on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

motion competition a variational approach to piecewise parametric motion segmentation we present a novel variational approach for segmenting the image plane into a set of regions of parametric motion on the basis of two consecutive frames from an image sequence our model is based on a conditional probability for the spatio temporal image gradient given a particular velocity model and on a geometric prior on the estimated motion field favoring motion boundaries of minimal length exploiting the bayesian framework we derive a cost functional which depends on parametric motion models for each of a set of regions and on the boundary separating these regions the resulting functional can be interpreted as an extension of the mumford shah functional from intensity segmentation to motion segmentation in contrast to most alternative approaches the problems of segmentation and motion estimation are jointly solved by continuous minimization of a single functional minimizing this functional with respect to its dynamic variables results in an eigenvalue problem for the motion parameters and in a gradient descent evolution for the motion discontinuity set we propose two different representations of this motion boundary an explicit spline based implementation which can be applied to the motion based tracking of a single moving object and an implicit multiphase level set implementation which allows for the segmentation of an arbitrary number of multiply connected moving objects numerical results both for simulated ground truth experiments and for real world sequences demonstrate the capacity of our approach to segment objects based exclusively on their relative motion

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

multiresolution feature extraction and selection for texture segmentation an approach is described for unsupervised segmentation of textured images local texture properties are extracted using local linear transforms that have been optimized for maximal texture discrimination local statistics texture energy measures are estimated at the output of an equivalent filter bank by means of a nonlinear transformation absolute value followed by an iterative gaussian smoothing algorithm this procedure generates a multiresolution sequence of feature planes with a half octave scale progression a feature reduction technique is then applied to the data and is determined by simultaneously diagonalizing scatter matrices evaluated at two different spatial resolutions this approach provides a good approximation of r a fisher s 1950 multiple linear discriminants and has the advantage of requiring no a priori knowledge this feature reduction methods appears to be an improvement on the commonly used karhunen loeve transform and allows efficient texture segmentation based on simple thresholding

random graph asymptotics on high dimensional tori we investigate the scaling of the largest critical percolation cluster on a large d dimensional torus for nearest neighbor percolation in sufficiently high dimensions or when d 6 for sufficiently spread out percolation we use a relatively simple coupling argument to show that this largest critical cluster is with high probability bounded above by a large constant times v 2 3 and below by a small constant times v 2 3 log v 4 3 where v is the volume of the torus we also give a simple criterion in terms of the subcritical percolation two point function on mathbb z d under which the lower bound can be improved to small constant times v 2 3 i e we prove random graph asymptotics for the largest critical cluster on the high dimensional torus this establishes a conjecture by 1 apart from logarithmic corrections we discuss implications of these results on the dependence on boundary conditions for high dimensional percolation

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

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

optical flow using spatiotemporal filters a model is presented consonant with current views regarding the neurophysiology and psychophysics of motion perception that combines the outputs of a set of spatiotemporal motion energy filters to estimate image velocity a parallel implementation computes a distributed representation of image velocity a measure of image flow uncertainty is formulated preliminary results indicate that this uncertainty measure may be used to recognize ambiguity due to the aperture problem the model appears to deal with the aperture problem as well as the human visual system since it extracts the correct velocity for some patterns that have large differences in contrast at different spatial orientations

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

analysis of superimposed oriented patterns estimation of local orientation in images may be posed as the problem of finding the minimum gray level variance axis in a local neighborhood in bivariate images the solution is given by the eigenvector corresponding to the smaller eigenvalue of a 2times2 tensor for an ideal single orientation the tensor is rank deficient i e the smaller eigenvalue vanishes a large minimal eigenvalue signals the presence of more than one local orientation what may be caused by non opaque additive or opaque occluding objects crossings bifurcations or corners we describe a framework for estimating such superimposed orientations our analysis is based on the eigensystem analysis of suitably extended tensors for both additive and occluding superpositions unlike in the single orientation case the eigensystem analysis does not directly yield the orientations rather it provides so called mixed orientation parameters mops we therefore show how to decompose the mops into the individual orientations we also show how to use tensor invariants to increase efficiency and derive a new feature for describing local neighborhoods which is invariant to rigid transformations applications are e g in texture analysis directional filtering and interpolation feature extraction for corners and crossings tracking and signal separation

random subgraphs of finite graphs ii the lace expansion and the triangle condition in a previous paper we defined a version of the percolation triangle condition that is suitable for the analysis of bond percolation on a finite connected transitive graph and showed that this triangle condition implies that the percolation phase transition has many features in common with the phase transition on the complete graph in this paper we use a new and simplified approach to the lace expansion to prove quite generally that for finite graphs that are tori the triangle condition for percolation is implied by a certain triangle condition for simple random walks on the graph the latter is readily verified for several graphs with vertex set 0 1 r 1 n including the hamming cube on an alphabet of r letters the n cube for r 2 the n dimensional torus with nearest neighbor bonds and n sufficiently large and the n dimensional torus with n 6 and sufficiently spread out long range bonds the conclusions of our previous paper thus apply to the percolation phase transition for each of the above examples

on parametric evolution inclusions of the subdifferential type with applications to optimal control problems in this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear infinite dimensional optimal control problems the parameter appears in all the data of the problem including the subdifferential operator first we establish several continuity results for the solution multifunction of the subdifferential inclusion then we study how these results can be used to examine the sensitivity properties variational stability of certain broad classes of nonlinear infinite dimensional optimal control problems some examples are worked out in detail illustrating the applicability of our work these include obstacle problems with time varying obstacles optimal control of distributed parameter systems and differential variational inequalities

correlation feedback technique in optical flow determination we present a new algorithm to determine optical flow that utilizes a correlation feedback technique several experiments are presented to demonstrate that our method performs generally better than some standard correlation and gradient based methods in terms of accuracy

fast computation of the difference of low pass transform this paper defines the difference of low pass dolp transform and describes a fast algorithm for its computation the dolp is a reversible transform which converts an image into a set of bandpass images a dolp transform is shown to require o n2 multiplies and produce o n log n samples from an n sample image when gaussian low pass filters are used the result is a set of images which have been convolved with difference of gaussian dog filters from an exponential set of sizes a fast computation technique based on resampling is described and shown to reduce the dolp transform complexity to o n log n multiplies and o n storage locations a second technique cascaded convolution with expansion is then defined and also shown to reduce the computational cost to o n log n multiplies combining these two techniques yields an algorithm for a dolp transform that requires o n storage cells and requires o n multiplies

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

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

generic neighborhood operators a method that treats linear neighborhood operators within a unified framework that enables linear combinations concatenations resolution changes or rotations of operators to be treated in a canonical manner is presented various families of operators with special kinds of symmetries such as translation rotation magnification are explicitly constructed in 1 d 2 d and 3 d a concept of order is defined and finite orthonormal bases of functions closely connected with the operators of various orders are constructed linear transformations between the various representations are considered the method is based on two fundamental assumptions a decrease of resolution should not introduce spurious detail and the local operators should be self similar under changes of resolution these assumptions merely sum up the even more general need for homogeneity isotropy scale invariance and separability of independent dimensions of front end processing in the absence of a priori information

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

the hermite transform theory the author introduces a scheme for the local processing of visual information called the hermite transform the problem is addressed from the point of view of image coding and therefore the scheme is presented as an analysis resynthesis system the objectives of the present work however are not restricted to coding the analysis part is designed so that it can also serve applications in the area of computer vision indeed derivatives of gaussians which have found widespread application in feature detection over the past few years play a central role in the hermite analysis it is also argued that the proposed processing scheme is in close agreement with current insight into the image processing that is carried out by the human visual system in particular it is demonstrated that the hermite transform is in better agreement with human visual modeling than gabor expansions

n folded symmetries by complex moments in gabor space and their application to unsupervised texture segmentation complex moments of the gabor power spectrum yield estimates of the n folded symmetry of the local image content at different frequency scales that is they allow to detect linear rectangular hexagonal triangular and so on structures with very fine to very coarse resolutions results from experiments on the unsupervised segmentation of real textures indicate their importance for image processing applications real geometric moments computed in gabor space also provide for very powerful texture features but lack the clear geometrical interpretation of complex moments

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

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

anisotropic morphological filters with spatially variant structuring elements based on image dependent gradient fields this paper deals with the theory and applications of spatially variant discrete mathematical morphology we review and formalize the definition of spatially variant dilation erosion and opening closing for binary and gray level images using exclusively the structuring function without resorting to complement this theoretical framework allows to build morphological operators whose structuring elements can locally adapt their shape and orientation across the dominant direction of the structures in the image the shape and orientation of the structuring element at each pixel are extracted from the image under study the orientation is given by means of a diffusion process of the average square gradient field which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image and the shape of the orientated structuring elements can be linear or it can be given by the distance to relevant edges of the objects the proposed filters are used on binary and gray level images for enhancement of anisotropic features such as coherent flow like structures results of spatially variant erosions dilations and openings closings based filters prove the validity of this theoretical sound and novel approach

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

nonlinear uncertain systems and necessary conditions of optimality in this paper we consider an optimal control problem for a class of systems governed by nonlinear evolution equations containing a nonlinear monotone operator and a nonmonotone operator with uncertain parameters we prove existence of solutions and present necessary conditions of optimality our result is illustrated by an example from quasi linear partial differential equations with uncertain coefficients this result is further illustrated by a more practical example

random graph asymptotics on high dimensional tori ii volume diameter and mixing time for critical bond percolation on high dimensional torus this paper proves sharp lower bounds on the size of the largest cluster removing a logarithmic correction in the lower bound in heydenreich and van der hofstad comm math phys 270 2 335 358 2007 this improvement finally settles a conjecture by aizenman nuclear phys b 485 3 551 582 1997 about the role of boundary conditions in critical high dimensional percolation and it is a key step in deriving further properties of critical percolation on the torus indeed a criterion of nachmias and peres ann probab 36 4 1267 1286 2008 implies appropriate bounds on diameter and mixing time of the largest clusters we further prove that the volume bounds apply also to any finite number of the largest clusters finally we show that any weak limit of the largest connected component is non degenerate which can be viewed as a significant sign of critical behavior the main conclusion of the paper is that the behavior of critical percolation on the high dimensional torus is the same as for critical erd s renyi random graphs

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

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

steerable wedge filters for local orientation analysis steerable filters have been used to analyze local orientation patterns in imagery such filters are typically based on directional derivatives whose symmetry produces orientation responses that are periodic with period spl pi independent of image structure we present a more general set of steerable filters that alleviate this problem

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

automatic parameter selection for denoising algorithms using a no reference measure of image content across the field of inverse problems in image and video processing nearly all algorithms have various parameters which need to be set in order to yield good results in practice usually the choice of such parameters is made empirically with trial and error if no ground truth reference is available some analytical methods such as cross validation and stein s unbiased risk estimate sure have been successfully used to set such parameters however these methods tend to be strongly reliant on restrictive assumptions on the noise and also computationally heavy in this paper we propose a no reference metric q which is based upon singular value decomposition of local image gradient matrix and provides a quantitative measure of true image content i e sharpness and contrast as manifested in visually salient geometric features such as edges in the presence of noise and other disturbances this measure 1 is easy to compute 2 reacts reasonably to both blur and random noise and 3 works well even when the noise is not gaussian the proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms ample simulated and real data experiments support our claims furthermore tests using the tid2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions

optimal filters for the detection of linear patterns in 2 d and higher dimensional images abstract it is shown that the rotation invariant operators form a set of orthogonal basis functions which is optimal for a wide range of 2 d and 3 d feature detection operations the optimality criterion used is based on the karhunen loeve expansion of the local image data this is a generalization of the work of zucker and hummel who showed that these filters are optimal filters for the detection of step edges in 2 d and 3 d images

general hermite and laguerre two dimensional polynomials general hermite and laguerre two dimensional 2d polynomials which form a complex three parameter unification of the special hermite and laguerre 2d polynomials are defined and investigated the general hermite 2d polynomials are related to the two variable hermite polynomials but are not the same the advantage of the newly introduced hermite and laguerre 2d polynomials is that they satisfy orthogonality relations in a direct way whereas for the purpose of orthonormalization of the two variable hermite polynomials two different sets of such polynomials are introduced which are biorthonormal to each other the matrix which plays a role in the new definition of hermite and laguerre 2d polynomials is in a considered sense the square root of the matrix which plays a role in the definition of two variable hermite polynomials two essentially different explicit representations of the hermite and laguerre 2d polynomials are derived where the first involves jacobi polynomials as coefficients in superpositions of special hermite or laguerre 2d polynomials and the second is a superposition of products of two hermite polynomials with decreasing indices and with coefficients related to the special laguerre 2d polynomials generating functions are derived for the hermite and laguerre 2d polynomials

robust photometric invariant features from the color tensor luminance based features are widely used as low level input for computer vision applications even when color data is available the extension of feature detection to the color domain prevents information loss due to isoluminance and allows us to exploit the photometric information to fully exploit the extra information in the color data the vector nature of color data has to be taken into account and a sound framework is needed to combine feature and photometric invariance theory in this paper we focus on the structure tensor or color tensor which adequately handles the vector nature of color images further we combine the features based on the color tensor with photometric invariant derivatives to arrive at photometric invariant features we circumvent the drawback of unstable photometric invariants by deriving an uncertainty measure to accompany the photometric invariant derivatives the uncertainty is incorporated in the color tensor hereby allowing the computation of robust photometric invariant features the combination of the photometric invariance theory and tensor based features allows for detection of a variety of features such as photometric invariant edges corners optical flow and curvature the proposed features are tested for noise characteristics and robustness to photometric changes experiments show that the proposed features are robust to scene incidental events and that the proposed uncertainty measure improves the applicability of full invariants

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

a sensitivity analysis of volterra integral inclusions with applications to optimal control problems abstract we consider a class of parametrized volterra integral inclusions associated to multivalued m accretive operators in a banach space we show that the solution set depends continuously on the parameter in a specified sense the continuous dependence results are used to study the variational stability of distributed parameter optimal control problems

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

a nonparametric riemannian framework on tensor field with application to foreground segmentation background modeling on tensor field has recently been proposed for foreground detection tasks taking into account the riemannian structure of the tensor manifold recent research has focused on developing parametric methods on the tensor domain e g mixture of gaussians gmm however in some scenarios simple parametric models do not accurately explain the physical processes kernel density estimators kdes have been successful to model on euclidean sample spaces the nonparametric nature of complex time varying and non static backgrounds founded on a mathematically rigorous kde paradigm on general riemannian manifolds recently proposed in the literature we define a kde specifically to operate on the tensor manifold in order to nonparametrically reformulate the existing tensor based algorithms we present a mathematically sound framework for nonparametric modeling on tensor field to foreground detection we endow the tensor manifold with two well founded riemannian metrics i e affine invariant and log euclidean theoretical aspects are presented and the metrics are compared experimentally by inducing a space with a null curvature the log euclidean metric considerably simplifies the scheme from a practical point of view while maintaining the mathematical soundness and the excellent segmentation performance theoretic analysis and experimental results demonstrate the promise and effectiveness of this framework

on gram charlier approximations a gram charlier series involves the expansion of one probability density function in terms of the derivatives of another density function this paper generalizes the original series introduced by gram an expansion that minimizes a weighted square error two new gram charlier expansions for the density of a finite variate are derived and recursion formulas for series coefficients are given

finding trajectories of feature points in a monocular image sequence identifying the same physical point in more than one image the correspondence problem is vital in motion analysis most research for establishing correspondence uses only two frames of a sequence to solve this problem by using a sequence of frames it is possible to exploit the fact that due to inertia the motion of an object cannot change instantaneously by using smoothness of motion it is possible to solve the correspondence problem for arbitrary motion of several nonrigid objects in a scene we formulate the correspondence problem as an optimization problem and propose an iterative algorithm to find trajectories of points in a monocular image sequence a modified form of this algorithm is useful in case of occlusion also we demonstrate the efficacy of this approach considering synthetic laboratory and real scenes

optimal detection and estimation of straight patterns this correspondence illustrates the optimal detector and slope estimator of straight patterns in particular it is recognized that the output of the likelihood processor constituted by the radon transform and a whitening filter provides a sufficient statistic for both problems of signal detection as well as orientation and offset estimation

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

necessary and sufficient conditions for l 1 strong weak lower semicontinuity of integral functionals soit t 7b f un espace fini de mesure nonatomique x ii ii un espace de banach non separable et v i i un espace de banach reflexif separable dont v est le dual soit f txxxv une fonction 7b f 7b b x v mesurable on etudie l integrale fonctionnelle associee i f l x 1 l v 1 definie par if x v f r x t v t dt

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

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

texture segmentation using independent scale component wise riemannian covariance gaussian mixture model in kl measure based multi scale nonlinear structure tensor space this paper proposes a novel texture segmentation approach using independent scale component wise riemannian covariance gaussian mixture model icrgmm in kullback leibler kl measure based multi scale nonlinear structure tensor msnst space we use the independent scale distribution and full covariance structure to replace the covariant scale distribution and 1d variance structure used in our previous research to construct the optimal full covariance structure we define the full covariance on kl euclidean log euclidean and riemannian gradient mappings and compare their performances the comparison experiments demonstrate that the riemannian gradient mapping leads to its optimum properties over other choices when constructing the full covariance to estimate and update the statistical parameters more accurately the component wise expectation maximization for mixtures cem 2 algorithm is proposed instead of the originally used k means algorithm the superiority of the proposed icrgmm has been demonstrated based on texture clustering and graph cuts based texture segmentation using a large number of synthesis texture images and real natural scene textured images and further analyzed in terms of error ratio and modified f measure respectively

the hermite transform applications it is demonstrated how the hermite transform can be used for image coding and analysis hierarchical coding structures based on increasingly specified basic patterns i e general 2 d patterns general 1 d patterns and specific 1 d patterns such as edges and corners are presented in the image coding application the relation with existing pyramid coders is described a new coding scheme based on local one dimensional image approximations is introduced in the image analysis application the relation between the hermite transform and existing line edge detection schemes is described it is shown that by concentrating on more specific patterns the coding efficiency can be increased since fewer coefficients have to be coded meanwhile sufficient descriptive power can be maintained for approximating the most interesting features in natural images

fast surface interpolation using hierarchical basis functions an alternative to multigrid relaxation that is much easier to implement and more generally applicable is presented conjugate gradient descent is used in conjunction with a hierarchical multiresolution set of basis functions the resultant algorithm uses a pyramid to smooth the residual vector before the direction is computed simulation results showing the speed of convergence and its dependence on the choice of interpolator the number of smoothing levels and other factors are presented the relationship of this approach to other multiresolution relaxation and representation schemes is also discussed

multiresolution moment filters theory and applications we introduce local weighted geometric moments that are computed from an image within a sliding window at multiple scales when the window function satisfies a two scale relation we prove that lower order moments can be computed efficiently at dyadic scales by using a multiresolution wavelet like algorithm we show that b splines are well suited window functions because in addition to being refinable they are positive symmetric separable and very nearly isotropic gaussian shape we present three applications of these multiscale local moments the first is a feature extraction method for detecting and characterizing elongated structures in images the second is a noise reduction method which can be viewed as a multiscale extension of savitzky golay filtering the third is a multiscale optical flow algorithm that uses a local affine model for the motion field extending the lucas kanade optical flow method the results obtained in all cases are promising

random subgraphs of the 2d hamming graph the supercritical phase we study random subgraphs of the 2 dimensional hamming graph h 2 n which is the cartesian product of two complete graphs on n vertices let p be the edge probability and write p 1 varepsilon 2 n 1 for some varepsilon in mathbb r in borgs et al random struct alg 27 137 184 2005 ann probab 33 1886 1944 2005 the size of the largest connected component was estimated precisely for a large class of graphs including h 2 n for varepsilon leq lambda v 1 3 where 0 is a constant and v n2 denotes the number of vertices in h 2 n until now no matching lower bound on the size in the supercritical regime has been obtained in this paper we prove that when varepsilon gg log v 1 3 v 1 3 then the largest connected component has size close to 2 varepsilon v with high probability we thus obtain a law of large numbers for the largest connected component size and show that the corresponding values of p are supercritical barring the factor log v 1 3 this identifies the size of the largest connected component all the way down to the critical p window

a quad tree approach to image segmentation which combines statistical and spatial information abstract a new approach to the problem of image segmentation is presented by combining a nonparametric classifier based on a clustering algorithm with a quad tree representation of the image the scheme is both simple to implement and performs well giving satisfactory results at signal to noise ratios well below 1 the results of an analysis of the algorithm are borne out by a comprehensive set of tests on gaussian images and synthetic textures which demonstrate its principal features

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

the curvelet transform for image denoising we describe approximate digital implementations of two new mathematical transforms namely the ridgelet transform and the curvelet transform our implementations offer exact reconstruction stability against perturbations ease of implementation and low computational complexity a central tool is fourier domain computation of an approximate digital radon transform we introduce a very simple interpolation in the fourier space which takes cartesian samples and yields samples on a rectopolar grid which is a pseudo polar sampling set based on a concentric squares geometry despite the crudeness of our interpolation the visual performance is surprisingly good our ridgelet transform applies to the radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain our curvelet transform uses our ridgelet transform as a component step and implements curvelet subbands using a filter bank of a spl grave trous wavelet filters our philosophy throughout is that transforms should be overcomplete rather than critically sampled we apply these digital transforms to the denoising of some standard images embedded in white noise in the tests reported here simple thresholding of the curvelet coefficients is very competitive with state of the art techniques based on wavelets including thresholding of decimated or undecimated wavelet transforms and also including tree based bayesian posterior mean methods moreover the curvelet reconstructions exhibit higher perceptual quality than wavelet based reconstructions offering visually sharper images and in particular higher quality recovery of edges and of faint linear and curvilinear features existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems the empirical results reported here are in encouraging agreement

a distance measure and a feature likelihood map concept for scale invariant model matching this paper presents two approaches for evaluating multi scale feature based object models within the first approach a scale invariant distance measure is proposed for comparing two image representations in terms of multi scale features based on this measure the maximisation of the likelihood of parameterised feature models allows for simultaneous model selection and parameter estimation the idea of the second approach is to avoid an explicit feature extraction step and to evaluate models using a function defined directly from the image data for this purpose we propose the concept of a feature likelihood map which is a function normalised to the interval 0 1 and that approximates the likelihood of image features at all points in scale space to illustrate the applicability of both methods we consider the area of hand gesture analysis and show how the proposed evaluation schemes can be integrated within a particle filtering approach for performing simultaneous tracking and recognition of hand models under variations in the position orientation size and posture of the hand the experiments demonstrate the feasibility of the approach and that real time performance can be obtained by pyramid implementations of the proposed concepts

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

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

the geometric median on riemannian manifolds with application to robust atlas estimation one of the primary goals of computational anatomy is the statistical analysis of anatomical variability in large populations of images the study of anatomical shape is inherently related to the construction of transformations of the underlying coordinate space which map one anatomy to another it is now well established that representing the geometry of shapes or images in euclidian spaces undermines our ability to represent natural variability in populations in our previous work we have extended classical statistical analysis techniques such as averaging principal components analysis and regression to riemannian manifolds which are more appropriate representations for describing anatomical variability in this paper we extend the notion of robust estimation a well established and powerful tool in traditional statistical analysis of euclidian data to manifold valued representations of anatomical variability in particular we extend the geometric median a classic robust estimator of centrality for data in euclidean spaces we formulate the geometric median of data on a riemannian manifold as the minimizer of the sum of geodesic distances to the data points we prove existence and uniqueness of the geometric median on manifolds with non positive sectional curvature and give sufficient conditions for uniqueness on positively curved manifolds generalizing the weiszfeld procedure for finding the geometric median of euclidean data we present an algorithm for computing the geometric median on an arbitrary manifold we show that this algorithm converges to the unique solution when it exists in this paper we exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images using this approach we also present a robust brain atlas estimation technique based on the geometric median in the space of deformable images

robust optical flow computation based on least median of squares regression an optical flow estimation technique is presented which is based on the least median of squares lmeds robust regression algorithm enabling more accurate flow estimates to be computed in the vicinity of motion discontinuities the flow is computed in a blockwise fashion using an affine model through the use of overlapping blocks coupled with a block shifting strategy redundancy is introduced into the computation of the flow this eliminates blocking effects common in most other techniques based on blockwise processing and also allows flow to be accurately computed in regions containing three distinct motions a multiresolution version of the technique is also presented again based on lmeds regression which enables image sequences containing large motions to be effectively handled an extensive set of quantitative comparisons with a wide range of previously published methods are carried out using synthetic realistic computer generated images of natural scenes with known flow and natural images both angular and absolute flow errors are calculated for those sequences with known optical flow displaced frame difference error used extensively in video compression is used for those natural scenes with unknown flow in all of the sequences tested a comparison with those methods that result in a dense flow field greater than 80 spatial coverage show that the lmeds technique produces the least error irrespective of the error measure used

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

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

flux based anisotropic diffusion applied to enhancement of 3 d angiogram we present a new approach to anisotropic diffusion based on a multidirectional diffusion flux the diffusion flux is decomposed in an orthogonal basis effectively enabling enhancement of contours as well as diffusion along the contours to this end we have selected a three dimensional basis that depicts the directions of principal curvature and has an interesting interpretation in the context of the vessels the diffusion function associated to each vector of the basis depends on the first order derivative of the intensity in this direction instead of the traditional norm of the smoothed gradient accordingly we present the results of a restoration of computed tomography data of the liver

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

minimax control of nonlinear evolution equations in this paper we study nonlinear parametric optimal control problems we formulate the relevant minimax problem and prove the existence of an optimal control also we derive necessary conditions for saddle point optimality we also associate to the original optimization problem a dual problem and then for the pair we prove a complete duality theorem finally we present two examples of parabolic distributed parameter systems which illustrate the abstract results

3 d shape estimation of dna molecules from stereo cryo electron micro graphs using a projection steerable snake we introduce a three dimensional 3 d parametric active contour algorithm for the shape estimation of dna molecules from stereo cryo electron micrographs we estimate the shape by matching the projections of a 3 d global shape model with the micrographs we choose the global model as a 3 d filament with a b spline skeleton and a specified radial profile the active contour algorithm iteratively updates the b spline coefficients which requires us to evaluate the projections and match them with the micrographs at every iteration since the evaluation of the projections of the global model is computationally expensive we propose a fast algorithm based on locally approximating it by elongated blob like templates we introduce the concept of projection steerability and derive a projection steerable elongated template since the two dimensional projections of such a blob at any 3 d orientation can be expressed as a linear combination of a few basis functions matching the projections of such a 3 d template involves evaluating a weighted sum of inner products between the basis functions and the micrographs the weights are simple functions of the 3 d orientation and the inner products are evaluated efficiently by separable filtering we choose an internal energy term that penalizes the average curvature magnitude since the exact length of the dna molecule is known a priori we introduce a constraint energy term that forces the curve to have this specified length the sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm we validate the algorithm using real as well as simulated data and show that it performs well

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

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

the radon transform and its properties this paper presents a summary of the fundamental properties of the radon transform including delay effects data shifting rotation scaling windowing bowtie events energy conservation etc and includes representative examples on standard data sets such as 2 d delta functions boxcar events gaussian bell and conic sections which reinforce the basic concepts of the radon transform

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

interconversion between truncated cartesian and polar expansions of images in this paper we propose an algorithm for lossless conversion of data between cartesian and polar coordinates when the data is sampled from a 2 d real valued function a mapping expressed as a particular kind of truncated expansion we use laguerre functions and the fourier basis for the polar coordinate expression hermite functions are used for the cartesian coordinate expression a finite number of coefficients for the truncated expansion specifies the function in each coordinate system we derive the relationship between the coefficients for the two coordinate systems based on this relationship we propose an algorithm for lossless conversion between the two coordinate systems resampling can be used to evaluate a truncated expansion on the complementary coordinate system without computing a new set of coefficients the resampled data is used to compute the new set of coefficients to avoid the numerical instability associated with direct conversion of the coefficients in order to apply our algorithm to discrete image data we propose a method to optimally fit a truncated expression to a given image we also quantify the error that this filtering process can produce finally the algorithm is applied to solve the polar cartesian interpolation problem

practical signal dependent noise parameter estimation from a single noisy image the additive white gaussian noise is widely assumed in many image processing algorithms however in the real world the noise from actual cameras is better modeled as signal dependent noise sdn in this paper we focus on the sdn model and propose an algorithm to automatically estimate its parameters from a single noisy image the proposed algorithm identifies the noise level function of signal dependent noise assuming the generalized signal dependent noise model and is also applicable to the poisson gaussian noise model the accuracy is achieved by improved estimation of local mean and local noise variance from the selected low rank patches we evaluate the proposed algorithm with both synthetic and real noisy images experiments demonstrate that the proposed estimation algorithm outperforms the state of the art methods

3 d motion estimation understanding and prediction from noisy image sequences this paper presents an approach to understanding general 3 d motion of a rigid body from image sequences based on dynamics a locally constant angular momentum lcam model is introduced the model is local in the sense that it is applied to a limited number of image frames at a time specifically the model constrains the motion over a local frame subsequence to be a superposition of precession and translation thus the instantaneous rotation axis of the object is allowed to change through the subsequence the trajectory of the rotation center is approximated by a vector polynomial the parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics the nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence the estimation algorithm presented in this paper is linear i e the algorithm consists of solving simultaneous linear equations based on the assumption that the motion is smooth object positions and motion in the near future can be predicted and short missing subsequences can be recovered noise smoothing is achieved by overdetermination and a leastsquares criterion the framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames

myocardial motion estimation from medical images using the monogenic signal we present a method for the analysis of heart motion from medical images the algorithm exploits monogenic signal theory recently introduced as an n dimensional generalization of the analytic signal the displacement is computed locally by assuming the conservation of the monogenic phase over time a local affine displacement model is considered to account for typical heart motions as contraction expansion and shear a coarse to fine b spline scheme allows a robust and effective computation of the model s parameters and a pyramidal refinement scheme helps to handle large motions robustness against noise is increased by replacing the standard point wise computation of the monogenic orientation with a robust least squares orientation estimate given its general formulation the algorithm is well suited for images from different modalities in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption this paper evaluates the method s feasibility on two emblematic cases cardiac tagged magnetic resonance and cardiac ultrasound in order to quantify the performance of the proposed method we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known a comparison is presented with state of the art methods for cardiac motion analysis on the data considered these conventional approaches are outperformed by the proposed algorithm a recent global optical flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison with respect to the latter the proposed framework provides along with higher accuracy superior robustness to noise and a considerably shorter computation time

the finite ridgelet transform for image representation the ridgelet transform was introduced as a sparse expansion for functions on continuous spaces that are smooth away from discontinuities along lines we propose an orthonormal version of the ridgelet transform for discrete and finite size images our construction uses the finite radon transform frat as a building block to overcome the periodization effect of a finite transform we introduce a novel ordering of the frat coefficients we also analyze the frat as a frame operator and derive the exact frame bounds the resulting finite ridgelet transform frit is invertible nonredundant and computed via fast algorithms furthermore this construction leads to a family of directional and orthonormal bases for images numerical results show that the frit is more effective than the wavelet transform in approximating and denoising images with straight edges

variational optical flow computation in real time this paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations although these numerical schemes are among the fastest methods for solving equation systems they are rarely applied in the field of computer vision we demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real time performance on standard pcs as a representative for variational optic flow methods we consider the recently introduced combined local global method it can be considered as a noise robust generalization of the horn and schunck technique we present a decoupled as well as a coupled version of the classical gau spl szlig seidel solver and we develop several multigrid implementations based on a discretization coarse grid approximation in contrast with standard bidirectional multigrid algorithms we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies as a consequence no restrictions concerning the image size or the number of traversed levels have to be imposed in the experimental section we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multigrid methods and nonhierachical solvers for the well known 316 spl times 252 yosemite sequence we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3 06 ghz pentium4 pc this corresponds to a frame rate of 18 flow fields per second which outperforms the widely used gau spl szlig seidel method by almost three orders of magnitude

pontryagin s principle for state constrained boundary control problems of semilinear parabolic equations this paper deals with state constrained optimal control problems governed by semilinear parabolic equations we establish a minimum principle of pontryagin s type to deal with the state constraints we introduce a penalty problem by using ekeland s principle the key tool for the proof is the use of a special kind of spike perturbations distributed in the domain where the controls are defined conditions for normality of optimality conditions are given

design of steerable filters for feature detection using canny like criteria we propose a general approach for the design of 2d feature detectors from a class of steerable functions based on the optimization of a canny like criterion in contrast with previous computational designs our approach is truly 2d and provides filters that have closed form expressions it also yields operators that have a better orientation selectivity than the classical gradient or hessian based detectors we illustrate the method with the design of operators for edge and ridge detection we present some experimental results that demonstrate the performance improvement of these new feature detectors we propose computationally efficient local optimization algorithms for the estimation of feature orientation we also introduce the notion of shape adaptable feature detection and use it for the detection of image corners

a shearlet approach to edge analysis and detection it is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges in this paper we propose a novel approach based on the shearlet transform a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges indeed unlike traditional wavelets shearlets are theoretically optimal in representing images with edges and in particular have the ability to fully capture directional and other geometrical features numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges and outperforms methods based on wavelets as well as other standard methods furthermore the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions

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