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

spectral 6dof registration of noisy 3d range data with partial overlap we present spectral registration with multilayer resampling srmr as a 6 degrees of freedom dof registration method for noisy 3d data with partial overlap the algorithm is based on decoupling 3d rotation from 3d translation by a corresponding resampling process of the spectral magnitude of a 3d fast fourier transform fft calculation on discretized 3d range data the registration of all 6dof is then subsequently carried out with spectral registrations using phase only matched filtering pomf there are two main aspects for the fast and robust registration of euler angles from spherical information in srmr first of all there is the permanent use of phase matching second based on the fft on a discrete cartesian grid not only one spherical layer but also a complete stack of layers are processed in one step experiments are presented with challenging datasets with respect to interference and overlap the results include the fast and robust registration of artificially transformed data for ground truth comparison scans from the stanford bunny dataset high end 3d laser range finder lrf scans of a city center and range data from a low cost actuated lrf in a disaster response scenario

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

zero crossings of a wavelet transform the completeness stability and application to pattern recognition of a multiscale representation based on zero crossings is discussed an alternative projection algorithm is described that reconstructs a signal from a zero crossing representation which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero crossings the reconstruction algorithm has a fast convergence and each iteration requires o n log sup 2 n computation for a signal of n samples the zero crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems as an example the implementation and results of a coarse to fine stereo matching algorithm are described

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

semi supervised linear spectral unmixing using a hierarchical bayesian model for hyperspectral imagery this paper proposes a hierarchical bayesian model that can be used for semi supervised hyperspectral image unmixing the model assumes that the pixel reflectances result from linear combinations of pure component spectra contaminated by an additive gaussian noise the abundance parameters appearing in this model satisfy positivity and additivity constraints these constraints are naturally expressed in a bayesian context by using appropriate abundance prior distributions the posterior distributions of the unknown model parameters are then derived a gibbs sampler allows one to draw samples distributed according to the posteriors of interest and to estimate the unknown abundances an extension of the algorithm is finally studied for mixtures with unknown numbers of spectral components belonging to a know library the performance of the different unmixing strategies is evaluated via simulations conducted on synthetic and real data

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

template matching using the parametric template vector with translation rotation and scale invariance a new method for the template matching invariant to image translation rotation and scaling is proposed in the first step of our approach the ring projection transform rpt process is used to convert the 2d template in a circular region into a 1d gray level signal as a function of radius the advantages of the rpt process are that it owns the characteristic of rotation invariance and reduces the computational complexity of normalized correlation nc then the template matching is performed by constructing a parametric template vector ptv of the 1d gray level signal with differently scaled templates of the object the merits of our approach are that it not only obtains rotation invariance but also scale invariance additionally our approach is conceptually simple easy to implement and only one training image is needed for the training phase experimental results show that the computational time of the proposed approach is faster and the performance is better than the parametric template pt method and the affine moment invariants amis method in the image rotation or scaling moreover our approach not only enjoys high accurate rate under the changes of translation rotation and scale but also estimates the scaling value of the target object in the input scene experiments with gaussian noise demonstrate that the proposed algorithm is robust to detect the target object with the changes of translation orientation and scale this indicates that our approach is suitable for on line template matching with scene translation rotation and scaling

a correlation based approach to calculate rotation and translation of moving cells we present a noniterative image cross correlation approach to track translation and rotation of crawling cells in time lapse video microscopy sequences the method does not rely on extracting features or moments and therefore does not impose specific requirements on the type of microscopy used for imaging here we use phase contrast images we calculate cell rotation and translation from one image to the next in two stages first rotation is calculated by cross correlating the images polar transformed magnitude spectra fourier magnitudes rotation of the cell about any center in the original images results in translation in this representation then we rotate the first image such that the cell has the same orientation in both images and cross correlate this image with the second image to calculate translation by calculating the rotation and translation over each interval in the movie and thereby tracking the cell s position and orientation in each image we can then map from the stationary reference frame in which the cell was observed to the cell s moving coordinate system we describe our modifications enabling application to nonidentical images from video sequences of moving cells and compare this method s performance with that of a feature extraction method and an iterative optimization method

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

digital analysis of rotated images the problem of estimating the relative rotations of two images taken from the same scene is considered and a numerical method for computing such rotations is presented the main features of the proposed method consist of the possibility of fast in place computations with no preliminary interpolation of the data and a considerable precision for moderate rotation angles the final estimate is performed with a least square criterion but in the present case even such computations can be substantially simplified a detailed analysis shows that for practical applications the influence of discretization errors does not affect in a relevant way the precision of the results that is also confirmed by numerical experiments

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

image registration using log polar mappings for recovery of large scale similarity and projective transformations this paper describes a novel technique to recover large similarity transformations rotation scale translation and moderate perspective deformations among image pairs we introduce a hybrid algorithm that features log polar mappings and nonlinear least squares optimization the use of log polar techniques in the spatial domain is introduced as a preprocessing module to recover large scale changes e g at least four fold and arbitrary rotations although log polar techniques are used in the fourier mellin transform to accommodate rotation and scale in the frequency domain its use in registering images subjected to very large scale changes has not yet been exploited in the spatial domain in this paper we demonstrate the superior performance of the log polar transform in featureless image registration in the spatial domain we achieve subpixel accuracy through the use of nonlinear least squares optimization the registration process yields the eight parameters of the perspective transformation that best aligns the two input images extensive testing was performed on uncalibrated real images and an array of 10 000 image pairs with known transformations derived from the corel stock photo library of royalty free photographic images

angular radon spectrum for rotation estimation abstract this paper presents a robust method for rotation estimation of planar point sets using the angular radon spectrum ars given a gaussian mixture model gmm representing the point distribution the ars is a continuous function derived from the radon transform of such distribution the ars characterizes the orientation of a point distribution by measuring its alignment w r t a pencil of parallel lines by exploting its translation and angular shift invariance the rotation angle between two point sets can be estimated through the correlation of the corresponding spectra beside its definition the novel contributions of this paper include the efficient computation of the ars and of the correlation function through their fourier expansion and a new algorithm for assessing the rotation between two point sets moreover experiments with standard benchmark datasets assess the performance of the proposed algorithm and other state of the art methods in presence of noisy and incomplete data

bayesian selection for the ell _2 potts model regularization parameter 1 d piecewise constant signal denoising piecewise constant denoising can be solved either by deterministic optimization approaches based on the potts model or by stochastic bayesian procedures the former lead to low computational time but require the selection of a regularization parameter whose value significantly impacts the achieved solution and whose automated selection remains an involved and challenging problem conversely fully bayesian formalisms encapsulate the regularization parameter selection into hierarchical models at the price of high computational costs this contribution proposes an operational strategy that combines hierarchical bayesian and potts model formulations with the double aim of automatically tuning the regularization parameter and maintaining computational efficiency the proposed procedure relies on formally connecting a bayesian framework to a ell 2 potts functional behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively and shown to compare favorably against those of a fully bayesian hierarchical procedure both in accuracy and computational load

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

joint segmentation of piecewise constant autoregressive processes by using a hierarchical model and a bayesian sampling approach we propose a joint segmentation algorithm for piecewise constant autoregressive ar processes recorded by several independent sensors the algorithm is based on a hierarchical bayesian model appropriate priors allow us to introduce correlations between the change locations of the observed signals numerical problems inherent to bayesian inference are solved by a gibbs sampling strategy the proposed joint segmentation methodology yields improved segmentation results when compared with parallel and independent individual signal segmentations the initial algorithm is derived for piecewise constant ar processes whose orders are fixed on each segment however an extension to models with unknown model orders is also discussed theoretical results are illustrated by many simulations conducted with synthetic signals and real arc tracking and speech signals

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

high accuracy sub pixel motion estimation from noisy images in fourier domain in this paper we propose a new method for estimating sub pixel motion via exploiting the principle of phase correlation in the fourier domain the method is based on linear weighting of the height of the main peak on the one hand and the difference between its two neighboring side peaks on the other using both synthetic and real data we show that the proposed method outperforms many established approaches and achieves improved accuracy even in the presence of noisy samples

joint bayesian endmember extraction and linear unmixing for hyperspectral imagery this paper studies a fully bayesian algorithm for endmember extraction and abundance estimation for hyperspectral imagery each pixel of the hyperspectral image is decomposed as a linear combination of pure endmember spectra following the linear mixing model the estimation of the unknown endmember spectra is conducted in a unified manner by generating the posterior distribution of abundances and endmember parameters under a hierarchical bayesian model this model assumes conjugate prior distributions for these parameters accounts for nonnegativity and full additivity constraints and exploits the fact that the endmember proportions lie on a lower dimensional simplex a gibbs sampler is proposed to overcome the complexity of evaluating the resulting posterior distribution this sampler generates samples distributed according to the posterior distribution and estimates the unknown parameters using these generated samples the accuracy of the joint bayesian estimator is illustrated by simulations conducted on synthetic and real aviris images

frequency domain motion estimation using a complex lapped transform a frequency domain algorithm for motion estimation based on overlapped transforms of the image data is developed as an alternative to block matching methods the complex lapped transform clt is first defined by extending the lapped orthogonal transform lot to have complex basis functions the clt basis functions decay smoothly to zero at their end points and overlap by 2 1 when a data sequence is transformed a method for estimating cross correlation functions in the clt domain is developed this forms the basis of a motion estimation algorithm that calculates vectors for overlapping windowed regions of data the overlapping data window used has no block edge discontinuities and results in smoother motion fields furthermore when motion compensation is performed using similar overlapping regions the algorithm gives comparable or smaller prediction errors than standard models using exhaustive search block matching and computational load is lower for larger displacement ranges and block sizes

digital image registration using projections in many application fields e g aerospace and biomedical image processing one has to deal with a sequence of images whose observation is made difficult by unpredictable relative movements of the camera and the scene in order to obtain a stable display the displacement of each image in the sequence with respect to one chosen as a reference must be preliminarily determined this would usually require two dimensional algorithms involving a considerable computational effort this work discusses a new algorithm for image registration which requires only one dimensional fourier transformations preliminary experimental results are reported

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

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

activity representation with motion hierarchies complex activities e g pole vaulting are composed of a variable number of sub events connected by complex spatio temporal relations whereas simple actions can be represented as sequences of short temporal parts in this paper we learn hierarchical representations of activity videos in an unsupervised manner these hierarchies of mid level motion components are data driven decompositions specific to each video we introduce a spectral divisive clustering algorithm to efficiently extract a hierarchy over a large number of tracklets i e local trajectories we use this structure to represent a video as an unordered binary tree we model this tree using nested histograms of local motion features we provide an efficient positive definite kernel that computes the structural and visual similarity of two hierarchical decompositions by relying on models of their parent child relations we present experimental results on four recent challenging benchmarks the high five dataset patron perez et al high five recognising human interactions in tv shows 2010 the olympics sports dataset niebles et al modeling temporal structure of decomposable motion segments for activity classification 2010 the hollywood 2 dataset marszalek et al actions in context 2009 and the hmdb dataset kuehne et al hmdb a large video database for human motion recognition 2011 we show that per video hierarchies provide additional information for activity recognition our approach improves over unstructured activity models baselines using other motion decomposition algorithms and the state of the art

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

exact bayesian curve fitting and signal segmentation we consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments we present an algorithm for perfect simulation from the posterior distribution of such a model even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment the algorithm is simple can scale well to large data sets and avoids the problem of diagnosing convergence that is present with monte carlo markov chain mcmc approaches to this problem we demonstrate our algorithm on standard denoising problems on a piecewise constant ar model and on a speech segmentation problem

optimal segmentation of random processes segmentation of a nonstationary process consists in assuming piecewise stationarity and in detecting the instants of change we consider the case where all the data is available at the same time and perform a global segmentation instead of a sequential procedure we build a change process and define arbitrarily its prior distribution this allows us to propose the map estimate as well as some minimum contrast estimate as a solution one of the interests of the method is its ability to give the best solution according to the resolution level required by the user that is to the prior distribution chosen the method can address a wide class of parametric and nonparametric models simulations and applications to real data are proposed

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

the discrete wavelet transform wedding the a trous and mallat algorithms two separately motivated implementations of the wavelet transform are brought together it is observed that these algorithms are both special cases of a single filter bank structure the discrete wavelet transform the behavior of which is governed by the choice of filters in fact the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact moreover it is shown that the commonly used lagrange a trous filters are in one to one correspondence with the convolutional squares of the daubechies filters for orthonormal wavelets of compact support a systematic framework for the discrete wavelet transform is provided and conditions are derived under which it computes the continuous wavelet transform exactly suitable filter constraints for finite energy and boundedness of the discrete transform are also derived relevant signal processing parameters are examined and it is observed that orthonormality is balanced by restrictions on resolution

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

vertex based features for recognition of projectively deformed polygons the paper deals with features of a general polygon which are invariant with respect to projective transform first some properties of the area of a triangle under projective transform are discussed new projective triangular invariants of polygons are derived as the quotient of two different products of the areas of triangles formed by the vertices of the polygon the features are proved to be invariant to numbering of the vertices of the polygon the number of projective triangular invariants for polygons with a given number of vertices is derived a method for reduction of the number of invariants in the case of polygons with a high number of vertices is presented numerical experiments dealing with three octagons and one polygon with 18 vertices deformed by projective transforms are described

radial and angular moment invariants for image identification radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation translation reflection and size changes without the aid of the theory of algebraic invariants hu s invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties

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

the bayesian choice a decision theoretic motivation contents introduction decision theoretic foundations of statistical inference from prior information to prior distributions bayesian point estimation tests and confidence regions admissibility and complete classes invariance haar measures and equivariant estimators hierarchical and empirical bayes extensions bayesian calculations a defense of the bayesian choice

invariant pattern recognition a review in this document we review and compare some of the classical and modern techniques for solving the problem of invariant pattern recognition such techniques include integral transforms construction of algebraic moments and the use of structured neural networks in all cases we assume that the nature of the invariance group is known a priori many of the methods described apply to specific geometrical transformation groups however some of the techniques are highly general and applicable to large classes of invariance groups we also review some results regarding the existence and structure of invariants under certain kinds of groups

bayesian inference and prediction for mean and variance shifts in autoregressive time series abstract this article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series we first extend the analysis of random mean shift models to random variance shift models we then consider a method for predicting when a shift is about to occur this involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables the basic computational tool we use in the proposed analysis is the gibbs sampler for illustration we apply the analysis to several examples

hierarchical bayesian sparse image reconstruction with application to mrfm this paper presents a hierarchical bayesian model to reconstruct sparse images when the observations are obtained from linear transformations and corrupted by an additive white gaussian noise our hierarchical bayes model is well suited to such naturally sparse image applications as it seamlessly accounts for properties such as sparsity and positivity of the image via appropriate bayes priors we propose a prior that is based on a weighted mixture of a positive exponential distribution and a mass at zero the prior has hyperparameters that are tuned automatically by marginalization over the hierarchical bayesian model to overcome the complexity of the posterior distribution a gibbs sampling strategy is proposed the gibbs samples can be used to estimate the image to be recovered e g by maximizing the estimated posterior distribution in our fully bayesian approach the posteriors of all the parameters are available thus our algorithm provides more information than other previously proposed sparse reconstruction methods that only give a point estimate the performance of the proposed hierarchical bayesian sparse reconstruction method is illustrated on synthetic data and real data collected from a tobacco virus sample using a prototype mrfm instrument

efficient and accurate set based registration of time separated aerial images this paper addresses the task of time separated aerial image registration the ability to solve this problem accurately and reliably is important for a variety of subsequent image understanding applications the principal challenge lies in the extent and nature of transient appearance variation that a land area can undergo such as that caused by the change under illumination conditions seasonal variations or the occlusion by non persistent objects people cars our work introduces several major novelties i unlike previous work on aerial image registration we approach the problem using a set based paradigm ii we show how image space local pair wise constraints can be used to enforce a globally good registration using a constraints graph structure iii we show how a simple holistic representation derived from raw aerial images can be used as a basic building block of the constraints graph in a manner which achieves both high registration accuracy and speed iv lastly we introduce a new and to the best of our knowledge the only data corpus suitable for the evaluation of set based aerial image registration algorithms using this data set we demonstrate i that the proposed method outperforms the state of the art for pair wise registration already achieving greater accuracy and reliability while at the same time reducing the computational cost of the task and ii that the increase in the number of available images in a set consistently reduces the average registration error with a major difference already for a single additional image highlightsexisting work limited to pair wise or ad hoc extensions of pair wise registrations quasi invariant representation employed at the local in image space level coarse to fine approach used for increased accuracy and reliability constraints graph used to propagate local information across the image set state of the art significantly outperformed in accuracy reliability and speed

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

exact solution of the ising model on group lattices of genus g 1 we discuss how to apply the dimer method to ising models on group lattices having nontrivial topological genus g we find that the use of group extension and the existence of both external and internal group isomorphisms greatly reduces the number of distinct pfaffians and leads to explicit topological formulas for their sign and weight in the expansion of the partition function the complete solution for the ising model on the klein lattice group l 2 7 with g 3 is given

a smooth transition model for multiple regime time series this study deals with the problem of fitting a time series modeled by a smooth transition regression function this model extends the standard linear piecewise model within the piecewise model the regression function parameters change abruptly at the changepoints in the smooth transition model parametric transition functions are introduced that allow for gradual changes of the regression function around the changepoints this model can very accurately reproduce both nonregular and smooth random processes moreover it allows the extraction of information about the changes in the regression function through the transition function parameters the estimation of the model is performed through a fully bayesian framework prior distributions are set for each parameter and the full joint posterior distribution is expressed the computation of standard bayesian estimates involves intractable multi dimensional integrals therefore a reversible jump markov chain monte carlo algorithm is derived to sample the joint posterior distributions a comparative simulation study shows that the smooth transition approach achieves competitive performances and provides more sparse representations of standard test functions finally the smooth transition framework is applied to estimate real world electrical transients which allows the extraction of the relevant features for signal classification

efficient least squares multimodal registration with a globally exhaustive alignment search there are many image registration situations in which the initial misalignment of the two images is large these registration problems often involving comparison of the two images only within a region of interest roi are difficult to solve most intensity based registration methods perform local optimization of their cost function and often miss the global optimum when the initial misregistration is large the registration of multimodal images makes the problem even more difficult since it limits the choice of available cost functions we have developed an efficient method capable of multimodal rigid body registration within an roi that performs an exhaustive search over all integer translations and a local search over rotations the method uses the fast fourier transform to efficiently compute the sum of squared differences cost function for all possible integer pixel shifts and for each shift models the relationship between the intensities of the two images using linear regression test cases involving medical imaging remote sensing and forensic science applications show that the method consistently brings the two images into close registration so that a local optimization method should have no trouble fine tuning the solution

implicit moment invariants the use of traditional moment invariants in object recognition is limited to simple geometric transforms such as rotation scaling and affine transformation of the image this paper introduces so called implicit moment invariants implicit invariants measure the similarity between two images factorized by admissible image deformations for many types of image deformations traditional invariants do not exist but implicit invariants can be used as features for object recognition in the paper we present implicit moment invariants with respect to polynomial transform of spatial coordinates describe their stable and efficient implementation by means of orthogonal moments and demonstrate their performance in artificial as well as real experiments

a pyramid approach to subpixel registration based on intensity we present an automatic subpixel registration algorithm that minimizes the mean square intensity difference between a reference and a test data set which can be either images two dimensional or volumes three dimensional it uses an explicit spline representation of the images in conjunction with spline processing and is based on a coarse to fine iterative strategy pyramid approach the minimization is performed according to a new variation ml of the marquardt levenberg algorithm for nonlinear least square optimization the geometric deformation model is a global three dimensional 3 d affine transformation that can be optionally restricted to rigid body motion rotation and translation combined with isometric scaling it also includes an optional adjustment of image contrast differences we obtain excellent results for the registration of intramodality positron emission tomography pet and functional magnetic resonance imaging fmri data we conclude that the multiresolution refinement strategy is more robust than a comparable single stage method being less likely to be trapped into a false local optimum in addition our improved version of the marquardt levenberg algorithm is faster

point configuration invariants under simultaneous projective and permutation transformations abstract the projective invariants used in computer vision today are permutation sensitive since their value depends on the order in which the features were considered in the computation we derive using tools from representation theory the projective and permutation p 2 invariants of the four collinear and the five coplanar points configurations the p 2 invariants are insensitive to both projective transformations and changes in the labeling of the points when used as model database indexing functions in object recognition systems the p 2 invariants yield a significant speedup permutation invariants for affine transformations are also discussed

polynomial time approximation algorithms for the ising model the paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic ising system to any specified degree of accuracy the running time of the algorithm in

spiral aggregation map splam this paper describes a robust template matching algorithm undergoing rotation scaling translation rst variations via our proposed spiral aggregation map splam which is a novel image warping scheme it not only provides an efficient method for generating the desired projection profiles for matching it also enables us to determine the rotation angle and is invariant to scale changes compared to other model based methods the proposed spiral projection model spm provides the structural and statistical information about the template in a more general and easier to comprehend format the spm is a model based texture description scheme that enables the simultaneous representation for each value of projection profile the profile a set of parametric projection values functions by angular indexing is the aggregate from a group of spiral sampling pixels the experimental evaluation shows that the properties of the algorithm achieved very attractive results this paper describes a robust and fast template matching algorithm we introduced a novel image warping scheme called the spiral aggregation map splam this descriptor is capable of expressing the template with high order texture characteristics

counting over non planar graphs abstract in a framework at the interface between statistical physics and computational complexity we discuss the extension of the pfaffian formalism for the evaluation of the ising partition function or of the weighted matching polynomial over planar lattices to the general case of non planar graphs the combinatorial features of the method acquire a simple topological character independent of the local details of the lattices as a by product we also give a simple formula for the evaluation of the permanent of 0 1 matrices in terms of determinants

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

rotation scale and translation resilient watermarking for images many electronic watermarks for still images and video content are sensitive to geometric distortions for example simple rotation scaling and or translation rst of an image can prevent blind detection of a public watermark in this paper we propose a watermarking algorithm that is robust to rst distortions the watermark is embedded into a one dimensional 1 d signal obtained by taking the fourier transform of the image resampling the fourier magnitudes into log polar coordinates and then summing a function of those magnitudes along the log radius axis rotation of the image results in a cyclical shift of the extracted signal scaling of the image results in amplification of the extracted signal and translation of the image has no effect on the extracted signal we can therefore compensate for rotation with a simple search and compensate for scaling by using the correlation coefficient as the detection measure false positive results on a database of 10 000 images are reported robustness results on a database of 2000 images are described it is shown that the watermark is robust to rotation scale and translation in addition we describe tests examining the watermarks resistance to cropping and jpeg compression

blind deconvolution of sparse pulse sequences under a minimum distance constraint a partially collapsed gibbs sampler method for blind deconvolution of an unknown sparse sequence convolved with an unknown pulse a powerful bayesian method employs the gibbs sampler in combination with a bernoulli gaussian prior modeling sparsity in this paper we extend this method by introducing a minimum distance constraint for the pulses in the sequence this is physically relevant in applications including layer detection medical imaging seismology and multipath parameter estimation we propose a bayesian method for blind deconvolution that is based on a modified bernoulli gaussian prior including a minimum distance constraint factor the core of our method is a partially collapsed gibbs sampler pcgs that tolerates and even exploits the strong local dependencies introduced by the minimum distance constraint simulation results demonstrate significant performance gains compared to a recently proposed pcgs the main advantages of the minimum distance constraint are a substantial reduction of computational complexity and of the number of spurious components in the deconvolution result

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

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

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

bayesian estimation of linear mixtures using the normal compositional model application to hyperspectral imagery this paper studies a new bayesian unmixing algorithm for hyperspectral images each pixel of the image is modeled as a linear combination of so called endmembers these endmembers are supposed to be random in order to model uncertainties regarding their knowledge more precisely we model endmembers as gaussian vectors whose means have been determined using an endmember extraction algorithm such as the famous n finder n findr or vertex component analysis vca algorithms this paper proposes to estimate the mixture coefficients referred to as abundances using a bayesian algorithm suitable priors are assigned to the abundances in order to satisfy positivity and additivity constraints whereas conjugate priors are chosen for the remaining parameters a hybrid gibbs sampler is then constructed to generate abundance and variance samples distributed according to the joint posterior of the abundances and noise variances the performance of the proposed methodology is evaluated by comparison with other unmixing algorithms on synthetic and real images

defocus blur invariant scale space feature extractions we propose modifications to scale space feature extraction techniques scale invariant feature transform sift and speeded up robust features surfs that make the feature detection and description invariant to defocus blur specifically the scale space blob detection relies on the second derivative responses of images our analysis of circular defocus blur which sufficiently approximates a real camera blur kernel and its effect on scale space blob detection suggests that fourth derivative and not the usual second derivative is optimal for detecting the blurred blobs while multi scale descriptors of blurred blobs are effective at establishing correspondences between the blurred images the proposed defocus blur invariant dbi scale space feature extraction techniques which we refer to as dbi sift and dbi surf do not require image deblurring nor blur kernel estimation meaning that their accuracy does not depend on the quality of image deblurring we offer empirical evidence of blur invariance by establishing interest point correspondences between sharp or blurred reference images and blurred target images

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

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

combinatorial and topological approach to the 3d ising model we extend the planar pfaffian formalism for the evaluation of the ising partition function to lattices of high topological genus g the 3d ising model on a cubic lattice where g is proportional to the number of sites is discussed in detail the expansion of the partition function is given in terms of 22g pfaffians classified by the oriented homology cycles of the lattice i e by its spin structures correct counting is guaranteed by a signature term which depends on the topological intersection of the oriented cycles through a simple bilinear formula the role of a gauge symmetry arising in the above expansion is discussed the same formalism can be applied to the counting problem of perfect matchings over general lattices and provides a determinant expansion of the permanent of 0 1 matrices

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

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

bayesian curve fitting using mcmc with applications to signal segmentation we propose some bayesian methods to address the problem of fitting a signal modeled by a sequence of piecewise constant linear in the parameters regression models for example autoregressive or volterra models a joint prior distribution is set up over the number of the changepoints knots their positions and over the orders of the linear regression models within each segment if these are unknown hierarchical priors are developed and as the resulting posterior probability distributions and bayesian estimators do not admit closed form analytical expressions reversible jump markov chain monte carlo mcmc methods are derived to estimate these quantities results are obtained for standard denoising and segmentation of speech data problems that have already been examined in the literature these results demonstrate the performance of our methods

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