extrapolative spatial models for detecting perceptual boundaries in colour images we present a novel approach for automatically building image specific extrapolative spatial models of non boundary local energy that can be used to perform local statistical tests to detect perceptual boundaries the non boundary model consists of statistics of local energy that are spatially extrapolated by a non boundary confidence map and a scale adaptive normalised filtering algorithm we exploit the flexibility of steerable filters to both extract oriented local energy and to provide local statistics of the energy distribution in the orientation domain to compute the non boundary confidence map finally we apply our local thresholding technique separately to the three channels of colour images and adopt a max operator to combine the results we provide a qualitative and quantitative comparison on real images from a hand segmented natural image database against the best combination of the most widely cited colour edge detectors and automatic global thresholding methods

design of multiparameter steerable functions using cascade basis reduction an efficient method of computing the least squares optimal basis functions to steer any function locally is presented the method combines the lie group theoretic and the singular value decomposition approaches its efficiency is demonstrated with the design of basis functions to steer a gabor function under the four parameter linear transformation group

sorted random projections for robust rotation invariant texture classification this paper presents a simple novel yet very powerful approach for robust rotation invariant texture classification based on random projection the proposed sorted random projection maintains the strengths of random projection in being computationally efficient and low dimensional with the addition of a straightforward sorting step to introduce rotation invariance at the feature extraction stage a small set of random measurements is extracted from sorted pixels or sorted pixel differences in local image patches the rotation invariant random features are embedded into a bag of words model to perform texture classification allowing us to achieve global rotation invariance the proposed unconventional and novel random features are very robust yet by leveraging the sparse nature of texture images our approach outperforms traditional feature extraction methods which involve careful design and complex steps we report extensive experiments comparing the proposed method to six state of the art methods rp patch lbp wmfs and the methods of lazebnik et al and zhang et al in texture classification on five databases curet brodatz uiuc umd and kth tips our approach leads to significant improvements in classification accuracy producing consistently good results on each database including what we believe to be the best reported results for brodatz umd and kth tips

supersymmetric kadomtsev petviashvili hierarchy ghost symmetry structure reductions and darboux backlund solutions this paper studies manin radul supersymmetric kadomtsev petviashvili hierarchy mr skp in three related aspects i we find an infinite set of additional ghost symmetry flows spanning the same anti commutation algebra as the ordinary mr skp flows ii the latter are used to construct consistent reductions skpr 2 m 2 of the initial unconstrained mr skp hierarchy which involves a nontrivial modification for the fermionic flows iii for the simplest constrained mr skp hierarchy skp12 12 we show that the orbit of darboux backlund transformations lies on a supersymmetric toda lattice being a square root of the standard one dimensional toda lattice and also we find explicit wronskian ratio solutions for the super tau function

receiver operating characteristic curves for a simple stochastic process that carries a static signal the detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic roc curve in which the probability of correct detection is plotted against the probability for a false positive this kind of analysis is typically applied to the situation in which signal and noise are stochastic variables the detection problem emerges however also often in a context in which both signal and noise are stochastic processes and the correct or false detection is said to take place when the process crosses a threshold in a given time window here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process the well known ornstein uhlenbeck process we give exact but difficult to evaluate quadrature expressions for the detection rates for false positives and correct detections investigate systematically a simple sampling approximation suggested earlier compare to an approximation by stratonovich for the limit of high threshold and briefly explore the case of multiplicative signal all theoretical results are compared to extensive numerical simulations of the corresponding langevin equation our results demonstrate that the sampling approximation provides a reasonable description of the roc curve for this system and it clarifies limit cases for the roc curve

a zernike moment phase based descriptor for local image representation and matching a local image descriptor robust to the common photometric transformations blur illumination noise and jpeg compression and geometric transformations rotation scaling translation and viewpoint is crucial to many image understanding and computer vision applications in this paper the representation and matching power of region descriptors are to be evaluated a common set of elliptical interest regions is used to evaluate the performance the elliptical regions are further normalized to be circular with a fixed size the normalized circular regions will become affine invariant up to a rotational ambiguity here a new distinctive image descriptor to represent the normalized region is proposed which primarily comprises the zernike moment zm phase information an accurate and robust estimation of the rotation angle between a pair of normalized regions is then described and used to measure the similarity between two matching regions the discriminative power of the new zm phase descriptor is compared with five major existing region descriptors sift gloh pca sift complex moments and steerable filters based on the precision recall criterion the experimental results involving more than 15 million region pairs indicate the proposed zm phase descriptor has generally speaking the best performance under the common photometric and geometric transformations both quantitative and qualitative analyses on the descriptor performances are given to account for the performance discrepancy first the key factor for its striking performance is due to the fact that the zm phase has accurate estimation accuracy of the rotation angle between two matching regions second the feature dimensionality and feature orthogonality also affect the descriptor performance third the zm phase is more robust under the nonuniform image intensity fluctuation finally a time complexity analysis is provided

feature vector field and feature matching in this paper we propose a feature vector field for images which is built by the inner products and exterior products of image gradients the feature vector field effectively represents image edges and feature points including corners and edge points with big curvature using the feature vector field some novel descriptors are constructed for point matching and curve matching the descriptors are all invariant to image euclidean transformations and linear intensity changes the experiments show that the descriptors also have a good adaptability to small image affine transformation jpeg compression and nonlinear changes of intensity

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

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

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

subband coding of images subband coding has become quite popular for the source encoding of speech this paper presents a simple yet efficient extension of this concept to the source coding of images we specify the constraints for a set of two dimensional quadrature mirror filters qmf s for a particular frequency domain partition and show that these constraints are satisfied by a separable combination of one dimensional qmf s bits are then optimally allocated among the subbands to minimize the mean squared error for dpcm coding of the subbands also an adaptive technique is developed to allocate the bits within each subband by means of a local variance mask optimum quantization is employed with quantizers matched to the laplacian distribution subband coded images are presented along with their signal to noise ratios snr s the snr performance of the subband coder is compared to that of the adaptive discrete cosine transform dct vector quantization and differential vector quantization for bit rates of 0 67 1 0 and 2 0 bits per pixel for 256 256 monochrome images the adaptive subband coder has the best snr performance

noise reduction procedures for gravity gradiometer data abstractnoise suppression of airborne gravity gradiometer data is a crucial part of the data processing stream we considered two approaches to removing noise kriging and directional filtering kriging is an estimation procedure for the interpolation of spatial data the estimator is calculated from the data variogram which characterizes the noise level and correlation length of the measurements directional filtering uses a user defined operator that is oriented to preferentially smooth the data along the strike but it leaves short wavelength components in the cross strike direction for definition of the trend edges both methods were applied to a recently collected offshore gravity gradient survey the kriging and directional filtering results revealed a similar level of smoothness but the main difference between them was the extra smoothing along the strike for the directionally filtered data because kriging is a data driven procedure it provides an objective estimate of the data noise level and

using basic image features for texture classification representing texture images statistically as histograms over a discrete vocabulary of local features has proven widely effective for texture classification tasks images are described locally by vectors of for example responses to some filter bank and a visual vocabulary is defined as a partition of this descriptor response space typically based on clustering in this paper we investigate the performance of an approach which represents textures as histograms over a visual vocabulary which is defined geometrically based on the basic image features of griffin and lillholm proc spie 6492 09 1 11 2007 rather than by clustering bifs provide a natural mathematical quantisation of a filter response space into qualitatively distinct types of local image structure we also extend our approach to deal with intra class variations in scale our algorithm is simple there is no need for a pre training step to learn a visual dictionary as in methods based on clustering and no tuning of parameters is required to deal with different datasets we have tested our implementation on three popular and challenging texture datasets and find that it produces consistently good classification results on each including what we believe to be the best reported for the kth tips and equal best reported for the uiuctex databases

on photometric issues in 3d visual recognition from asingle 2d image we describe the problem of recognition under changing illumination conditions and changing viewing positions from a computational and human vision perspective on the computational side we focus on the mathematical problems of creating an equivalence class for images of the same 3d object undergoing certain groups of transformations mostly those due to changing illumination and briefly discuss those due to changing viewing positions the computational treatment culminates in proposing a simple scheme for recognizing via alignment an image of a familiar object taken from a novel viewing position and a novel illumination condition on the human vision aspect the paper is motivated by empirical evidence inspired by mooney images of faces that suggest a relatively high level of visual processing is involved in compensating for photometric sources of variability and furthermore that certain limitations on the admissible representations of image information may exist the psychophysical observations and the computational results that follow agree in several important respects such as the same apparent limitations on image representations

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

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

nonlinearities in stereoscopic phase differencing exploiting the quasi linear relationship between local phase and disparity phase differencing registration algorithms provide a fast powerful means for disparity estimation unfortunately these phase differencing techniques suffer a significant impediment phase nonlinearities in regions of phase nonlinearity the signals under consideration possess properties that invalidate the use of phase for disparity estimation this paper uses the amenable properties of gaussian white noise images to analytically quantify these properties the improved understanding gained from this analysis enables us to better understand current methodologies for detecting regions of phase instability most importantly we introduce a new more effective means for identifying these regions based on the second derivative of phase

nonlocal hierarchical dictionary learning using wavelets for image denoising exploiting the sparsity within representation models for images is critical for image denoising the best currently available denoising methods take advantage of the sparsity from image self similarity pre learned and fixed representations most of these methods however still have difficulties in tackling high noise levels or noise models other than gaussian in this paper the multiresolution structure and sparsity of wavelets are employed by nonlocal dictionary learning in each decomposition level of the wavelets experimental results show that our proposed method outperforms two state of the art image denoising algorithms on higher noise levels furthermore our approach is more adaptive to the less extensively researched uniform noise

binary nonlinearization of the super akns system under an implicit symmetry constraint for the super akns system an implicit symmetry constraint between the potentials and the eigenfunctions is proposed after introducing some new variables to explicitly express potentials the super akns system is decomposed into two compatible finite dimensional super systems x part and tn part furthermore we show that the obtained super systems are integrable super hamiltonian systems in the supersymmetry manifold

stereoscopic ranging by matching image modulations we apply an am fm surface albedo model to analyze the projection of surface patterns viewed through a binocular camera system this is used to support the use of modulation based stereo matching where local image phase is used to compute stereo disparities the local image phase is an advantageous feature for image matching since the problem of computing disparities reduces to identifying local phase shifts between the stereoscopic image data local phase shifts however are problematic at high frequencies due to phase wrapping when disparities exceed spl plusmn spl pi we meld powerful multichannel gabor image demodulation techniques for multiscale coarse to fine computation of local image phase with a disparity channel model for depth computation the resulting framework unifies phase based matching approaches with am fm surface image models we demonstrate the concepts in a stereo algorithm that generates a dense accurate disparity map without the problems associated with phase wrapping

a modified k means algorithm for circular invariant clustering several important pattern recognition applications are based on feature vector extraction and vector clustering directional patterns are commonly represented by rotation variant vectors f sub d formed from features uniformly extracted in m directions it is often desirable that pattern recognition algorithms are invariant under pattern rotation this paper introduces a distance measure and a k means based algorithm namely circular k means ck means to cluster vectors containing directional information such as f sub d in a circular shift invariant manner a circular shift of f sub d corresponds to pattern rotation thus the algorithm is rotation invariant an efficient fourier domain representation of the proposed measure is presented to reduce computational complexity a split and merge approach smck means suited to the proposed ck means technique is proposed to reduce the possibility of converging at local minima and to estimate the correct number of clusters experiments performed for textural images illustrate the superior performance of the proposed algorithm for clustering directional vectors f sub d compared to the alternative approach that uses the original k means and rotation invariant feature vectors transformed from f sub d

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

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

solving the kp hierarchy by gauge transformations we show that it is convenient to use gauge transformations sometimes called explicit backlund transformations to generate new solutions for the kp hierarchy two particular kinds of gauge transformation operators constructed out of the initial wave functions are of fundamental importance in this approach through such gauge transformations a very simple formula for the tau function is obtained encompassing and unifying all kinds of existing solutions the corresponding free fermion representation and baker functions for the new function can also be constructed

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

a phase based approach to the estimation of the optical flow field using spatial filtering we introduce a new technique for estimating the optical flow field starting from image sequences as suggested by fleet and jepson 1990 we track contours of constant phase over time since these are more robust to variations in lighting conditions and deviations from pure translation than contours of constant amplitude our phase based approach proceeds in three stages first the image sequence is spatially filtered using a bank of quadrature pairs of gabor filters and the temporal phase gradient is computed yielding estimates of the velocity component in directions orthogonal to the filter pairs orientations second a component velocity is rejected if the corresponding filter pair s phase information is not linear over a given time span third the remaining component velocities at a single spatial location are combined and a recurrent neural network is used to derive the full velocity we test our approach on several image sequences both synthetic and realistic

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

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

n 4 super kdv hierarchy in n 4 and n 2 superspaces we present the results of further analysis of the integrability properties of the n 4 supersymmetric korteweg de vries kdv equation deduced earlier by two of us f delduc and e ivanov phys lett b 309 312 1993 as a hamiltonian flow on n 4 su 2 superconformal algebra in the harmonic n 4 superspace to make this equation and the relevant hamiltonian structures more tractable we reformulate it in the ordinary n 4 and further in n 2 superspaces in n 2 superspace it is represented by a coupled system of evolution equations for a general n 2 superfield and two chiral and antichiral superfields and involves two independent real parameters a and b we construct a few first bosonic conserved charges in involution of dimensions from 1 to 6 and show that they exist only for the following choices of the parameters i a 4 b 0 ii a 2 b 6 iii a 2 b 6 the same values are needed for the relevant evolution equations including n 4 kdv itself to be bi hamiltonian we demonstrate that the above three options are related via su 2 transformations and actually amount to the su 2 covariant integrability condition found in the harmonic superspace approach our results provide a strong evidence that the unique n 4 su 2 super kdv hierarchy exists upon reduction to n 2 kdv the above three possibilities cease to be equivalent they give rise to the a 4 and a 2 n 2 kdv hierarchies which thus prove to be different truncations of the single n 4 su 2 kdv one

computing optical flow with physical models of brightness variation although most optical flow techniques presume brightness constancy it is well known that this constraint is often violated producing poor estimates of image motion this paper describes a generalized formulation of optical flow estimation based on models of brightness variations that are caused by time dependent physical processes these include changing surface orientation with respect to a directional illuminant motion of the illuminant and physical models of heat transport in infrared images with these models we simultaneously estimate the 2d image motion and the relevant physical parameters of the brightness change model the estimation problem is formulated using total least squares with confidence bounds on the parameters experiments in four domains with both synthetic and natural inputs show how this formulation produces superior estimates of the 2d image motion

the geometry of the super kp flows a supersymmetric generalization of the krichever map is used to construct algebro geometric solutions to the various super kadomtsev petviashvili skp hierarchies the geometric data required consist of a suitable algebraic supercurve of genusg generallynot a super riemann surface with a distinguished point and local coordinates z there and a generic line bundle of degreeg 1 with a local trivialization near the point the resulting solutions to the manin radul skp system describe coupled deformations of the line bundle and the supercurve itself in contrast to the ordinary kp system which deforms line bundles but not curves two new skp systems are introduced an integrable jacobian system whose solutions describe genuine jacobian flows deforming the bundle but not the curve and a nonintegrable maximal system describing independent deformations of bundle and curve the kac van de leur skp system describes the same deformations as the maximal system but in a different parametrization

a theory of phase singularities for image representation and its applications to object tracking and image matching this paper studies phase singularities pss for image representation we show that pss calculated with laguerre gauss filters contain important information and provide a useful tool for image analysis pss are invariant to image translation and rotation we introduce several invariant features to characterize the core structures around pss and analyze the stability of pss to noise addition and scale change we also study the characteristics of pss in a scale space which lead to a method to select key scales along phase singularity curves we demonstrate two applications of pss object tracking and image matching in object tracking we use the iterative closest point algorithm to determine the correspondences of pss between two adjacent frames the use of pss allows us to precisely determine the motions of tracked objects in image matching we combine pss and scale invariant feature transform sift descriptor to deal with the variations between two images and examine the proposed method on a benchmark database the results indicate that our method can find more correct matching pairs with higher repeatability rates than some well known methods

accurate image rotation using hermite expansions in this paper we propose an approach for the accurate rotation of a digital image using hermite expansions this exploits the fact that if a 2 d continuous bandlimited hermite expansion is rotated the resulting function can be expressed as a hermite expansion with the same bandlimit furthermore the hermite coefficients of the initial 2 d expansion and the rotated expansion are mapped through an invertible linear relationship two efficient methods to compute the mapping between hermite coefficients during rotation are proposed we also propose a method for connecting the hermite expansion and a discrete image using this method we can obtain the hermite expansion from a discrete image and vice versa combining these techniques we propose new methods for the rotation of discrete images we assess the accuracy of our methods and compare them with an existing fft based method implementing three shears we find that the method proposed here consistently has better accuracy than the fft based method

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

n 2 kp and kdv hierarchies in extended superspace we give the formulation in extended superspace of an n 2 supersymmetric kp hierarchy using chirality preserving pseudo differential operators we obtain two quadratic hamiltonian structures which lead to different reductions of the kp hierarchy in particular we find two different hierarchies with the n 2 classical super algebra as a hamiltonian structure the relation with the formulation in n 1 superspace and the bosonic limit are carried out

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

supersymmetric extension of the integrable box ball system we introduce the supersymmetric extension of the box ball system by use of the isomorphism of the crystal base for the super lie algebra we define the time evolution operator and give the evolution equation explicitly we also construct the soliton solutions

flexible spatial configuration of local image features local image features have been designed to be informative and repeatable under rigid transformations and illumination deformations even though current state of the art local image features present a high degree of repeatability their local appearance alone usually does not bring enough discriminative power to support a reliable matching resulting in a relatively high number of mismatches in the correspondence set formed during the data association procedure as a result geometric filters commonly based on global spatial configuration have been used to reduce this number of mismatches however this approach presents a trade off between the effectiveness to reject mismatches and the robustness to nonrigid deformations in this paper we propose two geometric filters based on a semilocal spatial configuration of local features that are designed to be robust to nonrigid deformations and to rigid transformations without compromising its efficacy to reject mismatches we compare our methods to the hough transform which is an efficient and effective mismatch rejection step based on the global spatial configuration of features in these comparisons our methods are shown to be more effective in the task of rejecting mismatches for rigid transformations and nonrigid deformations at comparable time complexity figures finally we demonstrate how we can integrate these methods in a probabilistic recognition system such that the final verification step uses not only the similarity between features but also their semilocal configuration

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

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

curvilinear structure analysis by ranking the orientation responses of path operators the analysis of thin curvilinear objects in 3d images is a complex and challenging task in this article we introduce a new non linear operator called rorpo ranking the orientation responses of path operators inspired by the multidirectional paradigm currently used in linear filtering for thin structure analysis rorpo is built upon the notion of path operator from mathematical morphology this operator unlike most operators commonly used for 3d curvilinear structure analysis is discrete non linear and non local from this new operator two main curvilinear structure characteristics can be estimated an intensity feature that can be assimilated to a quantitative measure of curvilinearity and a directional feature providing a quantitative measure of the structure s orientation we provide a full description of the structural and algorithmic details for computing these two features from rorpo and we discuss computational issues we experimentally assess rorpo by comparison with three of the most popular curvilinear structure analysis filters namely frangi vesselness optimally oriented flux and hybrid diffusion with continuous switch in particular we show that our method provides up to 8 percent more true positive and 50 percent less false positives than the next best method on synthetic and real 3d images

the sure let approach to image denoising we propose a new approach to image denoising based on the image domain minimization of an estimate of the mean squared error stein s unbiased risk estimate sure unlike most existing denoising algorithms using the sure makes it needless to hypothesize a statistical model for the noiseless image a key point of our approach is that although the nonlinear processing is performed in a transformed domain typically an undecimated discrete wavelet transform but we also address nonorthonormal transforms this minimization is performed in the image domain indeed we demonstrate that when the transform is a ldquotightrdquo frame an undecimated wavelet transform using orthonormal filters separate subband minimization yields substantially worse results in order for our approach to be viable we add another principle that the denoising process can be expressed as a linear combination of elementary denoising processes linear expansion of thresholds let armed with the sure and let principles we show that a denoising algorithm merely amounts to solving a linear system of equations which is obviously fast and efficient quite remarkably the very competitive results obtained by performing a simple threshold image domain sure optimized on the undecimated haar wavelet coefficients show that the sure let principle has a huge potential

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

training less color object recognition for autonomous robotics abstract this paper looks at the challenge of object recognition from the perspective of achieving the final goals of practical real world autonomous robot vision applications that of identifying a target of interest in the robot s field of view and properly localizing its position in preparation for the higher level goal of tracking and navigation a unified framework is introduced that combines a multidimensional feature histogram approach with a multiscale pyramid approach for training less color object recognition and localization with direct application to autonomous robotic agents this framework addresses the high computational cost associated with multidimensional processing by deriving the multidimensional laplacian feature histogram pyramid a novel approach to a unified multidimensional multiscale histogram representation furthermore a taylor series formulation is employed to combine the multiscale levels of the multidimensional laplacian feature histogram pyramid into one efficient multidimensional multiscale laplacian taylor feature histogram for rapid object recognition and localization the paper describes the criteria for target detection and localization by autonomous robots and how this newly developed framework fits these needs comparative results demonstrate the robustness of this recognition framework to noise and localization of target objects in cluttered scenes

noise analysis of a new singularity index we analyze the noise sensitivity of a new singularity index that was designed to detect impulse singularities in signals of arbitrary dimensionality while rejecting step like singularities see muralidhar ieee signal process lett vol 20 no 1 pp 7 10 2013 and muralidhar proc ieee int conf image process 2012 for example the index responds strongly to curvilinear masses ridges in images while weakly to jump discontinuities edges we analyze the detection power of the index in the presence of noise our analysis is geared towards answering the following questions a in the presence of noise only what is the probability of falsely detecting an impulse given a threshold b given an impulse submerged in noise what is the probability of detecting it given a threshold and c since the index is designed to be edge suppressing what is the probability of incorrectly detecting an edge submerged in noise given a threshold we compare the detection power of the index with that of a nominal impulse detector the second derivative operator simulations and example applications in 1 d and 2 d reveal the efficacy of the new singularity index for correctly detecting impulses submerged in noise while suppressing edges a software version of the 2 d singularity index can be downloaded from http live ece utexas edu research singularityindex singularityindexcode zip

riemann liouville integrals of fractional order and extended kp hierarchy an attempt to formulate the extensions of the kp hierarchy by introducing fractional order pseudo differential operators is given in the case of the extension with the half order pseudo differential operators a system analogous to the supersymmetric extensions of the kp hierarchy is obtained unlike the supersymmetric extensions no grassmannian variable appears in the hierarchy considered here more general hierarchies constructed by the 1 nth order pseudo differential operators their integrability and the reduction procedure are also investigated in addition to finding the new extensions of the kp hierarchy a brief introduction to the riemann liouville integral is provided to yield a candidate for the fractional order pseudo differential operators

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

phase vector incompressible registration algorithm for motion estimation from tagged magnetic resonance images tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue it is challenging to obtain 3 d motion estimates due to a tradeoff between image slice density and acquisition time typically interpolation methods are used either to combine 2 d motion extracted from sparse slice acquisitions into 3 d motion or to construct a dense volume from sparse acquisitions before image registration methods are applied this paper proposes a new phase based 3 d motion estimation technique that first computes harmonic phase volumes from interpolated tagged slices and then matches them using an image registration framework the approach uses several concepts from diffeomorphic image registration with a key novelty that defines a symmetric similarity metric on harmonic phase volumes from multiple orientations the material property of harmonic phase solves the aperture problem of optical flow and intensity based methods and is robust to tag fading a harmonic magnitude volume is used in enforcing incompressibility in the tissue regions the estimated motion fields are dense incompressible diffeomorphic and inverse consistent at a 3 d voxel level the method was evaluated using simulated phantoms human brain data in mild head accelerations human tongue data during speech and an open cardiac data set the method shows comparable accuracy to three existing methods while demonstrating low computation time and robustness to tag fading and noise

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

steerable wavelet frames based on the riesz transform we consider an extension of the 1 d concept of analytical wavelet to n d which is by construction compatible with rotations this extension called a monogenic wavelet yields a decomposition of the wavelet coefficients into amplitude phase and phase direction the monogenic wavelet is based on the hypercomplex monogenic signal which is defined using riesz transforms and perfectly isotropic wavelets frames employing the new concept of clifford frames we can show that the monogenic wavelet generates a wavelet frame furthermore this approach yields wavelet frames that are steerable with respect to direction applications to descreening and contrast enhancement illustrate the versatility of this approach to image analysis and reconstruction

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

local shading analysis local analysis of image shading in the absence of prior knowledge about the viewed scene may be used to provide information about the scene the following has been proved every image point has the same image intensity and first and second derivatives as the image of some point on a lambertian surface with principal curvatures of equal magnitude further if the principal curvatures are assumed to be equal there is a unique combination of image formation parameters up to a mirror reversal that will produce a particular set of image intensity and first and second derivatives a solution for the unique combination of surface orientation etc is presented this solution has been extended to natural imagery by using general position and regional constraints to obtain estimates of the following surface orientation at each image point the qualitative type of the surface i e whether the surface is planar cylindrical convex concave or saddle the illuminant direction within a region algorithms to recover illuminant direction and estimate surface orientation have been evaluated on both natural and synthesized images and have been found to produce useful information about the scene

signal denoising and ultrasonic flaw detection via overcomplete and sparse representations sparse signal representations from overcomplete dictionaries are the most recent technique in the signal processing community applications of this technique extend into many fields in this paper this technique is utilized to cope with ultrasonic flaw detection and noise suppression problem in particular a noisy ultrasonic signal is decomposed into sparse representations using a sparse bayesian learning algorithm and an overcomplete dictionary customized from a gabor dictionary by incorporating some a priori information of the transducer used nonlinear postprocessing including thresholding and pruning is then applied to the decomposed coefficients to reduce the noise contribution and extract the flaw information because of the high compact essence of sparse representations flaw echoes are packed into a few significant coefficients and noise energy is likely scattered all over the dictionary atoms generating insignificant coefficients this property greatly increases the efficiency of the pruning and thresholding operations and is extremely useful for detecting flaw echoes embedded in background noise the performance of the proposed approach is verified experimentally and compared with the wavelet transform signal processor experimental results to detect ultrasonic flaw echoes contaminated by white gaussian additive noise or correlated noise are presented in the paper

a differential model of the complex cell the receptive fields of simple cells in the visual cortex can be understood as linear filters these filters can be modeled by gabor functions or gaussian derivatives gabor functions can also be combined in an energy model of the complex cell response this letter proposes an alternative model of the complex cell based on gaussian derivatives it is most important to account for the insensitivity of the complex response to small shifts of the image the new model uses a linear combination of the first few derivative filters at a single position to approximate the first derivative filter at a series of adjacent positions the maximum response over all positions gives a signal that is insensitive to small shifts of the image this model unlike previous approaches is based on the scale space theory of visual processing in particular the complex cell is built from filters that respond to the 2d differential structure of the image the computational aspects of the new model are studied in one and two dimensions using the steerability of the gaussian derivatives the response of the model to basic images such as edges and gratings is derived formally the response to natural images is also evaluated using statistical measures of shift insensitivity the neural implementation and predictions of the model are discussed

image filtering edge detection and edge tracing using fuzzy reasoning we characterize the problem of detecting edges in images as a fuzzy reasoning problem the edge detection problem is divided into three stages filtering detection and tracing images are filtered by applying fuzzy reasoning based on local pixel characteristics to control the degree of gaussian smoothing filtered images are then subjected to a simple edge detection algorithm which evaluates the edge fuzzy membership value for each pixel based on local image characteristics finally pixels having high edge membership are traced and assembled into structures again using fuzzy reasoning to guide the tracing process the filtering detection and tracing algorithms are tested on several test images comparison is made with a standard edge detection technique

method of squared eigenfunction potentials in integrable hierarchies of kp type the method of squared eigenfunction potentials sep is developed systematically to describe and gain new information about the kadomtsev petviashvili kp hierarchy and its reductions interrelation to the function method is discussed in detail the principal result which forms the basis of our sep method is the proof that any eigenfunction of the general kp hierarchy can be represented as a spectral integral over the baker akhiezer ba wave function with a spectral density expressed in terms of sep in fact the spectral representations of the adjoint ba functions can in turn be considered as defining equations for the kp hierarchy the sep method is subsequently used to show how the reduction of the full kp hierarchy to the constrained kp ckp rm hierarchies can be given entirely in terms of linear constraint equations on the pertinent functions the concept of sep turns out to be crucial in providing a description of ckp rm hierarchies in the language of the universal sato grassmannian and finding the non isospectral virasoro symmetry generators acting on the underlying functions the sep method is used to write down generalized binary darboux backlund transformations for constrained kp hierarchies whose orbits are shown to correspond to a new toda model on a square lattice as a result we obtain a series of new determinant solutions for the functions generalizing the known wronskian multi soliton solutions finally applications to random matrix models in condensed matter physics are briefly discussed

a morphological affine and galilean invariant scale space for movies we study a model of multiscale analysis or scale space applied to movies this model comes from a thorough formalization that has been done in the theory of scale space of static image this formulation has led one to associate with each multiscale analysis a partial differential equation pde we examine the case of movies and insist on the motion aspects more precisely it has been proved by alvarez guichard lions and morel 1993 that there exists a unique affine and morphological and galilean invariant scale space for movies the amg model this model is described by a partial differential equation we focus on terms appearing in that equation we show that this model provides a reliable definition of an optical multiscale acceleration at the practical level scale is interpreted as a way of characterizing reliable trajectories as we prove by experiments the amg model is a riddle for decimating spurious trajectories due to any kinds of nonadditive impurities and noise simple discrete formulae are given to implement the model

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

recognition by symmetry derivatives and the generalized structure tensor we suggest a set of complex differential operators that can be used to produce and filter dense orientation tensor fields for feature extraction matching and pattern recognition we present results on the invariance properties of these operators that we call symmetry derivatives these show that in contrast to ordinary derivatives all orders of symmetry derivatives of gaussians yield a remarkable invariance they are obtained by replacing the original differential polynomial with the same polynomial but using ordinary coordinates x and y corresponding to partial derivatives moreover the symmetry derivatives of gaussians are closed under the convolution operator and they are invariant to the fourier transform the equivalent of the structure tensor representing and extracting orientations of curve patterns had previously been shown to hold in harmonic coordinates in a nearly identical manner as a result positions orientations and certainties of intricate patterns e g spirals crosses parabolic shapes can be modeled by use of symmetry derivatives of gaussians with greater analytical precision as well as computational efficiency since gaussians and their derivatives are utilized extensively in image processing the revealed properties have practical consequences for local orientation based feature extraction the usefulness of these results is demonstrated by two applications 1 tracking cross markers in long image sequences from vehicle crash tests and 2 alignment of noisy fingerprints

generalized sampling expansion for functions on the sphere functions on the sphere appear in several applications including geodesics imaging and acoustics sampling of these functions may result in aliasing if the sampling condition is not met the generalized sampling expansion introduced by papoulis enables the reconstruction of a band limited function sampled at a frequency lower than the nyquist frequency using the outputs of several linear time invariant systems this paper formulates the generalized sampling expansion for functions on the sphere using spherical harmonics decomposition facilitating sub nyquit sampling without aliasing error an analysis of linear systems on the sphere and the aliasing phenomenon in the spherical harmonics domain is presented examples demonstrating the performance of the method and its limitations are studied

two view line matching algorithm based on context and appearance in low textured images a novel approach for line detection and matching is proposed aimed at achieving good performance with low textured scenes under uncontrolled illumination conditions line detection is performed by means of phase based edge detector over gaussian scale space followed by a multi scale fusion stage which has been proven to be profitable in minimizing the number of fragmented and overlapped segments line matching is performed by an iterative process that uses structural information collected through the use of different line neighborhoods making the set of matched lines grow robustly at each iteration results show that this approach is suitable to deal with low textured scenes and also robust under a wide variety of image transformations highlightsa novel approach for line detection and matching is proposed lines are detected through a fusion process over the gaussian scale space lines are matched based on their appearance geometric properties and neighborhoods our proposal minimizes the number of fragmented and overlapped segments our proposal is suitable for low textured scenes under uncontrolled illumination

image representations using multiscale differential operators differential operators have been widely used for multiscale geometric descriptions of images the efficient computation of these differential operators is always desirable moreover it has not been clear whether such representations are invertible for certain applications it is usually required that such representations should be invertible so that one can facilitate the processing of information in the transform domain and then recover it in this paper such problems are studied we consider multiscale differential representations of images using different types of operators such as the directional derivative operators and laplacian operators in particular we provide a general approach to represent images by their multiscale and multidirectional derivative components for practical implementation efficient pyramid like algorithms are derived using the spline technique for both the the composition and reconstruction of images it is shown that using these representations various meaningful geometric information of images can be extracted at multiple scales therefore these representations can be used for edge based image processing purposes furthermore the intrinsic relationships of the proposed representations with the compact wavelet models and some classical multiscale approaches are also elucidated in the paper

discriminative learning of local image descriptors in this paper we explore methods for learning local image descriptors from training data we describe a set of building blocks for constructing descriptors which can be combined together and jointly optimized so as to minimize the error of a nearest neighbor classifier we consider both linear and nonlinear transforms with dimensionality reduction and make use of discriminant learning techniques such as linear discriminant analysis lda and powell minimization to solve for the parameters using these techniques we obtain descriptors that exceed state of the art performance with low dimensionality in addition to new experiments and recommendations for descriptor learning we are also making available a new and realistic ground truth data set based on multiview stereo data

lapb locally adaptive patch based wavelet domain edge preserving image denoising abstract image denoising is one of the most diversified research areas in the field of image processing and computer vision it is highly desirable for a denoising technique to preserve important image features such as edges corners and other sharp structures of an image after denoising wavelet transforms show excellent proficiency in providing efficient edge preserving image denoising due to their capability of suppressing noisy signals from an image this paper presents a novel edge preserving image denoising technique based on wavelet transforms the multi level decomposition of the noisy image is carried out to transform the data into the wavelet domain a locally adaptive patch based lapb thresholding scheme is used to effectively reduce noise while preserving relevant features of the original image experimental results on benchmark test images demonstrate that the proposed method achieves competitive denoising performance in comparison to various state of the art algorithms

a least squares framework for component analysis over the last century component analysis ca methods such as principal component analysis pca linear discriminant analysis lda canonical correlation analysis cca locality preserving projections lpp and spectral clustering sc have been extensively used as a feature extraction step for modeling classification visualization and clustering ca techniques are appealing because many can be formulated as eigen problems offering great potential for learning linear and nonlinear representations of data in closed form however the eigen formulation often conceals important analytic and computational drawbacks of ca techniques such as solving generalized eigen problems with rank deficient matrices e g small sample size problem lacking intuitive interpretation of normalization factors and understanding commonalities and differences between ca methods this paper proposes a unified least squares framework to formulate many ca methods we show how pca lda cca lpp sc and its kernel and regularized extensions correspond to a particular instance of least squares weighted kernel reduced rank regression ls wkrrr the ls wkrrr formulation of ca methods has several benefits 1 provides a clean connection between many ca techniques and an intuitive framework to understand normalization factors 2 yields efficient numerical schemes to solve ca techniques 3 overcomes the small sample size problem 4 provides a framework to easily extend ca methods we derive weighted generalizations of pca lda sc and cca and several new ca techniques

effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise the behavior of a stochastic perfect integrate and fire pif model of neurons is considered the effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing levy type subordinator using a first passage time formulation we find exact expressions for the output interspike interval isi statistics particularly it is shown that at some parameter regimes the isi density exhibits a multimodal structure moreover it is demonstrated that the coefficient of variation the serial correlation coefficient and the fano factor display a nonmonotonic dependence on the mean input current i e the isi s regularity is maximized at an intermediate value of the features of spike statistics analytically revealed in our study are compared with previously obtained results for a perfect integrate and fire neuron model driven by dichotomous noise without subordination

rotation and illumination invariant interleaved intensity order based local descriptor the region descriptors using local intensity ordering patterns have become more popular recent years for image matching due to its enhanced discriminative ability however the dimension of these descriptors increases rapidly with the slight increase in the number of local neighbors under consideration and becomes unreasonable for image matching due to time constraint in this paper we reduce the dimension of the descriptor and matching time significantly while keeping up the comparable performance by considering the number of neighboring sample points in an interleaved manner the proposed interleaved order based local descriptor iold considers the local neighbors of a pixel as a set of interleaved neighbors and constructs the descriptor over each set separately and finally combines them to produce a single pattern we extract the local ordering pattern to cope up with the illumination effect in an inherent rotation invariant manner the novelty lies with using multiple neighboring sets in an interleaved fashion we also explored the local intensity order pattern in a multisupport region scenario results are compared over three challenging and widely adopted image matching data sets with other prominent descriptors under various image transformations results based on experiments suggest that the proposed iold descriptor outperforms in terms of both improved matching performance and reduced matching time we also found that the amount of improvement is significant under complex illumination difference while showing more robustness toward noise

analyzing looming motion components from their spatiotemporal spectral signature this paper addresses the use of spatio temporal transform methods applied to the analysis of dynamic image sequences and the characterization of image motion the image motion including a divergent component resulting from a looming camera component is analyzed in the spatio temporal mellin transform mt domain resulting in the separation of the spectrum into two parts a structural term corresponding to the spatial mt of the static image and a kinematic term depending on time to collision a motion support we examine potential applications of this property for the recovery of image motion from integral image brightness measurements and the computation of time to collision using spatio temporal mt analysis

asymmetric pulse modeling for fri sampling we consider sampling and reconstruction of finite rate of innovation fri signals such as a train of pulses where the pulses have varying degrees of asymmetry we address the problem of asymmetry modeling starting from a given symmetric prototype we show that among the class of unitary operators that are linear and invariant to translation and scale the fractional hilbert frh operator is unique for parametrically modeling pulse asymmetry the frh operator is obtained by a trigonometric interpolation between the standard hilbert and identity operators where the interpolation weights are determined by the degree of asymmetry the frh operators are also steerable which allows for estimation of the asymmetry factors in addition to the delays and amplitudes using the high resolution spectral estimation techniques that are used for solving standard fri problems we also develop the discrete counterpart using discrete frh operators and show that all the desirable properties carry over smoothly to the discrete setting as well we derive closed form expressions for the cramer rao bounds and hammersley chapman robbins bound on the variances of the estimators for continuous and discrete parameters respectively experimental results show that the proposed estimators have variances that meet the lower bounds we demonstrate an application of the proposed discrete frh methodology on real electrocardiogram ecg signals in the presence of noise specifically we show how the asymmetry of qrs complexes in various channels of an ecg signal could be modeled accurately

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

spatially adaptive estimation via fitted local likelihood techniques this paper offers a new technique for spatially adaptive estimation the local likelihood is exploited for nonparametric modeling of observations and estimated signals the approach is based on the assumption of a local homogeneity of the signal for every point there exists a neighborhood in which the signal can be well approximated by a constant the fitted local likelihood statistics are used for selection of an adaptive size and shape of this neighborhood the algorithm is developed for a quite general class of observations subject to the exponential distribution the estimated signal can be uni and multivariable we demonstrate a good performance of the new algorithm for image denoising and compare the new method versus the intersection of confidence interval ici technique that also exploits a selection of an adaptive neighborhood for estimation

wavelet based fingerprint image retrieval this paper presents a novel approach for personal identification based on a wavelet based fingerprint retrieval system which encompasses three image retrieval tasks namely feature extraction similarity measurement and feature indexing we propose the use of different types of wavelets for representing and describing the textural information presented in fingerprint images in a compact way for that purpose the feature vectors used to characterize the fingerprints are obtained by computing the mean and the standard deviation of the decomposed images in the wavelet domain these feature vectors are used both to retrieve the most similar fingerprints given a query image and their indexation is used to reduce the search spaces of candidate images the different types of wavelets used in our study include gabor wavelets tree structured wavelet decomposition using both orthogonal and bi orthogonal filter banks as well as the steerable wavelets to evaluate the retrieval accuracy of the proposed approach a total number of eight different data sets were considered we also took into account different combinations of the above wavelets with six similarity measures the results show that the gabor wavelets combined with the square chord similarity measure achieves the best retrieval effectiveness

evolution of moments and correlations in nonrenewal escape time processes the theoretical description of nonrenewal stochastic systems is a challenge analytical results are often not available or can be obtained only under strong conditions limiting their applicability also numerical results have mostly been obtained by ad hoc monte carlo simulations which are usually computationally expensive when a high degree of accuracy is needed to gain quantitative insight into these systems under general conditions we here introduce a numerical iterated first passage time approach based on solving the time dependent fokker planck equation fpe to describe the statistics of nonrenewal stochastic systems we illustrate the approach using spike triggered neuronal adaptation in the leaky and perfect integrate and fire model respectively the transition to stationarity of first passage time moments and their sequential correlations occur on a nontrivial time scale that depends on all system parameters surprisingly this is so for both single exponential and scale free power law adaptation the method works beyond the small noise and time scale separation approximations it shows excellent agreement with direct monte carlo simulations which allow for the computation of transient and stationary distributions we compare different methods to compute the evolution of the moments and serial correlation coefficients sccs and discuss the challenge of reliably computing the sccs which we find to be very sensitive to numerical inaccuracies for both the leaky and perfect integrate and fire models in conclusion our methods provide a general picture of nonrenewal dynamics in a wide range of stochastic systems exhibiting short and long range correlations

linear shape from shading in many situations the reflectance function of a surface is approximately linear and there is an effielent closed form solution to the shape from shading problem when boundary conditions e g edges singular points are not available good estimates of shape may still be extracted by using the assumption of general viewing position an improved method for estimating the illuminant direction is also presented

stability of phase information this paper concerns the robustness of local phase information for measuring image velocity and binocular disparity it addresses the dependence of phase behavior on the initial filters as well as the image variations that exist between different views of a 3d scene we are particularly interested in the stability of phase with respect to geometric deformations and its linearity as a function of spatial position these properties are important to the use of phase information and are shown to depend on the form of the filters as well as their frequency bandwidths phase instabilities are also discussed using the model of phase singularities described by jepson and fleet in addition to phase based methods these results are directly relevant to differential optical flow methods and zero crossing tracking

tau function formalism for supersymmetric kp hierarchies we consider the manin radul and jacobian supersymmetric kp hierarchies from the point of view of the tau function formalism solutions of their associated systems of sato equations are characterized in terms of correlation functions of supersymmetric vertex operators of superghost type the expression of the wave functions of these hierarchies in terms of tau functions is obtained and the corresponding bilinear identities are established explicit methods for generating soliton and rational solutions are given

natural image statistics for natural image segmentation we integrate a model for filter response statistics of natural images into a variational framework for image segmentation incorporated in a sound probabilistic distance measure the model drives level sets toward meaningful segmentations of complex textures and natural scenes despite its enhanced descriptive power our approach preserves the efficiency of level set based segmentation since each region comprises two model parameters only analyzing thousands of natural images we select suitable filter banks validate the statistical basis of our model and demonstrate that it outperforms variational segmentation methods using second order statistics

constraints of the kp hierarchy and multilinear forms we consider the trilinear form of the kaup broer system which gives rise to solutions in wronskian form the kaup broer system is connected with akns system through a gauge transformation the akns hierarchy can be understood as a generalized 1 constraint of the kp hierarchy imposing that constraint on sato s equation we obtain the basic trilinear form and moreover a hierarchy of trilinear equations governing the akns flows similary hierarchies of multilinear forms are derived in the case of generalized k constraints