matching by tone mapping photometric invariant template matching a fast pattern matching scheme termed matching by tone mapping mtm is introduced which allows matching under nonlinear tone mappings we show that when tone mapping is approximated by a piecewise constant linear function a fast computational scheme is possible requiring computational time similar to the fast implementation of normalized cross correlation ncc in fact the mtm measure can be viewed as a generalization of the ncc for nonlinear mappings and actually reduces to ncc when mappings are restricted to be linear we empirically show that the mtm is highly discriminative and robust to noise with comparable performance capability to that of the well performing mutual information but on par with ncc in terms of computation time

multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

adaptive support weight approach for correspondence search we present a new window based method for correspondence search using varying support weights we adjust the support weights of the pixels in a given support window based on color similarity and geometric proximity to reduce the image ambiguity our method outperforms other local methods on standard stereo benchmarks

variational geometric and statistical methods for modeling brain anatomy and function we survey the recent activities of the odyssee laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function we start with the problem of reconstructing sources in meg and eeg and discuss the variational approach we have developed for solving these inverse problems this motivates the need for geometric models of the head we present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance mr images anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but in the current state of the technology it must be preceded by a robust estimation and regularization stage we discuss our work based on variational principles and show how the results can be used to track fibers in the white matter wm as geodesics in some riemannian space we then go to the statistical modeling of functional magnetic resonance imaging fmri signals from the viewpoint of their decomposition in a pseudo deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory multimodal image matching is discussed next in the framework of image statistics and partial differential equations pdes with an eye on registering fmri to the anatomy the paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases

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

fast algorithms for low level vision a recursive filtering structure is proposed that drastically reduces the computational effort required for smoothing performing the first and second directional derivatives and carrying out the laplacian of an image these operations are done with a fixed number of multiplications and additions per output point independently of the size of the neighborhood considered the key to the approach is first the use of an exponentially based filter family and second the use of the recursive filtering applications to edge detection problems and multiresolution techniques are considered and an edge detector allowing the extraction of zero crossings of an image with only 14 operations per output element at any resolution is proposed various experimental results are shown

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

unwarping of unidirectionally distorted epi images echo planar imaging epi is a fast nuclear magnetic resonance imaging mri method unfortunately local magnetic field inhomogeneities induced mainly by the subject s presence cause significant geometrical distortion predominantly along the phase encoding direction which must be undone to allow for meaningful further processing so far this aspect has been too often neglected in this paper the authors suggest a new approach using an algorithm specifically developed for the automatic registration of distorted epi images with corresponding anatomically correct mri images they model the deformation field with splines which gives us a great deal of flexibility while comprising the affine transform as a special case the registration criterion is least squares interestingly the complexity of its evaluation does not depend on the resolution of the control grid the spline model gives the authors good accuracy thanks to its high approximation order the short support of splines leads to a fast algorithm a multiresolution approach yields robustness and additional speedup the algorithm was tested on real as well as synthetic data and the results were compared with a manual method a wavelet based sobolev type random deformation generator was developed for testing purposes a blind test indicates that the proposed automatic method is faster more reliable and more precise than the manual one

on quasi β power increasing sequences abstract we prove a theorem of savas and rhoades on summability factors under weaker conditions by using a quasi power increasing sequence instead of almost increasing sequence

inclusion theorems for absolute matrix summability methods in this paper we establish a general inclusion theorem for a nonnegative lower triangular matrix to be absolutely stronger than a weighted mean matrix several inclusion theorems for cesaro and weighted mean methods are then obtained as corollaries

diffeomorphisms groups and pattern matching in image analysis in a previous paper it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group we show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images using lie group ideas we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub optimal gradient pattern matching its links with fluid models are established

registration of 4d cardiac ct sequences under trajectory constraints with multichannel diffeomorphic demons we propose a framework for the nonlinear spatiotemporal registration of 4d time series of images based on the diffeomorphic demons dd algorithm in this framework the 4d spatiotemporal registration is decoupled into a 4d temporal registration defined as mapping physiological states and a 4d spatial registration defined as mapping trajectories of physical points our contribution focuses more specifically on the 4d spatial registration that should be consistent over time as opposed to 3d registration that solely aims at mapping homologous points at a given time point first we estimate in each sequence the motion displacement field which is a dense representation of the point trajectories we want to register then we perform simultaneously 3d registrations of corresponding time points with the constraints to map the same physical points over time called the trajectory constraints under these constraints we show that the 4d spatial registration can be formulated as a multichannel registration of 3d images to solve it we propose a novel version of the diffeomorphic demons dd algorithm extended to vector valued 3d images the multichannel diffeomorphic demons mdd for evaluation this framework is applied to the registration of 4d cardiac computed tomography ct sequences and compared to other standard methods with real patient data and synthetic data simulated from a physiologically realistic electromechanical cardiac model results show that the trajectory constraints act as a temporal regularization consistent with motion whereas the multichannel registration acts as a spatial regularization finally using these trajectory constraints with multichannel registration yields the best compromise between registration accuracy temporal and spatial smoothness and computation times a prospective example of application is also presented with the spatiotemporal registration of 4d cardiac ct sequences of the same patient before and after radiofrequency ablation rfa in case of atrial fibrillation af the intersequence spatial transformations over a cardiac cycle allow to analyze and quantify the regression of left ventricular hypertrophy and its impact on the cardiac function

determining optical flow for irregular domains by minimizing quadratic functionals of a certain class snyder 1989 has recently classified all smoothness terms which involve first order derivatives of the flowfield u x t and of the image grey value function g x t the physically plausible smoothness terms belonging to this class are known from the work of horn and schunck 1981 and nagel 1987 in this paper we discuss the possibilities of approximating the solutions to the minimization problems of horn schunk 1981 and nagel 1987 in particular it is shown that these solutions exist are unique and depend continuously on the input data these properties make it possible while taking into consideration arbitrary models of the grey value function to approximate efficiently the weak solutions of the associated boundary value problems in irregularly shaped domains with a sufficiently smooth boundary using finite elements experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in nagel s approach influences the results

carrying simplices in nonautonomous and random competitive kolmogorov systems abstract the purpose of this paper is to investigate the asymptotic behavior of positive solutions of nonautonomous and random competitive kolmogorov systems via the skew product flows approach it is shown that there exists an unordered carrying simplex which attracts all nontrivial positive orbits of the skew product flow associated with a nonautonomous random competitive kolmogorov system

robust stability of uncertain impulsive dynamical systems abstract this paper studies robust stability of uncertain impulsive dynamical systems by introducing the concepts of uniformly positive definite matrix functions and hamilton jacobi riccati inequalities several criteria on robust stability robust asymptotic stability and robust exponential stability are established an example is also worked through to illustrate our results

color constancy using natural image statistics and scene semantics existing color constancy methods are all based on specific assumptions such as the spatial and spectral characteristics of images as a consequence no algorithm can be considered as universal however with the large variety of available methods the question is how to select the method that performs best for a specific image to achieve selection and combining of color constancy algorithms in this paper natural image statistics are used to identify the most important characteristics of color images then based on these image characteristics the proper color constancy algorithm or best combination of algorithms is selected for a specific image to capture the image characteristics the weibull parameterization e g grain size and contrast is used it is shown that the weibull parameterization is related to the image attributes to which the used color constancy methods are sensitive an mog classifier is used to learn the correlation and weighting between the weibull parameters and the image attributes number of edges amount of texture and snr the output of the classifier is the selection of the best performing color constancy method for a certain image experimental results show a large improvement over state of the art single algorithms on a data set consisting of more than 11 000 images an increase in color constancy performance up to 20 percent median angular error can be obtained compared to the best performing single algorithm further it is shown that for certain scene categories one specific color constancy algorithm can be used instead of the classifier considering several algorithms

on the absolute summability factors of infinite series involving quasi power increasing sequences in this paper we prove two theorems on a k email protected 1 summability factors for an infinite series by replacing a riesz matrix with a lower triangular matrix and using quasi power increasing sequences instead of almost increasing sequences we obtain sufficient conditions for a email protected n to be summable a k email protected 1 by using quasi f increasing sequences

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

on the practical stability with respect to h manifolds of hybrid kolmogorov systems with variable impulsive perturbations abstract the present paper is devoted to the problems of practical stability with respect to h manifolds for impulsive kolmogorov systems variable impulsive perturbations are considered we will investigate these problems in the light of the vector lyapunov s method of piecewise continuous functions as an example the case of lotka volterra systems is elaborated the effect of uncertain parameters on the stability behavior of the model is also examined the obtained results extend and complement the existing stability results for kolmogorov and related systems

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

on the stability of invariant sets of functional differential equations abstract a system of functional differential equations with delay dz dt z t zt where z x y x rn y rm and z is the vector valued functional is considered it is supposed that this system has a positive invariant set x 0 definitions of its stability asymptotic stability and uniform asymptotic stability are given theorems on the uniform asymptotic stability are formulated and proved

locally orderless registration this paper presents a unifying approach for calculating a wide range of popular but seemingly very different similarity measures our domain is the registration of n dimensional images sampled on a regular grid and our approach is well suited for gradient based optimization algorithms our approach is based on local intensity histograms and built upon the technique of locally orderless images histograms by locally orderless images are well posed and offer explicit control over the three inherent and unavoidable scales the spatial resolution intensity levels and spatial extent of local histograms through locally orderless images we offer new insight into the relations between these scales we demonstrate our unification by developing a locally orderless registration algorithm for two quite different similarity measures namely normalized mutual information and sum of squared differences and we compare these variations both theoretically and empirically finally using our algorithm we explain the empirically observed differences between two popular joint density estimation techniques used in registration parzen windows and generalized partial volume

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

a nonlinear variational problem for image matching minimizing a nonlinear functional is presented as a way of obtaining a planar mapping that matches two similar images a smoothing term is added to the nonlinear functional to penalize discontinuous and irregular solutions one option for the smoothing term is a quadratic form generated by a linear differential operator the functional is then minimized using the fourier representation of the planar mapping with this representation the quadratic form is diagonalized another option is a quadratic form generated via a basis of compactly supported wavelets in both cases a natural approximation scheme is described both quadratic forms are shown to impose the same smoothing however in terms of the finite dimensional approximations it is easier to accommodate local deformations using the wavelet basis

quasi power increasing sequence for generalized absolute summability abstract in this paper we prove a theorem given in e savas on almost increasing sequences for generalized absolute summability math inequal appl preprint on summability factors under weaker conditions by using a quasi power increasing sequence instead of an almost increasing sequence

three dimensional nonrigid mr trus registration using dual optimization in this study we proposed an efficient nonrigid magnetic resonance mr to transrectal ultrasound trus deformable registration method in order to improve the accuracy of targeting suspicious regions during a three dimensional 3 d trus guided prostate biopsy the proposed deformable registration approach employs the multi channel modality independent neighborhood descriptor mind as the local similarity feature across the two modalities of mr and trus and a novel and efficient duality based convex optimization based algorithmic scheme was introduced to extract the deformations and align the two mind descriptors the registration accuracy was evaluated using 20 patient images by calculating the tre using manually identified corresponding intrinsic fiducials in the whole gland and peripheral zone additional performance metrics dice similarity coefficient dsc mean absolute surface distance mad and maximum absolute surface distance maxd were also calculated by comparing the mr and trus manually segmented prostate surfaces in the registered images experimental results showed that the proposed method yielded an overall median tre of 1 76 mm the results obtained in terms of dsc showed an average of 80 8 pm7 8 hbox for the apex of the prostate 92 0 pm3 4 hbox for the mid gland 81 7 pm6 4 hbox for the base and 85 7 pm4 7 hbox for the whole gland the surface distance calculations showed an overall average of 1 84 pm0 52 mm for mad and 6 90 pm2 07 mm for maxd

multiresolution gray scale and rotation invariant texture classification with local binary patterns presents a theoretically very simple yet efficient multiresolution approach to gray scale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions the method is based on recognizing that certain local binary patterns termed uniform are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature we derive a generalized gray scale and rotation invariant operator presentation that allows for detecting the uniform patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis the proposed approach is very robust in terms of gray scale variations since the operator is by definition invariant against any monotonic transformation of the gray scale another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table experimental results demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

simultaneous registration of multiple images similarity metrics and efficient optimization we address the alignment of a group of images with simultaneous registration therefore we provide further insights into a recently introduced framework for multivariate similarity measures referred to as accumulated pair wise estimates ape and derive efficient optimization methods for it more specifically we show a strict mathematical deduction of ape from a maximum likelihood framework and establish a connection to the congealing framework this is only possible after an extension of the congealing framework with neighborhood information moreover we address the increased computational complexity of simultaneous registration by deriving efficient gradient based optimization strategies for ape gauss newton and the efficient second order minimization esm we present next to ssd the usage of intrinsically nonsquared similarity measures in this least squares optimization framework the fundamental assumption of esm the approximation of the perfectly aligned moving image through the fixed image limits its application to monomodal registration we therefore incorporate recently proposed structural representations of images which allow us to perform multimodal registration with esm finally we evaluate the performance of the optimization strategies with respect to the similarity measures leading to very good results for esm the extension to multimodal registration is in this context very interesting because it offers further possibilities for evaluations due to publicly available datasets with ground truth alignment

well posedness of two nonrigid multimodal image registration methods image registration methods may be designed as solutions of minimization problems on a set of geometric deformations in the nonrigid case solving these problems often means computing the steady state of a system of evolution equations involving the gradient of the error criterion defined from the euler lagrange equations of the corresponding minimization problem the well posedness of the registration methodrequires showing the existence of a solution to the minimization problem as well as that of a stable solution of the evolution equations derived from it we provide such proofs in the case where the error criterion is derived from two different statistical similarity measures global mutual information and local cross covariance we also describe our numerical implementation for solving the corresponding evolution equations and show examples of registrations of real 2d and 3d images achieved with these algorithms the proofs are quite general and can be applied to most of the known nonrigid image

the periodic solutions for general periodic impulsive population systems of functional differential equations and its applications in this paper the general periodic impulsive population systems of functional differential equations are investigated by using the method of poincare map and horn s fixed point theorem we prove that the ultimate boundedness of all solutions implies the existence of periodic solutions as applications of this result the existence of positive periodic solutions for the general periodic impulsive kolmogorov type population dynamical systems are discussed we further prove that as long as the system is permanent there must exist at least one positive periodic solution in addition the permanence and existence of positive periodic solutions are discussed for the periodic impulsive single species logistic models and the periodic impulsive n species lotka volterra competitive models with delays

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

geodesic active fields a geometric framework for image registration in this paper we present a novel geometric framework called geodesic active fields for general image registration in image registration one looks for the underlying deformation field that best maps one image onto another this is a classic ill posed inverse problem which is usually solved by adding a regularization term here we propose a multiplicative coupling between the registration term and the regularization term which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem then the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem this proposed approach for registration shares close similarities with the well known geodesic active contours model in image segmentation where the segmentation term the edge detector function is coupled with the regularization term the length functional via multiplication as well as a matter of fact our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by caselles kimmel sapiro the energy of the deformation field is measured with the polyakov energy weighted by a suitable image distance borrowed from standard registration models we investigate three different weighting functions the squared error and the approximated absolute error for monomodal images and the local joint entropy for multimodal images as compared to specialized state of the art methods tailored for specific applications our geometric framework involves important contributions firstly our general formulation for registration works on any parametrizable smooth and differentiable surface including nonflat and multiscale images in the latter case multiscale images are registered at all scales simultaneously and the relations between space and scale are intrinsically being accounted for second this method is to the best of our knowledge the first reparametrization invariant registration method introduced in the literature thirdly the multiplicative coupling between the registration term i e local image discrepancy and the regularization term naturally results in a data dependent tuning of the regularization strength finally by choosing the metric on the deformation field one can freely interpolate between classic gaussian and more interesting anisotropic tv like regularization

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

group actions homeomorphisms and matching a general framework this paper constructs metrics on the space of images cal i defined as orbits under group actions cal g the groups studied include the finite dimensional matrix groups and their products as well as the infinite dimensional diffeomorphisms examined in trouve 1999 quaterly of applied math and dupuis et al 1998 quaterly of applied math left invariant metrics are defined on the product cal g times cal i thus allowing the generation of transformations of the background geometry as well as the image values examples of the application of such metrics are presented for rigid object matching with and without signature variation curves and volume matching and structural generation in which image values are changed supporting notions such as tissue creation in carrying one image to another

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

partial persistence and extinction in n dimensional competitive systems abstract in this paper we first consider an n dimensional system slightly more general than the lotka volterra system and give conditions that imply strong persistence of all species using this result we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in an n dimensional lotka volterra system

nonlinear registration using variational principle for mutual information we extend the multimodal image registration method described in alexander and summers fast registration algorithm using a variational principle for mutual information proc spie int soc opt eng 5032 2003 1053 1063 to nonlinear registration a variational principle maximizing mutual information leads to an euler lagrange el equation for the displacement field represented here in a basis of cubic b spline functions a cost function is constructed from the sum of squares of the residuals of the el equation at a subset of pixels where the magnitude of the spatial gradient of intensity exceeds a user chosen threshold the unknown coefficients in the displacement field representation are evaluated using a levenberg marquardt minimization procedure the proposed method was successfully applied to several image pairs of the same and different modalities and an artificially constructed series of images containing nonlinear distortions and noise

almost periodic solutions in the pc space for uncertain impulsive dynamical systems abstract this paper provides sufficient conditions for the existence of almost periodic solutions for an uncertain impulsive dynamical system the investigation is carried out by utilizing the concept of uniformly positive definite matrix functions hamilton jacobi riccati inequality and piecewise continuous functions of the lyapunov functions type

an image morphing technique based on optimal mass preserving mapping image morphing or image interpolation in the time domain deals with the metamorphosis of one image into another in this paper a new class of image morphing algorithms is proposed based on the theory of optimal mass transport the l2 mass moving energy functional is modified by adding an intensity penalizing term in order to reduce the undesired double exposure effect it is an intensity based approach and thus is parameter free the optimal warping function is computed using an iterative gradient descent approach this proposed morphing method is also extended to doubly connected domains using a harmonic parameterization technique along with finite element methods

average conditions for extinction in nonautonomous kolmogorov systems abstract in this paper we consider nonautonomous competitive kolmogorov systems which constitute a generalization of the classical lotka volterra competition model applying ahmad and lazer s definitions of lower and upper averages of a function we give the average conditions which guarantee that r of the n species are permanent while the remaining n r are driven to extinction

vector lyapunov functions for practical stability of nonlinear impulsive functional differential equations this paper studies the practical stability of the solutions of nonlinear impulsive functional differential equations the obtained results are based on the method of vector lyapunov functions and on differential inequalities for piecewise continuous functions examples are given to illustrate our results

average growth and extinction in a competitive lotka volterra system abstract in this paper we answer an earlier conjecture consider a class of nonautonomous competitive lotka volterra systems we show that certain inequalities involving the interaction coefficients and averages of the growth rates imply that the system is persistent however reversing one of these inequalities implies that the n th species goes to extinction

color by correlation a simple unifying framework for color constancy the paper considers the problem of illuminant estimation how given an image of a scene recorded under an unknown light we can recover an estimate of that light obtaining such an estimate is a central part of solving the color constancy problem thus the work presented will have applications in fields such as color based object recognition and digital photography rather than attempting to recover a single estimate of the illuminant we instead set out to recover a measure of the likelihood that each of a set of possible illuminants was the scene illuminant we begin by determining which image colors can occur and how these colors are distributed under each of a set of possible lights we discuss how for a given camera we can obtain this knowledge we then correlate this information with the colors in a particular image to obtain a measure of the likelihood that each of the possible lights was the scene illuminant finally we use this likelihood information to choose a single light as an estimate of the scene illuminant computation is expressed and performed in a generic correlation framework which we develop we propose a new probabilistic instantiation of this correlation framework and show that it delivers very good color constancy on both synthetic and real images we further show that the proposed framework is rich enough to allow many existing algorithms to be expressed within it the gray world and gamut mapping algorithms are presented in this framework and we also explore the relationship of these algorithms to other probabilistic and neural network approaches to color constancy

the limit cycles of a general kolmogorov system abstract in this paper the general kolmogorov system d x d t x f x y d y d t y g x y is studied by using the theory of generalized rotated vector fields and the poincare bendixson annular region theorem we prove the sufficient conditions for the existence and uniqueness of limit cycles in this system and our results extend almost all the related existing studies on the kolmogorov and predator prey systems

constructing diffeomorphic representations for the groupwise analysis of nonrigid registrations of medical images groupwise nonrigid registrations of medical images define dense correspondences across a set of images defined by a continuous deformation field that relates each target image in the group to some reference image these registrations can be automatic or based on the interpolation of a set of user defined landmarks but in both cases quantifying the normal and abnormal structural variation across the group of imaged structures implies analysis of the set of deformation fields we contend that the choice of representation of the deformation fields is an integral part of this analysis this paper presents methods for constructing a general class of multi dimensional diffeomorphic representations of deformations we demonstrate for the particular case of the polyharmonic clamped plate splines that these representations are suitable for the description of deformations of medical images in both two and three dimensions using a set of two dimensional annotated mri brain slices and a set of three dimensional segmented hippocampi with optimized correspondences the class of diffeomorphic representations also defines a non euclidean metric on the space of patterns and for the case of compactly supported deformations on the corresponding diffeomorphism group in an experimental study we show that this non euclidean metric is superior to the usual ad hoc euclidean metrics in that it enables more accurate classification of legal and illegal variations

lat local area transform for cross modal correspondence matching abstract establishing correspondences is a fundamental task in many image processing and computer vision applications in particular finding the correspondences between a non linearly deformed image pair induced by different modality conditions is a challenging problem this paper describes a simple but powerful image transform called local area transform lat for modality robust correspondence estimation specifically lat transforms an image from the intensity domain to the local area domain which is invariant under nonlinear intensity deformations especially radiometric photometric and spectral deformations experimental results show that latransformed images provide a consistency for nonlinearly deformed images even under random intensity deformations lat reduces the mean absolute difference by approximately 0 20 and the different pixel ratio by approximately 58 on average as compared to conventional methods furthermore the reformulation of descriptors with lat shows superiority to conventional methods which is a promising result for the tasks of cross spectral and modality correspondence matching lat gains an approximately 23 improvement in the correct detection ratio and a 10 improvement in the recognition rate for the tasks of rgb nir cross spectral template matching and cross spectral feature matching respectively lat reduces the bad pixel percentage by approximately 15 and the root mean squared errors by 13 5 in the task of cross radiation stereo matching lat also improves the cross modal dense flow estimation task in terms of warping error providing 50 error reduction

impulsive differential equations this paper deals with the periodic solutions problem for impulsive differential equations by using lyapunov s second method and the contraction mapping principle some conditions ensuring the existence and global attractiveness of unique periodic solutions are derived which are given from impulsive control and impulsive perturbation points of view as an application the existence and global attractiveness of unique periodic solutions for hopfield neural networks are discussed finally two numerical examples are provided to demonstrate the effectiveness of the proposed results

variational methods for multimodal image matching matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations handling complex nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years the thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities e g ssd can be extended to the multimodal case where more complex intensity similarity measures are necessary to this end we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures and use the results to generalize a recently proposed and very effective optical flow algorithm l alvarez j weickert and j sanchez 2000 technical report and ijcv 39 1 41 56 to the case of multimodal image registration our method readily extends to the case of locally computed similarity measures thus providing the flexibility to cope with spatial non stationarities in the way the intensities in the two images are related the well posedness of the resulting equations is proved in a complementary work o d faugeras and g hermosillo 2001 technical report 4235 inria using well established techniques in functional analysis we briefly describe our numerical implementation of these equations and show results on real and synthetic data