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

stabilized finite element formulation for elastic plastic finite deformations abstract this paper presents a stabilized finite element formulation for nearly incompressible finite deformations in hyperelastic plastic solids such as metals an updated lagrangian finite element formulation is developed where mesh dependent terms are added to enhance the stability of the mixed finite element formulation this formulation circumvents the restriction on the displacement and pressure fields due to the babuska brezzi condition and provides freedom in choosing interpolation functions in the incompressible or nearly incompressible limit typical in metal forming applications moreover it facilitates the use of low order simplex elements i e p1 p1 reducing the degrees of freedom required for the solution in the incompressible limit when stable elements are necessary linearization of the weak form is derived for implementation into a finite element code numerical experiments with p1 p1 elements show that the method is effective in incompressible conditions and can be advantageous in metal forming analysis

a review of geometric transformations for nonrigid body registration this paper provides a comprehensive and quantitative review of spatial transformations models for nonrigid image registration it explains the theoretical foundation of the models and classifies them according to this basis this results in two categories physically based models described by partial differential equations of continuum mechanics e g linear elasticity and fluid flow and basis function expansions derived from interpolation and approximation theory e g radial basis functions b splines and wavelets recent work on constraining the transformation so that it preserves the topology or is diffeomorphic is also described the final section reviews some recent evaluation studies the paper concludes by explaining under what conditions a particular transformation model is appropriate

structural image restoration through deformable templates abstract prior knowledge on the space of possible images is given in the form of a function or template in some domain the set of all possible true images is assumed to be formed by a composition of that function with continuous mappings of the domain into itself a prior gaussian distribution is given on the set of continuous mappings the observed image is assumed to be a degradation of the true image with additive noise given the observed image a posterior distribution is then obtained and has the form of a nonlinear perturbation of the gaussian measure on the space of mappings we present simulations of the posterior distribution that lead to structural reconstructions of the true image in the sense that it enables us to determine landmarks and other characteristic features of the image as well as to spot pathologies in it moreover we show that the reconstruction algorithm is relatively robust when the images are degraded by noise that is not necessarily additive

stabilized finite element method for viscoplastic flow formulation with state variable evolution a stabilized mixed finite element formulation for modelling viscoplastic flow which can be used to model approximately steady state metal forming processes is presented the mixed formulation is expressed in terms of the velocity pressure and state variable fields where the state variable is used to describe the evolution of the material s resistance to plastic flow the resulting system of equations has two sources of well known instabilities one due to the incompressibility constraint and one due to the convection type state variable equation both of these instabilities are handled by adding mesh dependent stabilization terms which are functions of the euler lagrange equations to the usual galerkin method linearization of the weak form is derived to enable a newton raphson implementation into an object oriented finite element framework a progressive solution strategy is used for improving convergence for highly non linear material behaviour typical for metals numerical experiments using the stabilization method with hierarchic shape functions for the velocity pressure and state variable fields in viscoplastic flow and metal forming problems show that the stabilized finite element method is effective and efficient for non linear steady forming problems finally the results are discussed and conclusions are inferred

a unified approach to fast image registration and a new curvature based registration technique abstract image registration is central to many challenges in medical imaging today it has a vast range of applications the purpose of this note is twofold first we review some of the most promising non linear registration strategies currently used in medical imaging we show that all these techniques may be phrased in terms of a variational problem and allow for a unified treatment second we introduce within the variational framework a new non linear registration model based on a curvature type smoother we show that affine linear transformations belong to the kernel of this regularizer as a result the approach becomes more robust against poor initializations of a pre registration step furthermore we develop a stable and fast implementation of the new scheme based on a real discrete cosine transformation we demonstrate the advantages of the new technique for synthetic data sets and present an application of the algorithm for registering mr mammography images

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

three dimensional elastic matching of volumes registering volumes that have been deformed with respect to each other involves recovery of the deformation a 3 d elastic matching algorithm has been developed to use surface information for registering volumes surface extraction is performed in two steps extraction of contours in 2 d image planes using active contours and forming triangular patch surface models from the stack of 2 d contours one volume is modeled as being deformed with respect to another goal volume correspondences between surfaces in the two image volumes are used to warp the deformed volume towards its goal this process of contour extraction surface formation and matching and warping is repeated a number of times with decreasing image volume stiffness as the iterations continue the stretched volume is refined towards its goal volume registration examples of deformed volumes are presented

a generalized galerkin method for steady convection diffusion problems with application to quadratic shape function elements abstract a generalization of the standard galerkin finite element method is considered to enable it to deal successfully with steady convection diffusion problems the proposed method employs a generalized governing equation which is obtained by subtracting from the original differential equation the scalar product of its gradient by a vector of free parameters associated with each of the coordinate directions the generalized equation is successively discretized by the standard bubnov galerkin finite element method the effectiveness of the method is illustrated for the case of quadratic local interpolations in one and two space dimensions

a stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

stabilized finite element method for viscoplastic flow formulation and a simple progressive solution strategy abstract this paper presents a stabilized finite element formulation for steady state viscoplastic flow and a simple strategy for solving the resulting non linear equations with a newton raphson algorithm an eulerian stabilized finite element formulation is presented where mesh dependent terms are added element wise to enhance the stability of the mixed finite element formulation a local reconstruction method is used for computing derivatives of the stress field needed when higher order elements are used linearization of the weak form is derived to enable a newton raphson solution procedure of the resulting non linear equations in order to get convergence in the newton raphson algorithm a trial solution is needed which is within the radius of convergence an effective strategy for progressively moving inside the radius of convergence for highly non linear viscoplastic constitutive equations typical of metals is presented numerical experiments using the stabilization method with both linear and quadratic shape functions for the velocity and pressure fields in viscoplastic flow problems show that the stabilized method and the progressive convergence strategy are effective in non linear steady forming problems finally conclusions are inferred and extensions of this work are discussed

topology preserving deformable image matching using constrained hierarchical parametric models in this paper we address the issue of topology preservation in deformable image matching a novel constrained hierarchical parametric approach is presented that ensures that the mapping is globally one to one and thus preserves topology in the deformed image the transformation between the source and target images is parameterized at different scales using a decomposition of the deformation vector field over a sequence of nested multiresolution subspaces the jacobian of the mapping is controlled over the continuous domain of the transformation ensuring actual topology preservation on the whole image support the resulting fast nonlinear constrained optimization algorithm enables to track large nonlinear deformations while preserving the topology experimental results are presented both on simulated data and on real medical images

iterative multigrid regularization techniques for image matching in this paper we consider the problem of matching images i e to find a deformation u which transforms a digital image into another such that the images have nearly equal gray values in every image element the difference of the two images is measured by their l2 difference which should be minimized this yields a nonlinear ill conditioned inverse problem for u so the numerical solution is quite difficult a tikhonov regularization method is considered to rule out discontinuous and irregular solutions to the minimization problem an important problem is a proper choice of the regularization parameter alpha for the practical choice of alpha we use iterative regularization methods based on multigrid techniques to obtain a suitable initial guess we use an approach similar to the full multigrid fmg developed by brandt math comp 31 1977 pp 333 390 the algorithms have optimal complexity the amount of work is proportional to the number of picture elements finally we present some experimental results for synthetic and real images

registration of translated and rotated images using finite fourier transforms a well known method for image registration is based on a conventional correlation between phase only or whitened versions of the two images to be realigned the method covering rigid translational movements is characterized by an outstanding robustness against correlated noise and disturbances such as those encountered with nonuniform time varying illumination this correspondence discusses an extension of the method to cover both translational and rotational movements

discrete analogues in harmonic analysis i l 2 estimates for singular radon transforms this paper studies the discrete analogues of singular radon transforms we prove the 2 boundedness for those operators that are quasi translation invariant the approach used is related to the circle method of hardy and littlewood and requires multi dimensional extensions of weyl sums and gauss sums as well as variants that replace scalar sums by operator sums 1 introduction the purpose of this paper is to study discrete analogues of singular radon transforms their analysis will involve considerations originating in analytic number theory related to the circle method of hardy and littlewood and necessitates an extension of the notion of weyl sums and gauss sums this will require that we pass from the usual setting of scalar valued sums to certain operator analogues of these sums

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100

a better consistency for low order stabilized finite element methods abstract the standard implementation of stabilized finite element methods with a piece wise function space of order lower than the highest derivative present in the partial differential equation often suffers from a weak consistency that can lead to reduced accuracy the popularity of these low order elements motivates the development of a new stabilization operator which globally reconstructs the derivatives not present in the local element function space this new method is seen to engender a stronger consistency leading to better convergence and improved accuracy applications to the navier stokes equations are given which illustrate the improvement at a negligible additional cost

computing large deformation metric mappings via geodesic flows of diffeomorphisms this paper examine the euler lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in dupuis et al 1998 and trouve 1995 in which two images i 0 i 1 are given and connected via the diffeomorphic change of coordinates i 0 1 i 1 where 1 is the end point at t 1 of curve t t 0 1 satisfying t v t t t 0 1 with 0 id the variational problem takes the form mathop arg text m in limits upsilon dot phi t upsilon t left dot phi right left int 0 1 left upsilon t right 2 text d t left i 0 circ phi 1 1 i 1 right l 2 2 right where v t v is an appropriate sobolev norm on the velocity field v t and the second term enforces matching of the images with l 2 representing the squared error norm in this paper we derive the euler lagrange equations characterizing the minimizing vector fields v t t 0 1 assuming sufficient smoothness of the norm to guarantee existence of solutions in the space of diffeomorphisms we describe the implementation of the euler equations using semi lagrangian method of computing particle flows and show the solutions for various examples as well we compute the metric distance on several anatomical configurations as measured by 0 1 v t v dt on the geodesic shortest paths

flirt with rigidity image registration with a local non rigidity penalty registration is a technique nowadays commonly used in medical imaging a drawback of most of the current registration schemes is that all tissue is being considered as non rigid staring et al proceedings of the spie 2006 vol 6144 pp 1 10 2006 therefore rigid objects in an image such as bony structures or surgical instruments may be transformed non rigidly in this paper we integrate the concept of local rigidity to the flexible image registration toolbox flirt haber and modersitzki in siam j sci comput 27 5 1594 1607 2006 modersitzki numerical methods for image registration 2004 the idea is to add a penalty for local non rigidity to the cost function and thus to penalize non rigid transformations of rigid objects as our examples show the new approach allows the maintenance of local rigidity in the desired fashion for example the new scheme can keep bony structures rigid during registration we show how the concept of local rigidity can be integrated in the flirt approach and present the variational backbone a proper discretization and a multilevel optimization scheme we compare the flirt approach to the b spline approach as expected from the more general setting of the flirt approach our examples demonstrate that the flirt results are superior much smoother smaller deformations visually much more pleasing

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

consistent image registration presents a new method for image registration based on jointly estimating the forward and reverse transformations between two images while constraining these transforms to be inverses of one another this approach produces a consistent set of transformations that have less pairwise registration error i e better correspondence than traditional methods that estimate the forward and reverse transformations independently the transformations are estimated iteratively and are restricted to preserve topology by constraining them to obey the laws of continuum mechanics the transformations are parameterized by a fourier series to diagonalize the covariance structure imposed by the continuum mechanics constraints and to provide a computationally efficient numerical implementation results using a linear elastic material constraint are presented using both magnetic resonance and x ray computed tomography image data the results show that the joint estimation of a consistent set of forward and reverse transformations constrained by linear elasticity give better registration results than using either constraint alone or none at all

reverse dynamic inequalities and higher integrability theorems abstract in this paper we prove some reverse dynamic inequalities and apply them to prove some new higher integrability theorems for nonincreasing functions on time scales as a special case we will derive the classical integral inequalities due to alzer and formulate the discrete versions of these inequalities which are essentially new

variable precision registration via wavelets optimal spatial scales for inter subject registration of functional mri abstract the detection of significantly activated brain regions in multi subject functional magnetic resonance imaging fmri studies almost invariably entails the coregistration of individual subjects data in a standard space here we investigate how sensitivity to detect loci of generic activation in such studies may be conditioned by the precision of anatomical registration we describe a novel algorithm implemented in the wavelet domain for inhomogeneous deformation of individual images to match a template the algorithm matches anatomical features in a coarse to fine fashion first minimising a cost function in terms of relatively coarse spatial features and then proceeding iteratively to match the images in terms of progressively more detailed anatomical features applying the method to data acquired from two groups of 12 healthy volunteers with mean age 27 and 70 years respectively during performance of a paired associate learning task we show that geometrical overlap between template and individual images is monotonically improved compared to an affine transform by additional inhomogeneous deformations informed by more detailed features likewise sensitivity to detect activated voxels can be substantially improved by a factor of 4 or more if wavelet mediated deformations informed by medium sized anatomical features are applied in addition to a preliminary affine transform however sensitivity to detect activated voxels was reduced by over registering data or matching anatomical features at the finest scales of the wavelet transform the benefits of variable precision registration are particularly salient for data acquired in older subjects which showed evidence of greater inter subject anatomic variability and generally required more extensive local deformation to achieve a satisfactory match to the template image we conclude that major benefits in sensitivity to detect functional activation in multi subject fmri studies can be attained with an inhomogeneous deformation applied over appropriate spatial scales

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

on the orthogonal subgrid scale pressure stabilization of finite deformation j2 plasticity the use of stabilization methods is becoming an increasingly well accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics in this paper a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at finite deformations is presented a j2 flow theory plasticity model at finite deformations is considered a mixed formulation involving pressure and displacement fields is used as starting point within the finite element discretization setting continuous linear interpolation for both fields is considered to overcome the babuska brezzi stability condition a multiscale stabilization method based on the orthogonal subgrid scale osgs technique is introduced a suitable nonlinear expression of the stabilization parameter is proposed the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate and therefore very convenient for practical industrial applications numerical results obtained using the osgs stabilization technique are compared with results provided by the p1 standard galerkin displacements linear triangular tetrahedral element p1 p1 standard mixed linear displacements linear pressure triangular tetrahedral element and q1 p0 mixed bilinear trilinear displacements constant pressure quadrilateral hexahedral element for 2d 3d nearly incompressible problems in the context of a nonlinear finite deformation j2 plasticity model

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

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

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

stabilized shock hydrodynamics i a lagrangian method abstract a new supg stabilized formulation for lagrangian hydrodynamics of materials satisfying mie gruneisen equation of state is proposed it allows the use of simplex type triangular tetrahedral meshes as well as the more commonly used brick type quadrilateral hexahedral meshes the proposed method yields a globally conservative formulation in which equal order interpolation p1 or q1 isoparametric finite elements is applied to velocities displacements and pressure as a direct consequence and in contrast to traditional cell centered multidimensional hydrocode implementations the proposed formulation allows a natural representation of the pressure gradient on element interiors the supg stabilization involves additional design requirements specific to the lagrangian formulation a discontinuity capturing operator in the form of a noh type viscosity with artificial heat flux is used to preserve stability and smoothness of the solution in shock regions a set of challenging shock hydrodynamics benchmark tests for the euler equations of gas dynamics in one and two space dimensions is presented in the two dimensional case computations performed on quadrilateral and triangular grids are analyzed and compared these results indicate that the new formulation is a promising technology for hydrocode applications

improvement of the flow formulation by recovery of the hydrostatic pressure using the finite point method most of the existing numerical methods based on penalty technique lead to pressure fields which are not satisfactory especially when crude meshes are used the present work for the first time using a simple and effective finite point approach approximates the total hydrostatic stresses by this new technique the nodal hydrostatic pressure values are calculated so that the gradient of hydrostatic pressure satisfies the equilibrium equation with regard to the current distribution of deviatoric stresses this approach is verified using a cantilever beam with known analytical stress field it is also applied to a typical 2d axisymmetric bulk metal forming process the calculated pressure field is then compared with available solutions the results of the present approach are very encouraging copyright 2005 john wiley sons ltd

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

image registration using the walsh transform this paper presents a new algorithm which can be used to register images of the same or different modalities e g images with multiple channels such as x rays temperature or elevation or simply images of different spectral bands in particular a correlation based scheme is used but instead of gray values it correlates numbers formulated by different combinations of the extracted local walsh coefficients of the images each image patch is expanded in terms of walsh basis functions each walsh basis function can be thought of as measuring a different aspect of local structure e g horizontal edge corner etc the coefficients of the expansion therefore can be thought of as dense local features estimating at each point the degree of presence of for example a horizontal edge a corner with contrast of a certain type etc these coefficients are normalized and used as digits in a chosen number system which allows one to create a unique number for each type of local structure the choice of the basis of the number system allows one to give different emphasis to different types of local feature e g corners versus edges and thus the method we present forms a unified framework in terms of which several feature matching methods may be interpreted the algorithm is compared with wavelet and contour based approaches using simulated and real images the two images are assumed to differ from each other by a rotation and a translation only

an adaptive descent method for non linear viscoplasticity a forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains a significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems the resultant non linear system of equations is solved by an adaptive descent method which combines the rapid convergence of newton s method near the solution with the robustness of a method of successive approximations the use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate insensitive range of behaviours exhibited for example by metals at low temperature where slow convergence of the non linear solution algorithm has traditionally hampered their use

multimodal image registration using a variational approach this paper presents an approach to obtain a deformation which matches two images acquired from different medical imaging modalities this problem arises in the investigation of human brains two distance functionals for the images are proposed with different pros and cons these functionals are to be minimized we add a smoothing term to the minimization problem which retains certain desired elastic features in the solution at each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration furthermore we use a multiresolution minimization approach to obtain a suitable initial guess finally we present some experimental results for registration problems of synthetic images and for a real computer tomography ct magnetic resonance imaging mri registration

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

graphical templates for model registration a new method of model registration is proposed using graphical templates a graph of landmarks is chosen in the template image all possible candidates for these landmarks are found in the data image using local operators a dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time this combination of local operators to describe points of interest landmarks and a graph to describe their geometric orientation in the plane yields fast and precise matches of the model to the data with no initialization required

alignment using distributions of local geometric properties we describe a framework for aligning images without needing to establish explicit feature correspondences we assume that the geometry between the two images can be adequately described by an affine transformation and develop a framework that uses the statistical distribution of geometric properties of image contours to estimate the relevant transformation parameters the estimates obtained using the proposed method are robust to illumination conditions sensor characteristics etc since image contours are relatively invariant to these changes moreover the distributional nature of our method alleviates some of the common problems due to contour fragmentation occlusion clutter etc we provide empirical evidence of the accuracy and robustness of our algorithm finally we demonstrate our method on both real and synthetic images including multisensor image pairs

applications of tensor theory to object recognition and orientation determination a method is developed by which images resulting from orthogonal projection of rigid planar patch objects arbitrarily oriented in three dimensional 3 d space may be used to form systems of linear equations which are solved for the affine transform relating the images the technique is applicable to complete images and to unlabeled feature sets derived from images and with small modification may be used to transform images of unknown objects such that they represent images of those objects from a known orientation for use in object identification no knowledge of point correspondence between images is required theoretical development of the method and experimental results are presented the method is shown to be computationally efficient requiring o n multiplications and additions where depending on the computation algorithm n may equal the number of object or edge picture elements

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

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

revisiting stabilized finite element methods for the advective diffusive equation we give a brief overview of stabilized finite element methods and illustrate the developments applied to the advection diffusion equation this article presents a concise perspective of the developments emanated from the works started in the 1980s through today 2005 elsevier b v all rights reserved pacs 47 11 j

affine invariant features from the trace transform the trace transform is a generalization of the radon transform that allows one to construct image features that are invariant to a chosen group of image transformations in this paper we propose a methodology and appropriate functionals that can be computed from the image function and which can be used to calculate features invariant to the group of affine transforms we demonstrate the usefulness of the constructed image descriptors in retrieving images from an image database and compare it with relevant state of the art object retrieval methods

discrete analogues in harmonic analysis spherical averages in this paper we prove an analogue in the discrete setting of d o fthe spherical maximal theorem for d the methods used are two fold the application of certain sampling techniques and ideas arising in the study of the number of representations of an integer as a sum of d squares in particular the circle method the results we obtained are by necessity limited to d 5 and moreover the range of p for the l p estimates differs from its analogue in d

moshfit algorithms for occlusion tolerant mean shape and rigid motion from 3d movement data this work addresses the use of 3d point data to measure rigid motions in the presence of occlusion and without reference to a prior model of relative point locations this is a problem where cluster based measurement techniques are used e g for measuring limb movements and no static calibration trial is available the same problem arises when performing the task known as roving capture in which a mobile 3d movement analysis system is moved through a volume with static markers in unknown locations and the ego motion of the system is required in order to understand biomechanical activity in the environment to provide a solution for both of these applications the new concept of a visibility graph is introduced and is combined with a generalised procrustes method adapted from ones used by the biological shape statistics and computer graphics communities recent results on shape space manifolds are applied to show sufficient conditions for convergence to unique solution algorithm source code is available and referenced here processing speed and rate of convergence are demonstrated using simulated data positional and angular accuracy are shown to be equivalent to approaches which require full calibration to within a small fraction of input resolution typical processing times for sub micron convergence are found to be fractions of a second so the method is suitable for workflows where there may be time pressure such as in sports science and clinical analysis

analysis of finite element discretizations of an optimal control formulation of the image registration problem the goal of image registration is to determine a transformation of an image so that the resulting image is close to another image we use an optimal control approach to determine the transformation we precisely define the optimal control problem that solves the image registration problem and state the optimality system corresponding to that control problem we then define finite element discretizations of the optimality system and derive error estimates for the approximate solutions we also define and prove the convergence of a gradient iterative method for the solution of the discrete optimality system

an improvement of the constants in a reverse integral inequality abstract we present an upper bound for the ratio formula where f is a positive decreasing function satisfying 1 t t 0 f x q dx cf t q 1 1 t t 0 f x dx for all t 0 a our result sharpens an inequality of l nania

deformation based curved shape representation in this paper we introduce a deformation based representation space for curved shapes in mathbb r n given an ordered set of points sampled from a curved shape the proposed method represents the set as an element of a finite dimensional matrix lie group variation due to scale and location are filtered in a preprocessing stage while shapes that vary only in rotation are identified by an equivalence relationship the use of a finite dimensional matrix lie group leads to a similarity metric with an explicit geodesic solution subsequently we discuss some of the properties of the metric and its relationship with a deformation by least action furthermore invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function thereafter two possible approaches are presented to solve the point correspondence estimation problem finally we propose an adaptation of k means clustering for shape analysis in the proposed representation space experimental results show that the proposed representation is robust to uninformative cues e g local shape perturbation and displacement in comparison to state of the art methods it achieves a high precision on the swedish and the flavia leaf datasets and a comparable result on mpeg 7 kimia99 and kimia216 datasets

point based rigid body registration using an unscented kalman filter we present and validate a novel registration algorithm mapping two data sets generated from a rigid object in the presence of gaussian noise the proposed method is based on the unscented kalman filter ukf algorithm that is generally employed for analyzing nonlinear systems corrupted by additive gaussian noise first we employ our proposed registration algorithm to fit two randomly generated data sets in the presence of isotropic gaussian noise when the corresponding points between the two data sets are assumed to be known then we extend the registration method to the case where the data with known correspondences is stimulated by anisotropic gaussian noise the new registration method not only reliably converges to the correct registration solution but it also estimates the variance as a confidence measure for each of the estimated registration transformation parameters furthermore we employ the proposed registration algorithm for rigid body point based registration where corresponding points between two registering data sets are unknown the algorithm is tested on point data sets which are garnered from a pelvic cadaver and a scaphoid bone phantom by means of computed tomography ct and tracked free hand ultrasound imaging the collected 3 d points in the ultrasound frame are registered to the 3 d meshes in the ct frame by using the proposed and the standard iterative closest points icp registration algorithms experimental results demonstrate that our proposed method significantly outperforms the icp registration algorithm in the presence of additive gaussian noise it is also shown that the proposed registration algorithm is more robust than the icp registration algorithm in terms of outliers in data sets and initial misalignment between the two data sets

hp version discontinuous galerkin methods for hyperbolic conservation laws abstract the development of hp version discontinuous galerkin methods for hyperbolic conservation laws is presented in this work a priori error estimates are derived for a model class of linear hyperbolic conservation laws these estimates are obtained using a new mesh dependent norm that reflects the dependence of the approximate solution on the local element size and the local order of approximation the results generalize and extend previous results on mesh dependent norms to hp version discontinuous galerkin methods a posteriori error estimates which provide bounds on the actual error are also developed in this work numerical experiments verify the a priori estimates and demonstrate the effectiveness of the a posteriori estimates in providing reliable estimates of the actual error in the numerical solution

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