hybrid feedback laws for a class of cascade nonlinear control systems a stabilization problem for a class of nonlinear control systems is considered systems in this class can be viewed as a cascade connection of a linear time invariant subsystem a nonlinear time periodic static subsystem and an integrator hybrid logic based feedback controllers are constructed to globally stabilize these systems to the origin the controllers operate by switching between various time periodic control functions at discrete time instants as specific applications we consider stabilization of nonholonomic control systems in power form to the origin and stabilization of trajectories for a class of nonlinear control systems numerical examples of global stabilization and tracking are reported

coherent states on the circle a careful study of the physical properties of a family of coherent states on the circle introduced some years ago by de bievre and gonzalez in 1992 semiclassical behaviour of the weyl correspondence on the circle group theoretical methods in physics vol i madrid ciemat is carried out they were obtained from the weyl heisenberg coherent states in by means of the weil brezin zak transformation they are labelled by the points of the cylinder and they provide a realization of by entire functions similar to the well known fock bargmann construction in particular we compute the expectation values of the position and momentum operators on the circle and we discuss the heisenberg uncertainty relation

soliton dynamics in computational anatomy computational anatomy ca has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms among these geometric structures landmarks and image outlines in ca are shown to be singular solutions of a partial differential equation that is called the geodesic epdiff equation a recently discovered momentum map for singular solutions of epdiff yields their canonical hamiltonian formulation which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta the momentum map provides an isomorphism between landmarks and outlines for images and singular soliton solutions of the epdiff equation this isomorphism suggests a new dynamical paradigm for ca as well as new data representation

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

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

the geometry of the universal teichmuller space and the euler weil petersson equation on the identity component of the universal teichmuller space endowed with the takhtajan teo topology the geodesics of the weil petersson metric are shown to exist for all time this component is naturally a subgroup of the quasisymmetric homeomorphisms of the circle viewed this way the regularity of its elements is shown to be h3 2 epsilon for all epsilon 0 the evolutionary pde associated to the spatial representation of the geodesics of the weil petersson metric is derived using multiplication and composition below the critical sobolev index 3 2 geodesic completeness is used to introduce special classes of solutions of this pde analogous to peakons our setting is used to prove that there exists a unique geodesic between each two shapes in the plane in the context of the application of the weil petersson metric in imaging c 2015 elsevier inc all rights reserved

a local stabilization theorem for interconnected systems abstract we prove that if a nonlinear control system is locally asymptotically stabilizable at its equilibrium by means of a continuous feedback then adding an integrator the resulting system is also locally asymptotically stabilizable by means of a feedback law which is smooth except possibly at the equilibrium our approach is based on previous works of arstein sontag and the author

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

geodesic warps by conformal mappings in recent years there has been considerable interest in methods for diffeomorphic warping of images with applications in e g medical imaging and evolutionary biology the original work generally cited is that of the evolutionary biologist d arcy wentworth thompson who demonstrated warps to deform images of one species into another however unlike the deformations in modern methods which are drawn from the full set of diffeomorphisms he deliberately chose lower dimensional sets of transformations such as planar conformal mappings in this paper we study warps composed of such conformal mappings the approach is to equip the infinite dimensional manifold of conformal embeddings with a riemannian metric and then use the corresponding geodesic equation in order to obtain diffeomorphic warps after deriving the geodesic equation a numerical discretisation method is developed several examples of geodesic warps are then given we also show that the equation admits totally geodesic solutions corresponding to scaling and translation but not to affine transformations

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

coherent states for a quantum particle on a circle the coherent states for a quantum particle on a circle are introduced the bargmann representation within the actual treatment provides the representation of the algebra where u is unitary which is a direct consequence of the heisenberg algebra but it is more adequate for the study of circular motion

asymptotic feedback stabilization a sufficient condition for the existence of control lyapunov functions abstract in this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control we offer sufficient conditions for the existence of control lyapunov functions that according to 3 23 and 28 30 guarantee stabilization at a specified equilibrium by means of a feedback law which is smooth except possibly at the equilibrium we note that the results of the paper present a local nature

a nonconservative lagrangian framework for statistical fluid registration safira in this paper we used a nonconservative lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3 d brain images this algorithm is named safira acronym for statistically assisted fluid image registration algorithm a nonstatistical version of this algorithm was implemented where the deformation was regularized by penalizing deviations from a zero rate of strain in the terms regularizing the deformation included the covariance of the deformation matrices and the vector fields q here we used a lagrangian framework to reformulate this algorithm showing that the regularizing terms essentially allow nonconservative work to occur during the flow given 3 d brain images from a group of subjects vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated separately or jointly in the nonconservative terms creating four versions of safira we evaluated and compared our algorithms performance on 92 3 d brain scans from healthy monozygotic and dizygotic twins 2 d validations are also shown for corpus callosum shapes delineated at midline in the same subjects after preliminary tests to demonstrate each method we compared their detection power using tensor based morphometry tbm a technique to analyze local volumetric differences in brain structure we compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields all these tests were also run with a traditional fluid method which has been quite widely used in tbm studies the versions incorporating vector based empirical statistics on brain variation were consistently more accurate than their counterparts when used for automated volumetric quantification in new brain images this suggests the advantages of this approach for large scale neuroimaging studies

an extended weyl wigner transformation for special finite spaces abstract we extend the weyl wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by schwinger discrete transformation kernels are presented instead of continuous coordinate momentum pair system and systems such as the one dimensional canonical continuous coordinate momentum pair system and the two dimensional rotation system are described by special limits expressions are explicitly given for the spin one half case

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

principal component based diffeomorphic surface mapping we present a new diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping lddmm unlike existing lddmm approaches this new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorphic shape space is represented by a linear space of initial momenta of diffeomorphic geodesic flows from a fixed template in addition for the first time the diffeomorphic mapping is formulated within a decision theoretic scheme based on bayesian modeling in which an empirical shape prior is characterized by a low dimensional gaussian distribution on initial momentum this is achieved using principal component analysis pca to construct the eigenspace of the initial momentum a likelihood function is formulated as the conditional probability of observing surfaces given any particular value of the initial momentum which is modeled as a random field of vector valued measures characterizing the geometry of surfaces we define the diffeomorphic mapping as a problem that maximizes a posterior distribution of the initial momentum given observable surfaces over the eigenspace of the initial momentum we demonstrate the stability of the initial momentum eigenspace when altering training samples using a bootstrapping method we then validate the mapping accuracy and show robustness to outliers whose shape variation is not incorporated into the shape prior

computable elastic distances between shapes we dene distances between geometric curves by the square root of the minimal energy required to transform one curve into the other the energy is formally dened from a left invariant riemannian distance on an innite dimensional group acting on the curves which can be explicitly computed the obtained distance boils down to a variational problem for which an optimal matching between the curves has to be computed an analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem which can eciently be implemented as illustrated by experiments 1 1 generalities the problem of matching two objects together is very impor tant in computer vision and shape recognition in many cases recognition is based on shapes outlines with the help of some suitably designed distance a general principle is to associate with any pair o1 o 2 of objects to be compared a measure of discrepancy d o1 o 2 the recognition of an observed object o may be done by nding from a dictionary of templates the previously recorded object otemp for which d o otemp is minimal clearly the denition of the distance is the crucial step of the method and much research has been done in this direction we shall not try here to provide a review of the huge literature existing on the subject see for example 17 but rather focus on methods related to deformable templates with which we are directly concerned instead of basing recognition on a nite collection of points of interest primitives taken from the outline of an object corners inflexion points etc which is a popular way of handling the problem our purpose is to base the comparison on the whole outline considered as a plane curve the distance we shall dene incorporates some deformation energy between the curves the approach as we will see turns out to be intrinsic and robust to usual euclidean transformations the method is related to the wide literature on snakes 14 7 21 etc in the way that our distance corresponds to some continuous process of deformation of one curve into another it is also related to papers on elastic matching such as 8 however we provide an elastic matching algorithm which is based on a true distance between intrinsic properties of the shapes taking into account possible invariance to scaling or euclidean transformations in the case they are required from this point of view our results are indebted to the seminal work of grenander on group theory applied to pattern recognition cf 10 and 11 in particular see also 1 2 12 another source of inspiration may come from mathematical physics since we are going to look to the path process of lowest energy which deforms one object into

feedback stabilization of single input nonlinear systems abstract nonlinear geometric techniques partial feedback linearization and center manifold theory allow to reduce the design of a feedback stabilizing control for single input nonlinear systems into a lower dimensional stabilization problem the reduced order control system is explicitly constructed

constructing an atlas for the diffeomorphism group of a compact manifold with boundary with application to the analysis of image registrations this paper considers the problem of defining a parameterization chart on the group of diffeomorphisms with compact support motivated primarily by a problem in image registration where diffeomorphic warps are used to align images constructing a chart on the diffeomorphism group will enable the quantitative analysis of these warps to discover the normal and abnormal variation of structures in a population we construct a chart for particular choices of boundary conditions on the space on which the diffeomorphism acts and for a particular class of metrics on the diffeomorphism group which define a class of diffeomorphic interpolating splines the geodesic equation is computed for this class of metrics and we show how it can be solved in the spline representation furthermore we demonstrate that the spline representation generates submanifolds of the diffeomorphism group and we study this mapping explicit computational examples are included showing how this chart can be constructed in practice and that the use of the geodesic distance allows better classification of variation than those obtained using just a euclidean metric on the space of warps

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

dt refind diffusion tensor registration with exact finite strain differential in this paper we propose the dt refind algorithm for the diffeomorphic nonlinear registration of diffusion tensor images unlike scalar images deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently these methods often approximate the gradient of the objective function in the case of the finite strain fs reorientation strategy we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function by utilizing the closed form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms the resulting registration algorithm is diffeomorphic and fast we contrast the algorithm with a traditional fs alternative that ignores the reorientation in the gradient computation we show that the exact gradient leads to significantly better registration at the cost of computation time independently of the choice of euclidean or log euclidean interpolation and sum of squared differences dissimilarity measure the exact gradient achieves better alignment over an entire spectrum of deformation penalties alignment quality is assessed with a battery of metrics including tensor overlap fractional anisotropy inverse consistency and closeness to synthetic warps the improvements persist even when a different reorientation scheme preservation of principal directions is used to apply the final deformations

semi global stabilization of partially linear composite systems via feedback of the state of the linear part abstract we consider the problem of semi global stabilization of a class of partially linear composite systems we show by explicit construction of the control laws that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi globally stabilizable by a dynamic feedback of the state of the linear subsystem if a the linear subsystem is right invertible and has all its invariant zeros in the closed left half s plane and b the only linear variables entering the nonlinear subsystem are the output of the linear subsystem our work generalizes previous results by c i byrnes and a isidori 1991 h j sussmann and p v kokotovic 1991 and a r teel 1992

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

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

feedback stabilization of planar nonlinear systems abstract the stabilization of second order control systems by smooth state feedback is addressed a reduction procedure proposed in 8 is applied in order to reduce the problem to the stabilization of a first order control system by a c 2 feedback function generic sufficient conditions are given for the solution of the last problem and by the reduction procedure of the first problem as well counter examples show that the conditions are not necessary and which kind of pathologies may arise

brain structural mapping using a novel hybrid implicit explicit framework based on the level set method this paper presents a novel approach to feature based brain image warping by using a hybrid implicit explicit framework which unifies many prior approaches in a common framework in the first step we develop links between image warping and the level set method and we formulate the fundamental mathematics required for this hybrid implicit explicit approach in the second step we incorporate the large deformation models into these formulations leading to a complete and elegant treatment of anatomical structure matching in this latest approach exact matching of anatomy is achieved by comparing the target to the warped source structure under the forward mapping and the source to the warped target structure under the backward mapping because anatomy is represented nonparametrically a path is constructed linking the source to the target structure without prior knowledge of their point correspondence the final point correspondence is constructed based on the linking path with the minimal energy intensity similarity measures can be naturally incorporated in the same framework as landmark constraints by combining them in the gradient descent body forces we illustrate the approach with two applications 1 tensor based morphometry of the corpus callosum in autistic children and 2 matching cortical surfaces to measure the profile of cortical anatomic variation in summary the new mathematical techniques introduced here contribute fundamentally to the mapping of brain structure and its variation and provide a framework that unites feature and intensity based image registration techniques

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

schwinger and pegg barnett approaches and a relationship between angular and cartesian quantum descriptions ii phase spaces following the discussion in state space language presented in a preceding paper we work on the passage from the phase space description of a degree of freedom described by a finite number of states without classical counterpart to one described by an infinite and continuously labelled number of states with this it is possible to relate an original schwinger idea to the pegg barnett approach to the phase problem in phase space language this discussion shows that one can obtain the weyl wigner formalism for both cartesian and angular coordinates as limiting elements of the discrete phase space formalism

strongly consistent estimation of the sample distribution of noisy continuous parameter fields the general problem of defining and determining the sample distribution in the case of continuous parameter random fields is addressed defining a distribution in the case of deterministic functions is straightforward based on measures of sublevel sets however the fields we consider are the sum of a deterministic component nonrandom multidimensional function and an i i d random field an attempt to extend the same notion to the stochastic case immediately raises some fundamental difficulties we show that by uniformly sampling such random fields the difficulties may be avoided and a sample distribution may be compatibly defined and determined not surprisingly the obtained result resembles the known fact that the probability distribution of the sum of two independent random variables is the convolution of their distributions finally we apply the results to derive a solution to the problem of deformation estimation of one and multidimensional signals in the presence of measurement noise

stabilization of non linear control systems the role of newton diagrams abstract the stabilization of two dimensional non linear control systems is treated although the main technique is applicable to more general systems it combines the theory of centre manifolds and singularities of algebraic functions to design continuous but not necessarily lipschitz stabilizing feedback control laws in particular the devices known as the newton diagram and the newton or puiseux polygon are employed to construct uniformizing transformations finally remarks are made about systems for which no continuous stabilizing feedback control law exists

large deformation diffeomorphism and momentum based hippocampal shape discrimination in dementia of the alzheimer type in large deformation diffeomorphic metric mapping lddmm the diffeomorphic matching of images are modeled as evolution in time or a flow of an associated smooth velocity vector field v controlling the evolution the initial momentum parameterizes the whole geodesic and encodes the shape and form of the target image thus methods such as principal component analysis pca of the initial momentum leads to analysis of anatomical shape and form in target images without being restricted to small deformation assumption in the analysis of linear displacements we apply this approach to a study of dementia of the alzheimer type dat the left hippocampus in the dat group shows significant shape abnormality while the right hippocampus shows similar pattern of abnormality further pca of the initial momentum leads to correct classification of 12 out of 18 dat subjects and 22 out of 26 control subjects

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

algebraic properties of rogers szego functions i applications in quantum optics by means of a well established algebraic framework rogers szego functions associated with a circular geometry in the complex plane are introduced in the context of q special functions and their properties are discussed in detail the eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of rogers szego functions the coefficients being determined through proper eigenvalue equations in each situation furthermore a complementary study on the robertson schrodinger and symmetrical uncertainty relations for the cosine sine and nondeformed number operators is also conducted corroborating in this way certain features of q deformed coherent states

a multiscale theory for image registration and nonlinear inverse problems abstract in an influential paper tadmor et al 2004 42 introduced a hierarchical decomposition of an image as a sum of constituents of different scales here we construct analogous hierarchical expansions for diffeomorphisms in the context of image registration with the sum replaced by composition of maps we treat this as a special case of a general framework for multiscale decompositions applicable to a wide range of imaging and nonlinear inverse problems as a paradigmatic example of the latter we consider the calderon inverse conductivity problem we prove that we can simultaneously perform a numerical reconstruction and a multiscale decomposition of the unknown conductivity driven by the inverse problem itself we provide novel convergence proofs which work in the general abstract settings yet are sharp enough to prove that the hierarchical decomposition of tadmor nezzar and vese converges for arbitrary functions in l 2 a problem left open in their paper we also give counterexamples that show the optimality of our general results

model driven harmonic parameterization of the cortical surface hip hop in the context of inter subject brain surface matching we present a parameterization of the cortical surface constrained by a model of cortical organization the parameterization is defined via an harmonic mapping of each hemisphere surface to a rectangular planar domain that integrates a representation of the model as opposed to previous landmark based registration methods we do not match folds between individuals but instead optimize the fit between cortical sulci and specific iso coordinate axis in the model this strategy overcomes some limitation to sulcus based registration techniques such as topological variability in sulcal landmarks across subjects experiments on 62 subjects with manually traced sulci are presented and compared with the result of the freesurfer software the evaluation involves a measure of dispersion of sulci with both angular and area distortions we show that the model based strategy can lead to a natural efficient and very fast less than 5 min per hemisphere method for defining inter subjects correspondences we discuss how this approach also reduces the problems inherent to anatomically defined landmarks and open the way to the investigation of cortical organization through the notion of orientation and alignment of structures across the cortex

deformable templates using large deformation kinematics a general automatic approach is presented for accommodating local shape variation when mapping a two dimensional 2 d or three dimensional 3 d template image into alignment with a topologically similar target image local shape variability is accommodated by applying a vector field transformation to the underlying material coordinate system of the template while constraining the transformation to be smooth globally positive definite jacobian smoothness is guaranteed without specifically penalizing large magnitude deformations of small subvolumes by constraining the transformation on the basis of a stokesian limit of the fluid dynamical navier stokes equations this differs fundamentally from quadratic penalty methods such as those based on linearized elasticity or thin plate splines in that stress restraining the motion relaxes over time allowing large magnitude deformations kinematic nonlinearities are inherently necessary to maintain continuity of structures during large magnitude deformations and are included in all results after initial global registration final mappings are obtained by numerically solving a set of nonlinear partial differential equations associated with the constrained optimization problem automatic regridding is performed by propagating templates as the nonlinear transformations evaluated on a finite lattice become singular application of the method to intersubject registration of neuroanatomical structures illustrates the ability to account for local anatomical variability

a level set approach for shape driven segmentation and tracking of the left ventricle knowledge based segmentation has been explored significantly in medical imaging prior anatomical knowledge can be used to define constraints that can improve performance of segmentation algorithms to physically corrupted and incomplete data in this paper the objective is to introduce such knowledge based constraints while preserving the ability of dealing with local deformations toward this end we propose a variational level set framework that can account for global shape consistency as well as for local deformations in order to improve performance the problems of segmentation and tracking of the structure of interest are dealt with simultaneously by introducing the notion of time in the process and looking for a solution that satisfies that prior constraints while being consistent along consecutive frames promising experimental results in magnetic resonance and ultrasonic cardiac images demonstrate the potentials of our approach

locally linear diffeomorphic metric embedding lldme for surface based anatomical shape modeling this paper presents the algorithm locally linear diffeomorphic metric embedding lldme for constructing efficient and compact representations of surface based brain shapes whose variations are characterized using large deformation diffeomorphic metric mapping lddmm our hypothesis is that the shape variations in the infinite dimensional diffeomorphic metric space can be captured by a low dimensional space to do so traditional locally linear embedding lle that reconstructs a data point from its neighbors in euclidean space is extended to lldme that requires interpolating a shape from its neighbors in the infinite dimensional diffeomorphic metric space this is made possible through the conservation law of momentum derived from lddmm it indicates that initial momentum a linear transformation of the initial velocity of diffeomorphic flows at a fixed template shape determines the geodesic connecting the template to a subject s shape in the diffeomorphic metric space and becomes the shape signature of an individual subject this leads to the compact linear representation of the nonlinear diffeomorphisms in terms of the initial momentum since the initial momentum is in a linear space a shape can be approximated by a linear combination of its neighbors in the diffeomorphic metric space in addition we provide efficient computations for the metric distance between two shapes through the first order approximation of the geodesic using the initial momentum as well as for the reconstruction of a shape given its low dimensional euclidean coordinates using the geodesic shooting with the initial momentum as the initial condition experiments are performed on the hippocampal shapes of 302 normal subjects across the whole life span 18 94years compared with principal component analysis and isomap lldme provides the most compact and efficient representation of the age related hippocampal shapes even though the hippocampal volumes among young adults are as variable as those in older adults lldme disentangles the hippocampal local shape variation from the hippocampal size and thus reveals the nonlinear relationship of the hippocampal morphometry with age

spherical demons fast diffeomorphic landmark free surface registration we present the spherical demons algorithm for registering two spherical images by exploiting spherical vector spline interpolation theory we show that a large class of regularizors for the modified demons objective function can be efficiently approximated on the sphere using iterative smoothing based on one parameter subgroups of diffeomorphisms the resulting registration is diffeomorphic and fast the spherical demons algorithm can also be modified to register a given spherical image to a probabilistic atlas we demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject registration of a cortical surface mesh to an atlas mesh both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a xeon 3 2 ghz single processor machine this is comparable to the fastest nondiffeomorphic landmark free surface registration algorithms furthermore the accuracy of our method compares favorably to the popular freesurfer registration algorithm we validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1 parcellation of in vivo cortical surfaces and 2 brodmann area localization in ex vivo cortical surfaces

global asymptotic stabilisation of non linear systems in this article the problem of global asymptotic stabilisation of non linear systems is considered first of all the global asymptotic stability of a class of non linear systems is considered it is proved that the class of non linear systems is globally asymptotically stable under certain appropriate conditions secondly based on the result obtained the global asymptotic stabilisation of a class of non linear systems is investigated and the feedback control laws which globally stabilise the class of systems are designed thirdly by the coordinate change and the results obtained the global stabilisation of the affine non linear systems are studied and then some sufficient conditions of stabilisation are presented finally the global asymptotic stabilisation of partially linear cascade non linear system is considered the sufficient conditions of global stabilisation are obtained and the corresponding feedback control laws which stabilise the non linear systems are designed in addition some

3 d deformable image registration a topology preservation scheme based on hierarchical deformation models and interval analysis optimization this paper deals with topology preservation in three dimensional 3 d deformable image registration this work is a nontrivial extension of which addresses the case of two dimensional 2 d topology preserving mappings in both cases the deformation map is modeled as a hierarchical displacement field decomposed on a multiresolution b spline basis topology preservation is enforced by controlling the jacobian of the transformation finding the optimal displacement parameters amounts to solving a constrained optimization problem the residual energy between the target image and the deformed source image is minimized under constraints on the jacobian unlike the 2 d case in which simple linear constraints are derived the 3 d b spline based deformable mapping yields a difficult until now unsolved optimization problem in this paper we tackle the problem by resorting to interval analysis optimization techniques care is taken to keep the computational burden as low as possible results on multipatient 3 d mri registration illustrate the ability of the method to preserve topology on the continuous image domain

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

on the largest feedback linearizable subsystem abstract a feedback invariant set of integers is associated with any nonlinear multivariable system which is linear with respect to the inputs it is shown to be the set of controllability indices of the largest feedback linearizable subsystem i e the largest subsystem which can be made locally linear and controllable by means of nonsingular feedback transformations

improved myocardial motion estimation combining tissue doppler and b mode echocardiographic images we propose a technique for myocardial motion estimation based on image registration using both b mode echocardiographic images and tissue doppler sequences acquired interleaved the velocity field is modeled continuously using b splines and the spatiotemporal transform is constrained to be diffeomorphic images before scan conversion are used to improve the accuracy of the estimation the similarity measure includes a model of the speckle pattern distribution of b mode images it also penalizes the disagreement between tissue doppler velocities and the estimated velocity field registration accuracy is evaluated and compared to other alternatives using a realistic synthetic dataset obtaining mean displacement errors of about 1 mm finally the method is demonstrated on data acquired from six volunteers both at rest and during exercise robustness is tested against low image quality and fast heart rates during exercise results show that our method provides a robust motion estimate in these situations

q μ and p q ζ exponential functions rogers szegő polynomials and fourier gauss transform from the realization of q oscillator algebra in terms of generalized derivative we compute the matrix elements from deformed exponential functions and deduce generating functions associated with rogers szeg polynomials as well as their relevant properties we also compute the matrix elements associated with the p q oscillator algebra a generalization of the q one and perform the fourier gauss transform of a generalization of the deformed exponential functions

bounded input bounded output stabilization of nonlinear systems using state detectors abstract this paper is devoted to the study of relations between lyapunov stabilization and bounded input bounded output bibo stabilization of nonlinear systems when the state is not available for measurement and various state detectors are employed for implementing feedback control it is found that with some constraints imposed on the detectors lyapunov stabilization implies bibo stabilization a feedback control scheme for achieving bibo stability is presented

new maximum likelihood motion estimation schemes for noisy ultrasound images when performing block matching based motion estimation with the ml estimator one would try to match blocks from the two images within a predefined search area the estimated motion vector is that which maximizes a likelihood function formulated according to the image formation model two new maximum likelihood motion estimation schemes for ultrasound images are presented the new likelihood functions are based on the assumption that both images are contaminated by a rayleigh distributed multiplicative noise the new approach enables motion estimation in cases where a noiseless reference image is not available experimental results show a motion estimation improvement with regards to other known ml estimation methods

zero dynamics of regularly perturbed systems may be singularly abstract in this paper we present new results on the structure of the zeros of linear and nonlinear systems under perturbation in particular we show that when state space descriptions of linear or nonlinear single input single output systems with relative degree 2 are regularly perturbed then their zero dynamics may be singularly perturbed and show a separation of time scales in the siso case we give asymptotic formulas for the new high frequency zero dynamics arising from the regular perturbation

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

eigenvalues and eigenvectors of the finite fourier transform the eigenvalues and eigenvectors of the n n unitary matrix of finite fourier transform whose j k element is 1 n 1 2 exp 2 i n jk i 1 1 2 is determined in doing so a multitude of identities some of which may be new are encountered a conjecture is advanced

local feedback stabilization and bifurcation control ii stationary bifurcation abstract local feedback stabilization and bifurcation control of nonlinear systems are studied for the case in which the critical linearized system possesses a simple zero eigenvalue sufficient conditions are obtained for local stabilizability of the equilibrium point at criticality and for local stabilizability of bifurcated equilibria these conditions involve assumptions on the controllability of the critical mode for the linearized system explicit stabilizing feedback controls are constructed the projection method of analysis of stationary bifurcations is employed this work complements an earlier study by the same authors systems control lett 7 1986 11 17 of stabilization and bifurcation control in the hopf bifurcation case of two pure imaginary eigenvalues of the linearized system at criticality

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

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

a pattern theoretic characterization of biological growth mathematical and statistical modeling of biological growth is an important problem in medical diagnostics here we seek tools to analyze changes in anatomical parts using images collected over time we introduce a structured model called growth by random iterated diffeomorphisms grid that treats a cumulative growth deformation as a composition of several elementary deformations each elementary deformation applies to a small region by capturing deformation local to that region and is characterized by a seed and a radial deformation pattern around that seed these grid variables seed locations and radial deformation patterns are estimated from observed images in two steps 1 estimate a cumulative deformation over an observation interval 2 estimate grid variables using maximum likelihood criterion from this estimated cumulative deformation we demonstrate this framework using an mri image data of a rat s brain growth for future statistical analysis we propose a time varying poisson process for the seed placements and a random drawing from a predetermined catalog of deformations for the radial deformation patterns

sparse adaptive parameterization of variability in image ensembles this paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a hamiltonian flow of self interacting particles the proposed approach estimates a template image representative of a given image set an optimal set of control points that focuses on the most variable parts of the image and template to image registrations that quantify the variability within the image set the method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain the optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent the selection of the control points is done by adding a l 1 prior to the objective function which is optimized using the fista algorithm

a kernel class allowing for fast computations in shape spaces induced by diffeomorphisms reproducing kernel hilbert spaces play an important role in diffeomorphic matching of shapes and in which they intervene in the construction of riemannian metrics on diffeomorphisms and shape spaces in such contexts they are directly involved in the expressions of geodesic equations and in their numerical solutions via particle evolutions solving such equations however involves computing kernel sums over irregular grids which can be a big computational overhead if the number of particles is large in this paper we introduce and establish properties of a finitely generated kernel class in which the kernel is defined using a double interpolation from a discrete kernel supported by a regular grid covering the domain of the system of particles under consideration it not only speeds up the calculations by utilizing standard algorithms for faster computations over regular grids but also maintains the exactness and consistency of the system we provide experimental results in support of this comparing in particular the computation time and accuracy to similar competing methods

the wigner function associated with the rogers szego polynomials a wigner function associated with the rogers szego polynomials is proposed and its properties are discussed it is shown that from such a wigner function it is possible to obtain well behaved probability distribution functions for both angle and action variables defined on the compact support and for m 0 respectively the width of the angle probability density is governed by the free parameter q characterizing the polynomials

on the rogers szego polynomials an orthogonality relation on the full real line for the rogers szego polynomials is discussed it is argued that fourier transformation with the standard exponential kernel exp ixy relates the rogers szego and stieltjes wigert functions

a variational problem arising from speech recognition by following the general approach of deformable templates the problem of recognizing a single word independently of the speaker is shown to lead to the computation of the minimum value of some particular functional more precisely this allows us to recover for each possible word in a prespecified set the best matching with the recorded signal by selecting the minimum value the recognition problem can be solved in this paper we are concerned with the detailed study of the variational problem associated with this sort of functional namely the existence of a minimum point and the features of such a minimum finally we discuss the convergence of a discretized finite dimensional approximation suggested by the engineering literature on this subject

shape tracking with occlusions via coarse to fine region based sobolev descent we present a method to track the shape of an object from video the method uses a joint shape and appearance model of the object which is propagated to match shape and radiance in subsequent frames determining object shape self occlusions and dis occlusions of the object from camera and object motion pose difficulties to joint shape and appearance models in tracking they are unable to adapt to new shape and appearance information leading to inaccurate shape detection in this work we model self occlusions and dis occlusions in a joint shape and appearance tracking framework self occlusions and the warp to propagate the model are coupled thus we formulate a joint optimization problem we derive a coarse to fine optimization method advantageous in tracking that initially perturbs the model by coarse perturbations before transitioning to finer scale perturbations seamlessly this coarse to fine behavior is automatically induced by gradient descent on a novel infinite dimensional riemannian manifold that we introduce the manifold consists of planar parameterized regions and the metric that we introduce is a novel sobolev metric experiments on video exhibiting occlusions dis occlusions complex radiance and background show that occlusion dis occlusion modeling leads to superior shape accuracy

image registration with guaranteed displacement regularity the goal of image registration is twofold one goal is to enforce a certain similarity of two images by geometrically transforming one of the images the second goal is to keep this transformation meaningful or regular there exists a large amount of approaches aiming for regularity most of those are based on certain regularization techniques others use so called regridding options here we present a mathematically sound formulation that explicitly controls the deformation in terms of the determinant of the jacobian of the transformation in contrast to similar work we use pointwise inequality constraints i e the volume is controlled voxel by voxel and not by integral measures this approach guaranties grid regularity and prevent folding as it turns out the discretization of the volume constraint inequality is not straightforward therefore we present a new type of discretization enabling the detection of twists in a pixel or a voxel such detection is crucial since a twists indicates that a transformation is physically meaningless to solve the large scale inequality constrained optimization problem we present a numerical approach based on an interior point method we finally present some numerical examples that demonstrate the advantage of including inequality constraints explicitly

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

local feedback stabilization and bifurcation control i hopf bifurcation abstract local bifurcation control problems are defined and employed in the study of the local feedback stabilization problem for nonlinear systems in critical cases sufficient conditions are obtained for the local stabilizability of general nonlinear systems whose linearizations have a pair of simple nonzero imaginary eigenvalues the conditions show in particular that generically these nonlinear critical systems can be stabilized locally even if the critical modes are uncontrollable the analysis also yields a direct method for computing stabilizing feedback controls use is made of bifurcation formulae which require only a series expansion of the vector field

transformations based on continuous piecewise affine velocity fields we propose novel finite dimensional spaces of well behaved mathbb r n rightarrow mathbb r n transformations the latter are obtained by fast and highly accurate integration of continuous piecewise affine velocity fields the proposed method is simple yet highly expressive effortlessly handles optional constraints e g volume preservation and or boundary conditions and supports convenient modeling choices such as smoothing priors and coarse to fine analysis importantly the proposed approach partly due to its rapid likelihood evaluations and partly due to its other properties facilitates tractable inference over rich transformation spaces including using markov chain monte carlo methods its applications include but are not limited to monotonic regression more generally optimization over monotonic functions modeling cumulative distribution functions or histograms time warping image warping image registration real time diffeomorphic image editing data augmentation for image classifiers our gpu based code is publicly available

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

diffeomorphic metric landmark mapping using stationary velocity field parameterization large deformation diffeomorphic metric mapping lddmm has been shown as an effective computational paradigm to measure anatomical variability however its time varying vector field parameterization of diffeomorphism flow leads to computationally expensive implementation as well as some theoretical issues in metric based shape analysis e g high order metric approximation via baker campbell hausdorff bch formula to address these problems we study the role of stationary vector field parameterization in context of lddmm under this setting registration is formulated as finding the lie group exponential path with minimal energy in riemannian manifold of diffeomorphisms bringing two shapes together accurate derivation of euler lagrange equation shows that optimal vector field for landmark matching is associated with singular momenta at landmark trajectories in whole time domain and a new momentum optimization scheme is proposed to solve the variational problem length of group exponential path is also proposed as an alternative shape metric to geodesic distance and pair wise metrics among a population are computed through an approximation method via bch formula which only needs registrations to a template the proposed methods have been tested on both synthesized data and real database compared to non stationary parameterization this method can achieve comparable registration accuracy in significantly reduced time second order metric approximation by this method also improves significantly over first order which can not be achieved by non stationary parameterization correlation between the two shape metrics is also investigated and their statistical power in clinical study compared

a general methodology for the determination of 2d bodies elastic deformation invariants application to the automatic identification of parasites a novel methodology is introduced here that exploits 2d images of arbitrary elastic body deformation instances so as to quantify mechanoelastic characteristics that are deformation invariant determination of such characteristics allows for developing methods offering an image of the undeformed body general assumptions about the mechanoelastic properties of the bodies are stated which lead to two different approaches for obtaining bodies deformation invariants one was developed to spot a deformed body s neutral line and its cross sections while the other solves deformation pdes by performing a set of equivalent image operations on the deformed body images both of these processes may furnish a body undeformed version from its deformed image this was confirmed by obtaining the undeformed shape of deformed parasites cells protozoa fibers and human lips in addition the method has been applied to the important problem of parasite automatic classification from their microscopic images to achieve this we first apply the previous method to straighten the highly deformed parasites and then apply a dedicated curve classification method to the straightened parasite contours it is demonstrated that essentially different deformations of the same parasite give rise to practically the same undeformed shape thus confirming the consistency of the introduced methodology finally the developed pattern recognition method classifies the unwrapped parasites into six families with an accuracy rate of 97 6 percent

global stabilization of a certain class of nonlinear systems abstract systems are considered which can be reduced to a regular form and possess an invariant manifold such that the restriction of the system to the manifold is globally asymptotically stable gas we construct a feedback which renders the manifold globally attracting it was proved that in this situation boundedness of all orbits is necessary and sufficient for the control system to be gas a lyapunov type condition for the latter property adapted to the situation in question is given results of andreini bacciotti and stefani are shown to be a special case of our result

kernel density estimation and intrinsic alignment for shape priors in level set segmentation in this paper we make two contributions to the field of level set based image segmentation firstly we propose shape dissimilarity measures on the space of level set functions which are analytically invariant under the action of certain transformation groups the invariance is obtained by an intrinsic registration of the evolving level set function in contrast to existing approaches to invariance in the level set framework this closed form solution removes the need to iteratively optimize explicit pose parameters the resulting shape gradient is more accurate in that it takes into account the effect of boundary variation on the object s pose secondly based on these invariant shape dissimilarity measures we propose a statistical shape prior which allows to accurately encode multiple fairly distinct training shapes this prior constitutes an extension of kernel density estimators to the level set domain in contrast to the commonly employed gaussian distribution such nonparametric density estimators are suited to model aribtrary distributions we demonstrate the advantages of this multi modal shape prior applied to the segmentation and tracking of a partially occluded walking person in a video sequence and on the segmentation of the left ventricle in cardiac ultrasound images we give quantitative results on segmentation accuracy and on the dependency of segmentation results on the number of training shapes