holds are specified by the sampling theorem shiftability may also be applied in the context of other domains particularly orientation and scale jointly shiftable transforms that are simultaneously shiftable in more than one domain are explored two examples of jointly shiftable transforms are designed and implemented a 1 d transform that is jointly shiftable in position and scale and a 2 d transform that is jointly shiftable in position and orientation the usefulness of these image representations for scale space analysis stereo disparity measurement and image enhancement is demonstrated

error analysis in stereo determination of 3 d point positions the relationship between the geometry of a stereo camera setup and the accuracy in obtaining three dimensional position information is of great practical importance in many imaging applications assuming a point in a scene has been correctly identified in each image its three dimensional position can be recovered via a simple geometrical method known as triangulation the probability that position estimates from triangulation are within some specified error tolerance is derived an ideal pinhole camera model is used and the error is modeled as known spatial image plane quantization a point s measured position maps to a small volume in 3 d determined by the finite resolution of the stereo setup with the assumption that the point s actual position is uniformly distributed inside this volume closed form expressions for the probability distribution of error in position along each coordinate direction horizontal vertical and range are derived following this the probability that range error dominates over errors in the point s horizontal or vertical position is determined it is hoped that the results presented will have an impact upon both sensor design and error modeling of position measuring systems for computer vision and related applications

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

a relationship between quantization and watermarking rates in the presence of additive gaussian attacks a system which embeds watermarks in n dimensional gaussian data and distributes them in compressed form is studied the watermarked compressed data have to satisfy a distortion constraint and the watermark has to be recoverable in a private scenario in which the original data are available at the watermark detector the performance of the system in the presence of additive gaussian attacks is considered and the region of achievable quantization and watermarking rate pairs r sub q r sub w is established moreover two surprising facts are demonstrated 1 at low r sub q the maximum achievable r sub w is the same as when there are no attacks and 2 at high but finite r sub q the maximum achievable r sub w is the same as when there is no compression r sub q spl infin finally the performance of related schemes is also discussed

template free wavelet based detection of local symmetries our goal is to detect and group different kinds of local symmetries in images in a scale and rotation invariant way we propose an efficient wavelet based method to determine the order of local symmetry at each location our algorithm relies on circular harmonic wavelets which are used to generate steerable wavelet channels corresponding to different symmetry orders to give a measure of local symmetry we use the f test to examine the distribution of the energy across different channels we provide experimental results on synthetic images biological micrographs and electron microscopy images to demonstrate the performance of the algorithm

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

efficient steerable circular harmonic functions two dimensional 2d filtering and pattern matching applications often involve processing of images using a set sf which includes several transformed e g rotated scaled warped versions of the same 2d function f depending on the application f may correspond to a filter kernel or a pattern in general image processing using all functions in sf poses a computational burden steerability offers a solution to the problem specifically each function in sf can be exactly expressed or closely approximated by a linear combination of a few basis or steering functions in such cases processing images by employing steering functions and obtaining linear combinations of the associated responses may be preferable over utilizing all functions in sf however employing the steering functions is still a computationally expensive process this paper presents a method to significantly improve the computational efficiency of circular harmonic functions which are the steering functions when rotation is the transformation of interest the method is presented mainly in the context of image filtering yet 2d pattern matching is also discussed the advantages of the proposed technique in relation to other techniques are presented and its efficiency is demonstrated in terms of execution time and number of operations an extension of the technique to more general cases where sf includes rotated but also otherwise transformed versions of f is also discussed highlightsvery efficient circular harmonic function chf steerable filter technique presented chf implementation several times faster than direct convolution and fft conditionally technique provides exact results as direct convolution comparisons presented for pattern matching orientation analysis and denoising

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow

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