the monogenic signal this paper introduces a two dimensional 2 d generalization of the analytic signal this novel approach is based on the riesz transform which is used instead of the hilbert transform the combination of a 2 d signal with the riesz transformed one yields a sophisticated 2 d analytic signal the monogenic signal the approach is derived analytically from irrotational and solenoidal vector fields based on local amplitude and local phase an appropriate local signal representation that preserves the split of identity i e the invariance equivariance property of signal decomposition is presented this is one of the central properties of the one dimensional 1 d analytic signal that decomposes a signal into structural and energetic information we show that further properties of the analytic signal concerning symmetry energy allpass transfer function and orthogonality are also preserved and we compare this with the behavior of other approaches for a 2 d analytic signal as a central topic of this paper a geometric phase interpretation that is based on the relation between the 1 d analytic signal and the 2 d monogenic signal established by the radon 1986 transform is introduced possible applications of this relationship are sketched and references to other applications of the monogenic signal are given

image registration based on autocorrelation of local structure registration of images in the presence of intra image signal fluctuations is a challenging task the definition of an appropriate objective function measuring the similarity between the images is crucial for accurate registration this paper introduces an objective function that embeds local phase features derived from the monogenic signal in the modality independent neighborhood descriptor mind the image similarity relies on the autocorrelation of local structure alost which has two important properties 1 low sensitivity to space variant intensity distortions e g differences in contrast enhancement in mri 2 high distinctiveness for salient image features such as edges the alost method is quantitatively compared to the mind approach based on three different datasets thoracic ct images synthetic and real abdominal mr images the proposed method outperformed the nmi and mind similarity measures on these three datasets the registration of dynamic contrast enhanced and post contrast mr images of patients with crohn s disease led to relative contrast enhancement measures with the highest correlation rm r 0 56 to the crohn s disease endoscopic index of severity

optimal maps for the multidimensional monge kantorovich problem let 1 n be borel probability measures on d denote by 1 n the set of all n tuples t t1 tn such that ti d d i 1 n are borel measurable and satisfy 1 i v for all borel v d the multidimensional monge kantorovich problem investigated in this paper consists of finding s s1 sn 1 n minimizing over the set 1 n we study the case where the i s have finite second moments and vanish on d 1 rectifiable sets we prove existence and uniqueness of optimal maps s when we impose that s1 x x and give an explicit form of the maps si the result is obtained by variational methods and to the best of our knowledge is the first available in the literature in this generality as a consequence we obtain uniqueness and characterization of an optimal measure for the multidimensional kantorovich problem 1998 john wiley sons inc

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

time scales in homogenization of periodic flows with vanishing molecular diffusion abstract we study the long time transport property of conservative systems perturbed by a small white noise we introduce the dissipation and martingale times and show how they are related to the diffusion time on which a limit theorem is valid the limit theorem is a probabilistic version of homogenization with vanishing molecular diffusion examples of nontrivial time scales are given

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

identifying regional cardiac abnormalities from myocardial strains using nontracking based strain estimation and spatio temporal tensor analysis myocardial strain is a critical indicator of many cardiac diseases and dysfunctions the goal of this paper is to extract and use the myocardial strain pattern from tagged magnetic resonance imaging mri to identify and localize regional abnormal cardiac function in human subjects in order to extract the myocardial strains from the tagged images we developed a novel nontracking based strain estimation method for tagged mri this method is based on the direct extraction of tag deformation and therefore avoids some limitations of conventional displacement or tracking based strain estimators based on the extracted spatio temporal strain patterns we have also developed a novel tensor based classification framework that better conserves the spatio temporal structure of the myocardial strain pattern than conventional vector based classification algorithms in addition the tensor based projection function keeps more of the information of the original feature space so that abnormal tensors in the subspace can be back projected to reveal the regional cardiac abnormality in a more physically meaningful way we have tested our novel methods on 41 human image sequences and achieved a classification rate of 87 80 the regional abnormalities recovered from our algorithm agree well with the patient s pathology and clinical image interpretation and provide a promising avenue for regional cardiac function analysis

multiresolution monogenic signal analysis using the riesz laplace wavelet transform the monogenic signal is the natural 2d counterpart of the 1d analytic signal we propose to transpose the concept to the wavelet domain by considering a complexified version of the riesz transform which has the remarkable property of mapping a real valued primary wavelet basis of l2 r2 into a complex one the riesz operator is also steerable in the sense that it give access to the hilbert transform of the signal along any orientation having set those foundations we specify a primary polyharmonic spline wavelet basis of l2 r2 that involves a single mexican hat like mother wavelet laplacian of a b spline the important point is that our primary wavelets are quasi isotropic they behave like multiscale versions of the fractional laplace operator from which they are derived which ensures steerability we propose to pair these real valued basis functions with their complex riesz counterparts to specify a multiresolution monogenic signal analysis this yields a representation where each wavelet index is associated with a local orientation an amplitude and a phase we give a corresponding wavelet domain method for estimating the underlying instantaneous frequency we also provide a mechanism for improving the shift and rotation invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect reconstruction filterbanks we illustrate the specific feature extraction capabilities of the representation and present novel examples of wavelet domain processing in particular a robust tensor based analysis of directional image patterns the demodulation of interferograms and the reconstruction of digital holograms

adaptive image contrast enhancement using generalizations of histogram equalization this paper proposes a scheme for adaptive image contrast enhancement based on a generalization of histogram equalization he he is a useful technique for improving image contrast but its effect is too severe for many purposes however dramatically different results can be obtained with relatively minor modifications a concise description of adaptive he is set out and this framework is used in a discussion of past suggestions for variations on he a key feature of this formalism is a cumulation function which is used to generate a grey level mapping from the local histogram by choosing alternative forms of cumulation function one can achieve a wide variety of effects a specific form is proposed through the variation of one or two parameters the resulting process can produce a range of degrees of contrast enhancement at one extreme leaving the image unchanged at another yielding full adaptive equalization

local histogram based segmentation using the wasserstein distance we propose and analyze a nonparametric region based active contour model for segmenting cluttered scenes the proposed model is unsupervised and assumes pixel intensity is independently identically distributed our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region based image term that uses histograms of pixel intensity to distinguish different regions more specifically the region data encourages segmentation so that local histograms within each region are approximately homogeneous an advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem we use wasserstein distance with exponent 1 to determine the dissimilarity between two histograms the wasserstein distance is a metric and is able to faithfully measure the distance between two histograms compared to many pointwise distances moreover it is insensitive to oscillations and therefore our model is robust to noise a fast global minimization method based on chan et al in siam j appl math 66 5 1632 1648 2006 bresson et al in j math imaging vis 28 2 151 167 2007 is employed to solve the proposed model the advantages of using this method are two fold first the computational time is less than that of the method by gradient descent of the associated euler lagrange equation chan et al in proc of ssvm pp 697 708 2007 second it is able to find a global minimizer finally we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes

optimal gabor filters for texture segmentation texture segmentation involves subdividing an image into differently textured regions many texture segmentation schemes are based on a filter bank model where the filters called gabor filters are derived from gabor elementary functions the goal is to transform texture differences into detectable filter output discontinuities at texture boundaries by locating these discontinuities one can segment the image into differently textured regions distinct discontinuities occur however only if the gabor filter parameters are suitably chosen some previous analysis has shown how to design filters for discriminating simple textures designing filters for more general natural textures though has largely been done ad hoc we have devised a more rigorously based method for designing gabor filters it assumes that an image contains two different textures and that prototype samples of the textures are given a priori we argue that gabor filter outputs can be modeled as rician random variables often approximated well as gaussian rv s and develop a decision theoretic algorithm for selecting optimal filter parameters to improve segmentations for difficult texture pairs we also propose a multiple filter segmentation scheme motivated by the rician model experimental results indicate that our method is superior to previous methods in providing useful gabor filters for a wide range of texture pairs

variational approach for the fusion of exposure bracketed pairs when taking pictures of a dark scene with artificial lighting ambient light is not sufficient for most cameras to obtain both accurate color and detail information the exposure bracketing feature usually available in many camera models enables the user to obtain a series of pictures taken in rapid succession with different exposure times the implicit idea is that the user picks the best image from this set but in many cases none of these images is good enough in general good brightness and color information are retained from longer exposure settings whereas sharp details are obtained from shorter ones in this paper we propose a variational method for automatically combining an exposure bracketed pair of images within a single picture that reflects the desired properties of each one we introduce an energy functional consisting of two terms one measuring the difference in edge information with the short exposure image and the other measuring the local color difference with a warped version of the long exposure image this method is able to handle camera and subject motion as well as noise and the results compare favorably with the state of the art

random perturbations of 2 dimensional hamiltonian flows we consider the motion of a particle in a periodic two dimensional flow perturbed by small molecular diffusion the flow is generated by a divergence free zero mean vector field the long time behavior corresponds to the behavior of the homogenized process that is diffusion process with the constant diffusion matrix effective diffusivity we obtain the asymptotics of the effective diffusivity when the molecular diffusion tends to zero

noise induced dissipation in lebesgue measure preserving maps on d dimensional torus we consider dissipative systems resulting from the gaussian and alpha stable noise perturbations of measure preserving maps on the d dimensional torus we study the dissipation time scale and its physical implications as the noise level e vanishes we show that nonergodic maps give rise to an o 1 e dissipation time whereas ergodic toral automorphisms including cat maps and their d dimensional generalizations have an o ln 1 e dissipation time with a constant related to the minimal dimensionally averaged entropy among the automorphism s irreducible blocks our approach reduces the calculation of the dissipation time to a nonlinear arithmetic optimization problem which is solved asymptotically by means of some fundamental theorems in theories of convexity diophantine approximation and arithmetic progression we show that the same asymptotic can be reproduced by degenerate noises as well as mere coarse graining we also discuss the implication of the dissipation time in kinematic dynamo

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

classification on the monogenic scale space application to target recognition in sar image this paper introduces a novel classification strategy based on the monogenic scale space for target recognition in synthetic aperture radar sar image the proposed method exploits monogenic signal theory a multidimensional generalization of the analytic signal to capture the characteristics of sar image e g broad spectral information and simultaneous spatial localization the components derived from the monogenic signal at different scales are then applied into a recently developed framework sparse representation based classification src moreover to deal with the data set whose target classes are not linearly separable the classification via kernel combination is proposed where the multiple components of the monogenic signal are jointly considered into a unifying framework for target recognition the novelty of this paper comes from 1 the development of monogenic feature via uniformly downsampling normalization and concatenation of the components at various scales 2 the development of score level fusion for srcs and 3 the development of composite kernel learning for classification in particular the comparative experimental studies under nonliteral operating conditions e g structural modifications random noise corruption and variations in depression angle are performed the comparative experimental studies of various algorithms including the linear support vector machine and the kernel version the src and the variants kernel src kernel linear representation and sparse representation of monogenic signal are performed too the feasibility of the proposed method has been successfully verified using moving and stationary target acquiration and recognition database the experimental results demonstrate that significant improvement for recognition accuracy can be achieved by the proposed method in comparison with the baseline algorithms

image editing with spatiograms transfer histogram equalization is a well known method for image contrast enhancement nevertheless as histograms do not include any information on the spatial repartition of colors their application to local image editing problems remains limited to cope with this lack of spatial information spatiograms have been recently proposed for tracking purposes a spatiogram is an image descriptor that combines a histogram with the mean and the variance of the position of each color in this paper we address the problem of local retouching of images by proposing a variational method for spatiogram transfer more precisely a reference spatiogram is used to modify the color value of a given region of interest of the processed image experiments on shadow removal and inpainting demonstrate the strength of the proposed approach

a fixed point approach to barycenters in wasserstein space abstract let p 2 a c be the set of borel probabilities on r d with finite second moment and absolutely continuous with respect to lebesgue measure we consider the problem of finding the barycenter or frechet mean of a finite set of probabilities 1 k p 2 a c with respect to the l 2 wasserstein metric for this task we introduce an operator on p 2 a c related to the optimal transport maps pushing forward any p 2 a c to 1 k under very general conditions we prove that the barycenter must be a fixed point for this operator and introduce an iterative procedure which consistently approximates the barycenter the procedure allows effective computation of barycenters in any location scatter family including the gaussian case in such cases the barycenter must belong to the family thus it is characterized by its mean and covariance matrix while its mean is just the weighted mean of the means of the probabilities the covariance matrix is characterized in terms of their covariance matrices 1 k through a nonlinear matrix equation the performance of the iterative procedure in this case is illustrated through numerical simulations which show fast convergence towards the barycenter

unsupervised texture segmentation using gabor filters abstract this paper presents a texture segmentation algorithm inspired by the multi channel filtering theory for visual information processing in the early stages of human visual system the channels are characterized by a bank of gabor filters that nearly uniformly covers the spatial frequency domain and a systematic filter selection scheme is proposed which is based on reconstruction of the input image from the filtered images texture features are obtained by subjecting each selected filtered image to a nonlinear transformation and computing a measure of energy in a window around each pixel a square error clustering algorithm is then used to integrate the feature images and produce a segmentation a simple procedure to incorporate spatial information in the clustering process is proposed a relative index is used to estimate the true number of texture categories

texture segmentation using 2 d gabor elementary functions many texture segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint space spatial frequency representation although these schemes show promise and although some analytical work has been done the relationship between texture differences and the filter configurations required to distinguish them remain largely unknown this paper examines the issue of designing individual filters using a 2 d texture model we show analytically that applying a properly configured bandpass filter to a textured image produces distinct output discontinuities at texture boundaries the analysis is based on gabor elementary functions but it is the bandpass nature of the filter that is essential depending on the type of texture difference these discontinuities form one of four characteristic signatures a step ridge valley or a step change in average local output variation accompanying experimental evidence indicates that these signatures are useful for segmenting an image the analysis indicates those texture characteristics that are responsible for each signature type detailed criteria are provided for designing filters that can produce quality output signatures we also illustrate occasions when asymmetric filters are beneficial an issue not previously addressed

perceptual color correction through variational techniques in this paper we present a discussion about perceptual based color correction of digital images in the framework of variational techniques we propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original the variational formulation permits a more flexible local control of contrast adjustment and attachment to data we show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement ace a particular perceptual based model of color enhancement moreover we prove that a numerical approximation of the euler lagrange equation reduces the computational complexity of ace from o n2 to o nlogn where n is the total number of pixels in the image

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

analysis of asymmetry in mammograms via directional filtering with gabor wavelets this paper presents a procedure for the analysis of left right bilateral asymmetry in mammograms the procedure is based upon the detection of linear directional components by using a multiresolution representation based upon gabor wavelets a particular wavelet scheme with two dimensional gabor filters as elementary functions with varying tuning frequency and orientation specifically designed in order to reduce the redundancy in the wavelet based representation is applied to the given image the filter responses for different scales and orientation are analyzed by using the karhunen loeve kl transform and otsu s method of thresholding the kl transform is applied to select the principal components of the filter responses preserving only the most relevant directional elements appearing at all scales the selected principal components thresholded by using otsu s method are used to obtain the magnitude and phase of the directional components of the image rose diagrams computed from the phase images and statistical measures computed thereof are used for quantitative and qualitative analysis of the oriented patterns a total of 80 images from 20 normal cases 14 asymmetric cases and six architectural distortion cases from the mini mias mammographic image analysis society london u k database were used to evaluate the scheme using the leave one out methodology average classification accuracy rates of up to 74 4 were achieved

diffusion and mixing in fluid flow we study enhancement of diffusive mixing on a compact riemannian manifold by a fast incompressible flow our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small in an arbitrarily short time provided that the flow amplitude is large enough the necessary and suficient condition on such flows is expressed naturally in terms of the spectral properties of the dynamical system associated with the flow in particular we find that weakly mixing flows always enhance dissipation in this sense the proofs are based on a general criterion for the decay of the semigroup generated by an operator of the form g ial with a negative unbounded self adjoint operator g a self adjoint operator l and parameter a 1 in particular they employ the rage theorem describing evolution of a quantum state belonging to the continuous spectral subspace of the hamiltonian related to a classical theorem of wiener on fourier transforms of measures applications to quenching in reaction diffusion equations are also considered

highly accurate optic flow computation with theoretically justified warping in this paper we suggest a variational model for optic flow computation based on non linearised and higher order constancy assumptions besides the common grey value constancy assumption also gradient constancy as well as the constancy of the hessian and the laplacian are proposed since the model strictly refrains from a linearisation of these assumptions it is also capable to deal with large displacements for the minimisation of the rather complex energy functional we present an efficient numerical scheme employing two nested fixed point iterations following a coarse to fine strategy it turns out that there is a theoretical foundation of so called warping techniques hitherto justified only on an experimental basis since our algorithm consists of the integration of various concepts ranging from different constancy assumptions to numerical implementation issues a detailed account of the effect of each of these concepts is included in the experimental section the superior performance of the proposed method shows up by significantly smaller estimation errors when compared to previous techniques further experiments also confirm excellent robustness under noise and insensitivity to parameter variations

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

segmentation of textured images and gestalt organization using spatial spatial frequency representations the generic issue of clustering grouping is addressed recent research both in computer and human vision suggests the use of joint spatial spatial frequency s sf representations the spectrogram the difference of gaussians representation the gabor representation and the wigner distribution are discussed and compared it is noted that the wigner distribution gives superior joint resolution experimental results in the area of texture segmentation and gestalt grouping using the wigner distribution are presented proving the feasibility of using s sf representations for low level early preattentive vision

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

efficient gabor filter design for texture segmentation gabor filters have been successfully applied to a broad range of image processing tasks the present paper considers the design of a single filter to segment a two texture image a new efficient algorithm for gabor filter design is presented along with methods for estimating filter output statistics the algorithm draws upon previous results that showed that the output of a gabor filtered texture is modeled well by a rician distribution a measure of the total output power is used to select the center frequency of the filter and is used to estimate the rician statistics of the gabor filtered image the method is further generalized to include the statistics of postfiltered outputs that are generated by a gaussian filtering operation following the gabor filter the new method typically requires an order of magnitude less computation to design a filter than a previously proposed method experimental results demonstrate the efficacy of the method

texture edge detection by modelling visual cortical channels a simple and fast multi channel filtering algorithm is presented in this paper for texture edge detection the algorithm requires only a small number of channels and automatically determines the important channel parameters it does not assume a priori knowledge about the type and number of textures occurring in the input image it operates in an essentially unsupervised mode and involves only limited human intervention the algorithm is tested extensively with a variety of synthetic and natural textures despite the simplicity of the overall algorithm the segmentation results obtained are encouraging

classification via sparse representation of steerable wavelet frames on grassmann manifold application to target recognition in sar image automatic target recognition has been widely studied over the years yet it is still an open problem the main obstacle consists in extended operating conditions e g depression angle change configuration variation articulation and occlusion to deal with them this paper proposes a new classification strategy we develop a new representation model via the steerable wavelet frames the proposed representation model is entirely viewed as an element on grassmann manifolds to achieve target classification we embed grassmann manifolds into an implicit reproducing kernel hilbert space rkhs where the kernel sparse learning can be applied specifically the mappings of training sample in rkhs are concatenated to form an overcomplete dictionary it is then used to encode the counterpart of query as a linear combination of its atoms by designed grassmann kernel function it is capable to obtain the sparse representation from which the inference can be reached the novelty of this paper comes from 1 the development of representation model by the set of directional components of riesz transform 2 the quantitative measure of similarity for proposed representation model by grassmann metric and 3 the generation of global kernel function by grassmann kernel extensive comparative studies are performed to demonstrate the advantage of proposed strategy

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

filling in by joint interpolation of vector fields and gray levels a variational approach for filling in regions of missing data in digital images is introduced the approach is based on joint interpolation of the image gray levels and gradient isophotes directions smoothly extending in an automatic fashion the isophote lines into the holes of missing data this interpolation is computed by solving the variational problem via its gradient descent flow which leads to a set of coupled second order partial differential equations one for the gray levels and one for the gradient orientations the process underlying this approach can be considered as an interpretation of the gestaltist s principle of good continuation no limitations are imposed on the topology of the holes and all regions of missing data can be simultaneously processed even if they are surrounded by completely different structures applications of this technique include the restoration of old photographs and removal of superimposed text like dates subtitles or publicity examples of these applications are given we conclude the paper with a number of theoretical results on the proposed variational approach and its corresponding gradient descent flow

estimation of myocardial strain and contraction phase from cine mri using variational data assimilation this paper presents a new method to estimate left ventricle deformations using variational data assimilation that combines image observations from cine mri and a dynamic evolution model of the heart the main contribution of the model is that it embeds parameters modeling the contraction relaxation process it estimates myocardial motion and contraction parameters simultaneously providing accurate complementary information for diagnosis the method was applied to synthetic datasets with known ground truth motion and to 47 patients mri datasets acquired at three slice locations base mid ventricle and apex radial and circumferential strain components were compared to those obtained with a reference tag tracking software exhibiting good agreement with intraclass correlation coefficients icc above 0 8 results were also evaluated against wall motion score indices used to assess cardiac kinetics in clinical practice the assimilation process overcame issues caused by temporal artifacts as a result of the dynamic model compared to using the observation term alone moreover we found that the new dynamic model consisting of a piecewise transport model acting independently on systole and diastole performed better than the standard continuous transport model which oversmooths temporal variations estimated strain and contraction parameters significantly correlated to clinical scores making them promising features for diagnosing not only hypokinesia but also dyskinesia

self similar blow up for a reaction diffusion system abstract this work is concerned with the following system which is a model to describe several phenomena in which aggregation plays a crucial role as for instance motion of bacteria by chemotaxis and equilibrium of self attracting clusters when the space dimension n is equal to three we show here that s has radial solutions with finite mass that blow up in finite time in a self similar manner when n 2 however no radial solution with finite mass may give rise to self similar blow up

estimation of orientation of a textured planar surface using projective equations and separable analysis with m channel wavelet decomposition estimation of the orientation of a textured planar surface is one of the basic tasks in the area of shape from texture for the solution of this task many successful approaches were proposed in this paper we have examined a few unaddressed questions first is there a mathematical formulation that relates the spectral characteristics of the texture pattern and the orientation of an inclined planar surface in a polar coordinate system second is there a good wavelet based approach that produces an accurate estimate of the orientation angle of the textured planar surface by analyzing the spectral behavior of one single uncalibrated image to answer these questions at first we present the formulation of a texture projective equation which relates the depth and orientation of an inclined planar surface in a polar coordinate system with the spectral properties of its image texture a suitable imaging geometry has been considered to enable separable analysis of the effect of inclination of the texture surface next a method for shape from texture is presented based on discrete wavelet analysis to estimate the orientation of the planar surface this approach although designed mainly for m channel wavelets is also applicable for dyadic wavelet analysis texture characteristics in the subbands of wavelet decomposition are analyzed using scalograms and quantitatively evaluated based on texture projective equations the proposed method of estimation of the orientation of a planar texture surface is evaluated using a set of simulated and real world textured images

a brief survey of bandwidth selection for density estimation abstract there has been major progress in recent years in data based bandwidth selection for kernel density estimation some second generation methods including plug in and smoothed bootstrap techniques have been developed that are far superior to well known first generation methods such as rules of thumb least squares cross validation and biased cross validation we recommend a solve the equation plug in bandwidth selector as being most reliable in terms of overall performance this article is intended to provide easy accessibility to the main ideas for nonexperts

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

exponential self similar mixing by incompressible flows we study the problem of the optimal mixing of a passive scalar under the action of an incompressible flow in two space dimensions the scalar solves the continuity equation with a divergence free velocity field which satisfies a bound in the sobolev space ws p where s 0 and 1 p the mixing properties are given in terms of a characteristic length scale called the mixing scale we consider two notions of mixing scale one functional expressed in terms of the homogeneous sobolev norm h 1 the other geometric related to rearrangements of sets we study rates of decay in time of both scales under self similar mixing for the case s 1 and 1 p including the case of lipschitz continuous velocities and the case of physical interest of enstrophy constrained flows we present examples of velocity fields and initial configurations for the scalar that saturate the exponential lower bound established in previous works on the time decay of both scales we also present several consequences for the geometry of regular lagrangian flows associated to sobolev velocity fields

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

a comprehensive framework for image inpainting inpainting is the art of modifying an image in a form that is not detectable by an ordinary observer there are numerous and very different approaches to tackle the inpainting problem though as explained in this paper the most successful algorithms are based upon one or two of the following three basic techniques copy and paste texture synthesis geometric partial differential equations pdes and coherence among neighboring pixels we combine these three building blocks in a variational model and provide a working algorithm for image inpainting trying to approximate the minimum of the proposed energy functional our experiments show that the combination of all three terms of the proposed energy works better than taking each term separately and the results obtained are within the state of the art

elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena this paper is concerned with the asymptotic behaviour of the principal eigenvalue of some linear elliptic equations in the limit of high first order coefficients roughly speaking one of the main results says that the principal eigenvalue with dirichlet boundary conditions is bounded as the amplitude of the coefficients of the first order derivatives goes to infinity if and only if the associated dynamical system has a first integral and the limiting eigenvalue is then determined through the minimization of the dirichlet functional over all first integrals a parabolic version of these results as well as other results for more general equations are given some of the main consequences concern the influence of high advection or drift on the speed of propagation of pulsating travelling fronts

universal mixers in all dimensions abstract we construct universal mixers incompressible flows that mix arbitrarily well general solutions to the corresponding transport equation in all dimensions this mixing is exponential in time i e essentially optimal for any initial condition with at least some regularity and we also show that a uniform mixing rate for all initial conditions cannot be achieved the flows are time periodic and uniformly in time bounded in spaces w s p for a range of s p that includes points with s 1 and p 2

spatio temporal nonrigid registration for ultrasound cardiac motion estimation we propose a new spatio temporal elastic registration algorithm for motion reconstruction from a series of images the specific application is to estimate displacement fields from two dimensional ultrasound sequences of the heart the basic idea is to find a spatio temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame the key feature of our method is the use of a semi local spatio temporal parametric model for the deformation using splines and the reformulation of the registration task as a global optimization problem the scale of the spline model controls the smoothness of the displacement field our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness we evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package together with a realistic cardiac motion model we compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency finally we applied the algorithm to the regional analysis of the left ventricle displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments thereby illustrating the clinical applicability of our method

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

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

a two component model of texture for analysis and synthesis a model of natural texture based on a structural component that uses affine coordinate transformations and a stochastic residual component is presented it is argued that the selection of an appropriate analysis scale can be formulated in terms of a tradeoff between the rate at which parameters are generated and the distortion resulting from the approximation by the structural component an efficient algorithm for identifying the parameters of the structural model is described and its utility demonstrated on a number of synthetic and natural textures

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

svd based modeling for image texture classification using wavelet transformation this paper introduces a new model for image texture classification based on wavelet transformation and singular value decomposition the probability density function of the singular values of wavelet transformation coefficients of image textures is modeled as an exponential function the model parameter of the exponential function is estimated using maximum likelihood estimation technique truncation of lower singular values is employed to classify textures in the presence of noise kullback leibler distance kld between estimated model parameters of image textures is used as a similarity metric to perform the classification using minimum distance classifier the exponential function permits us to have closed form expressions for the estimate of the model parameter and computation of the kld these closed form expressions reduce the computational complexity of the proposed approach experimental results are presented to demonstrate the effectiveness of this approach on the entire 111 textures from brodatz database the experimental results demonstrate that the proposed approach improves recognition rates using a lower number of parameters on large databases the proposed approach achieves higher recognition rates compared to the traditional subband energy based approach the hybrid imm svm approach and the ggd based approach

a convexity principle for interacting gases a new set of inequalities is introduced based on a novel but natural interpolation between borel probability measures on r d using these estimates in lieu of convexity or rearrangement inequalities the existence and uniqueness problems are solved for a family of attracting gas models in these models the gas interacts with itself through a force which increases with distance and is governed by an equation of state p p relating pressure to density p d 1 d is assumed non decreasing for a d dimensional gas by showing that the internal and potential energies for the system are convex functions of the interpolation parameter an energy minimizing stateunique up to translationis proven to exist the concavity established for t pd q as a function of t 0 1 generalizes the brunnminkowski inequality from sets to measures 1997 academic press

quenching of combustion by shear flows we consider a model describing premixed combustion in the presence of fluid flow reaction diffusion equation with passive advection and ignition type nonlinearity what kinds of velocity profiles are capable of quenching suppressing any given flame provided the velocity s amplitude is adequately large even for shear flows the solution turns out to be surprisingly subtle in this paper we provide a sharp characterization of quenching for shear flows the flow can quench any initial data if and only if the velocity profile does not have an interval larger than a certain critical size where it is identically constant the efficiency of quenching depends strongly on the geometry and scaling of the flow we discuss the cases of slowly and quickly varying flows proving rigorously scaling laws that have been observed earlier in numerical experiments the results require new estimates on the behavior of the solutions to advectionenhanced diffusion equation also known as passive scalar in physical literature a classical model describing a wealth of phenomena in nature the technique involves probabilistic and pde estimates in particular applications of malliavin calculus and central limit theorem for martingales

data driven optimal transport the problem of optimal transport between two distributions x and y is extended to situations where the distributions are only known through a finite number of samples xi and yj a weak formulation is proposed based on the dual of the kantorovich formulation with two main modifications replacing the expected values in the objective function by their empirical means over the xi and yj and restricting the dual variables u x and v y to a suitable set of test functions adapted to the local availability of sample points a procedure is proposed and tested for the numerical solution of this problem based on a fluidlike flow in phase space where the sample points play the role of active lagrangian markers 2016 wiley periodicals inc

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

filtering for texture classification a comparative study in this paper we review most major filtering approaches to texture feature extraction and perform a comparative study filtering approaches included are laws masks 1980 ring wedge filters dyadic gabor filter banks wavelet transforms wavelet packets and wavelet frames quadrature mirror filters discrete cosine transform eigenfilters optimized gabor filters linear predictors and optimized finite impulse response filters the features are computed as the local energy of the filter responses the effect of the filtering is highlighted keeping the local energy function and the classification algorithm identical for most approaches for reference comparisons with two classical nonfiltering approaches co occurrence statistical and autoregressive model based features are given we present a ranking of the tested approaches based on extensive experiments

myocardial motion analysis from b mode echocardiograms the quantitative assessment of cardiac motion is a fundamental concept to evaluate ventricular malfunction we present a new optical flow based method for estimating heart motion from two dimensional echocardiographic sequences to account for typical heart motions such as contraction expansion and shear we analyze the images locally by using a local affine model for the velocity in space and a linear model in time the regional motion parameters are estimated in the least squares sense inside a sliding spatiotemporal b spline window robustness and spatial adaptability is achieved by estimating the model parameters at multiple scales within a coarse to fine multiresolution framework we use a wavelet like algorithm for computing b spline weighted inner products and moments at dyadic scales to increase computational efficiency in order to characterize myocardial contractility and to simplify the detection of myocardial dysfunction the radial component of the velocity with respect to a reference point is color coded and visualized inside a time varying region of interest the algorithm was first validated on synthetic data sets that simulate a beating heart with a speckle like appearance of echocardiograms the ability to estimate motion from real ultrasound sequences was demonstrated by a rotating phantom experiment the method was also applied to a set of in vivo echocardiograms from an animal study motion estimation results were in good agreement with the expert echocardiographic reading

correction to rotation and gray scale transform invariant texture classification using spiral resampling subband decomposition and hidden markov model this paper proposes a new texture classification algorithm that is invariant to rotation and gray scale transformation first we convert two dimensional 2 d texture images to one dimensional 1 d signals by spiral resampling then we use a quadrature mirror filter qmf bank to decompose sampled signals into subbands in each band we take high order autocorrelation functions as features features in different bands which form a vector sequence are then modeled as a hidden markov model bmm during classification the unknown texture is matched against all the models and the best match is taken as the classification result simulations showed that the highest correct classification rate for 16 kinds of texture was 95 14

mean shift mode seeking and clustering mean shift a simple interactive procedure that shifts each data point to the average of data points in its neighborhood is generalized and analyzed in the paper this generalization makes some k means like clustering algorithms its special cases it is shown that mean shift is a mode seeking process on the surface constructed with a shadow kernal for gaussian kernels mean shift is a gradient mapping convergence is studied for mean shift iterations cluster analysis if treated as a deterministic problem of finding a fixed point of mean shift that characterizes the data applications in clustering and hough transform are demonstrated mean shift is also considered as an evolutionary strategy that performs multistart global optimization

a variational model for histogram transfer of color images in this paper we propose a variational formulation for histogram transfer of two or more color images we study an energy functional composed by three terms one tends to approach the cumulative histograms of the transformed images the other two tend to maintain the colors and geometry of the original images by minimizing this energy we obtain an algorithm that balances equalization and the conservation of features of the original images as a result they evolve while approaching an intermediate histogram between them this intermediate histogram does not need to be specified in advance but it is a natural result of the model finally we provide experiments showing that the proposed method compares well with the state of the art

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

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159