conformal geometry and its applications on 3d shape matching recognition and stitching three dimensional shape matching is a fundamental issue in computer vision with many applications such as shape registration 3d object recognition and classification however shape matching with noise occlusion and clutter is a challenging problem in this paper we analyze a family of quasi conformal maps including harmonic maps conformal maps and least squares conformal maps with regards to 3d shape matching as a result we propose a novel and computationally efficient shape matching framework by using least squares conformal maps according to conformal geometry theory each 3d surface with disk topology can be mapped to a 2d domain through a global optimization and the resulting map is a diffeomorphism i e one to one and onto this allows us to simplify the 3d shape matching problem to a 2d image matching problem by comparing the resulting 2d parametric maps which are stable insensitive to resolution changes and robust to occlusion and noise therefore highly accurate and efficient 3d shape matching algorithms can be achieved by using the above three parametric maps finally the robustness of least squares conformal maps is evaluated and analyzed comprehensively in 3d shape matching with occlusion noise and resolution variation in order to further demonstrate the performance of our proposed method we also conduct a series of experiments on two computer vision applications i e 3d face recognition and 3d nonrigid surface alignment and stitching

some new results in the theory of negative imaginary systems with symmetric transfer matrix function abstract this note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of analyticity along the same lines of the classic definition of positive real systems under the standing assumption of symmetric transfer functions we then derive a necessary and sufficient condition that characterises negative imaginary transfer functions in terms of a matrix sign condition restricted to the imaginary axis once again following the same line of argument of the standard positive real case using this definition even transfer functions with a pole at the origin with double multiplicity as well as with a possibly negative relative degree can be negative imaginary

nondistorting flattening maps and the 3 d visualization of colon ct images considers a novel three dimensional 3 d visualization technique based on surface flattening for virtual colonoscopy such visualization methods could be important in virtual colonoscopy because they have the potential for noninvasively determining the presence of polyps and other pathologies further the authors demonstrate a method that presents a surface scan of the entire colon as a cine and affords the viewer the opportunity to examine each point on the surface without distortion the authors use certain angle preserving mappings from differential geometry to derive an explicit method for flattening surfaces obtained from 3 d colon computed tomography ct imagery indeed the authors describe a general method based on a discretization of the laplace beltrami operator for flattening a surface into the plane in a conformal manner from a triangulated surface representation of the colon the authors indicate how the procedure may be implemented using a finite element technique which takes into account special boundary conditions they also provide simple formulas that may be used in a real time cine to correct for distortion

negative imaginary lemmas for descriptor systems this technical note studies the negative imaginary properties of descriptor linear systems based on state space realizations under the assumption of a minimal realization necessary and sufficient conditions are established to characterize the negative imaginary properties of descriptor systems in terms of linear matrix inequalities with equality constraints in particular a negative imaginary lemma a strict negative imaginary lemma and a lossless negative imaginary lemma are developed a multiple input and multiple output rlc circuit network is used as an illustrative example to validate the developed theory

conformal spherical representation of 3d genus zero meshes this paper describes an approach of representing 3d shape by using a set of invariant spherical harmonic sh coefficients after conformal mapping specifically a genus zero 3d mesh object is first conformally mapped onto the unit sphere by using a modified discrete conformal mapping where the modification is based on mobius factorization and aims at obtaining a canonical conformal mapping then a sh analysis is applied to the resulting conformal spherical mesh the obtained sh coefficients are further made invariant to translation and rotation while at the same time retain the completeness thanks to which the original shape information has been faithfully preserved

bilinear transformation for discrete time positive real and negative imaginary systems this paper studies the connection between discrete time and continuous time negative imaginary systems first we analyze differences between two statements that are claimed to provide equivalent conditions for systems to be discrete time positive real our conclusion is that one is equivalent to the definition of discrete time positive real transfer matrices the other is not second by means of the bilinear transformation a connection between discrete time and continuous time negative imaginary transfer matrices is established third the concept of discrete time lossless negative imaginary systems is introduced and a discrete time lossless negative imaginary lemma is developed to characterize the lossless negative imaginary properties in terms of minimal state space realization some properties of discrete time lossless negative imaginary transfer matrices are also studied several numerical examples illustrate the developed theory

a direct proof of the equivalence of side conditions for strictly positive real matrix transfer functions this brief note proves in a direct way that two different side conditions which have been used in the literature to characterize strictly positive real matrix transfer functions in the frequency domain are equivalent

algorithms to automatically quantify the geometric similarity of anatomical surfaces we describe approaches for distances between pairs of two dimensional surfaces embedded in three dimensional space that use local structures and global information contained in interstructure geometric relationships we present algorithms to automatically determine these distances as well as geometric correspondences this approach is motivated by the aspiration of students of natural science to understand the continuity of form that unites the diversity of life at present scientists using physical traits to study evolutionary relationships among living and extinct animals analyze data extracted from carefully defined anatomical correspondence points landmarks identifying and recording these landmarks is time consuming and can be done accurately only by trained morphologists this necessity renders these studies inaccessible to nonmorphologists and causes phenomics to lag behind genomics in elucidating evolutionary patterns unlike other algorithms presented for morphological correspondences our approach does not require any preliminary marking of special features or landmarks by the user it also differs from other seminal work in computational geometry in that our algorithms are polynomial in nature and thus faster making pairwise comparisons feasible for significantly larger numbers of digitized surfaces we illustrate our approach using three datasets representing teeth and different bones of primates and humans and show that it leads to highly accurate results

on decentralized integral controllability of stable negative imaginary systems and some related extensions abstract this paper exploits the decentralized integral controllability dic of stable negative imaginary ni systems with non singular dc gain matrix to develop a constant input tracking framework with failure tolerance property in the event of sensor and or actuator faults by virtue of the dic property of ni systems it is shown that a positive feedback interconnection of two ni systems of which one is a decentralized integrator system with non negative gains and the other one is a stable ni system having negative definite dc gain matrix is internally stable this is in contrast to the existing results where for internal stability at least one of the systems needs to be strictly negative imaginary sni further it is shown that in a positive feedback interconnection stable ni systems with negative definite dc gain matrix exhibit integral controllability ic property for any positive value of the integral gain k which is a distinct property of stable ni systems having negative definite dc gain matrix since the existing notion of ic for lti systems offers only a finite range of k using the dic property and the eigenvalue loci technique some new results and research directions for the ni systems have also been presented in this paper

implicit brain imaging we describe how implicit surface representations can be used to solve fundamental problems in brain imaging this kind of representation is not only natural following the state of the art segmentation algorithms reported in the literature to extract the different brain tissues but it is also as shown in this paper the most appropriate one from the computational point of view examples are provided for finding constrained special curves on the cortex such as sulcal beds regularizing surface based measures such as cortical thickness and for computing warping fields between surfaces such as the brain cortex all these result from efficiently solving partial differential equations pdes and variational problems on surfaces represented in implicit form the implicit framework avoids the need to construct intermediate mappings between 3 d anatomical surfaces and parametric objects such planes or spheres a complex step that introduces errors and is required by many other cortical processing approaches

brief paper on lossless negative imaginary systems the paper is concerned with the notion of lossless negative imaginary systems and their stabilization using strictly negative imaginary controllers through positive feedback firstly the concept of lossless negative imaginary transfer functions is introduced and some properties of such transfer functions are studied secondly a lossless negative imaginary lemma is given which establishes conditions on matrices appearing in a minimal state space realization that are necessary and sufficient for a transfer function to be lossless negative imaginary thirdly a necessary and sufficient condition is provided for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller finally a flexible structure example is presented to illustrate the theory

fast generation of 2 d node distributions for mesh free pde discretizations abstract many applications require that nodes be scattered locally quasi uniformly within 2 d regions or on curved surfaces in 3 d space while obeying some prescribed spatially varying density function this study focuses on creating variable density node layouts that are suitable for mesh free discretizations of pdes another application is dithering to simulate half tone images the method is an advancing front type scheme inspired by the physical process of dropping of variable sized grains into a bucket

efficient computation of isometry invariant distances between surfaces we present an efficient computational framework for isometry invariant comparison of smooth surfaces we formulate the gromov hausdorff distance as a multidimensional scaling like continuous optimization problem in order to construct an efficient optimization scheme we develop a numerical tool for interpolating geodesic distances on a sampled surface from precomputed geodesic distances between the samples for isometry invariant comparison of surfaces in the case of partially missing data we present the partial embedding distance which is computed using a similar scheme the main idea is finding a minimum distortion mapping from one surface to another while considering only relevant geodesic distances we discuss numerical implementation issues and present experimental results that demonstrate its accuracy and efficiency

a new coherent paired state with possible applications to fluctuation dissipation phenomena the authors extend their previous work on coherent paired states associated with the lie group su 1 1 whereas the earlier states were defined with respect to a single type of canonical boson or linear quantum harmonic oscillator the new states are defined in terms of two distinct types of bosons or oscillators the new coherent states may again on the one hand be viewed as ordinary glauber coherent states in the two boson hilbert space spanned by arbitrary numbers of two distinct bogoliubov quasiparticles associated with the original bosons via a generalised bogoliubov transformation alternatively expressed wholly in terms of the original bosons these new coherent states are reached from the ordinary coherent states via a unitary pairing transformation which is shown to be associated with the entire so called discrete series of representations of the group su 1 1 as an important illustration of the use of these states and transformations they study in detail a rather general class of quantum lagrangians which includes the damped linear harmonic oscillator they thereby illustrate their possible usefulness in applications to quantum many body or field theoretic processes involving fluctuation dissipation phenomena in general

stability robustness of a feedback interconnection of systems with negative imaginary frequency response a necessary and sufficient condition expressed simply as the dc loop gain i e the loop gain at zero frequency being less than unity is given in this note to guarantee the internal stability of a feedback interconnection of linear time invariant lti multiple input multiple output systems with negative imaginary frequency response systems with negative imaginary frequency response arise for example when considering transfer functions from force actuators to colocated position sensors and are commonly important in for example lightly damped structures the key result presented here has similar application to the small gain theorem which refers to the stability of feedback interconnections of contractive gain systems and the passivity theorem which refers to the stability of feedback interconnections of positive real or passive systems a complete state space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided

coherent mixed states and a generalised p representation the pure glauber harmonic oscillator coherent states provide a very useful basis for many purposes they are complete in the sense that an arbitrary state in the hilbert space may be expanded in terms of them furthermore the well known p representation provides a diagonal expansion of an arbitrary operator in the hilbert space in terms of the projection operators onto the coherent states the authors study the extensions of these results to the analogous mixed states which describe comparable harmonic oscillator systems in thermodynamic equilibrium at non zero temperatures their results are given for the general density operator which describes the mixed squeezed coherent states of the displaced and squeezed harmonic oscillator they show how these squeezed coherent mixed states similarly provide a very convenient complete description of a hilbert space in particular they show how the usual p and q representations of operators in terms of pure states may be extended to finite temperatures with the corresponding mixed states and various relations between them are demonstrated the question of the existence of the generalised p representation for an arbitrary operator is further examined and some pertinent theorems are proven they also show how their results relate to the glauber lachs formalism in quantum optics for mixtures of coherent and incoherent radiation particular attention is focused both on the interplay between the quantum mechanical and thermodynamical uncertainties and on the entropy associated with such mixed states

teichmuller shape descriptor and its application to alzheimer s disease study we propose a novel method to apply teichmuller space theory to study the signature of a family of nonintersecting closed 3d curves on a general genus zero closed surface our algorithm provides an efficient method to encode both global surface and local contour shape information the signature teichmuller shape descriptor is computed by surface ricci flow method which is equivalent to solving an elliptic partial differential equation on surfaces and is numerically stable we propose to apply the new signature to analyze abnormalities in brain cortical morphometry experimental results with 3d mri data from alzheimer s disease neuroimaging initiative adni dataset 152 healthy control subjects versus 169 alzheimer s disease ad patients demonstrate the effectiveness of our method and illustrate its potential as a novel surface based cortical morphometry measurement in ad research

foundations of not necessarily rational negative imaginary systems theory relations between classes of negative imaginary and positive real systems in this technical note we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory in analogy with the theory of positive real functions in our general framework negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain in this way we do not require to restrict the attention to systems with a rational transfer function in this work we also define various grades of negative imaginary systems and aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems and to show how these notions are characterized and linked to each other

quantitative evaluation of lddmm freesurfer and caret for cortical surface mapping cortical surface mapping has been widely used to compensate for individual variability of cortical shape and topology in anatomical and functional studies while many surface mapping methods were proposed based on landmarks curves spherical or native cortical coordinates few studies have extensively and quantitatively evaluated surface mapping methods across different methodologies in this study we compared five cortical surface mapping algorithms including large deformation diffeomorphic metric mapping lddmm for curves lddmm curve for surfaces lddmm surface multi manifold lddmm mm lddmm freesurfer and caret using 40 mri scans and 10 simulated datasets we computed curve variation errors and surface alignment consistency for assessing the mapping accuracy of local cortical features e g gyral sulcal curves and sulcal regions and the curvature correlation for measuring the mapping accuracy in terms of overall cortical shape in addition the simulated datasets facilitated the investigation of mapping error distribution over the cortical surface when the mm lddmm freesurfer and caret mapping algorithms were applied our results revealed that the lddmm curve mm lddmm and caret approaches best aligned the local curve features with their own curves the mm lddmm approach was also found to be the best in aligning the local regions and cortical folding patterns e g curvature as compared to the other mapping approaches the simulation experiment showed that the mm lddmm mapping yielded less local and global deformation errors than the caret and freesurfer mappings

a geometry driven optical flow warping for spatial normalization of cortical surfaces spatial normalization is frequently used to map data to a standard coordinate system by removing intersubject morphological differences thereby allowing for group analysis to be carried out the work presented in this paper is motivated by the need for an automated cortical surface normalization technique that will automatically identify homologous cortical landmarks and map them to the same coordinates on a standard manifold the geometry of a cortical surface is analyzed using two shape measures that distinguish the sulcal and gyral regions in a multiscale framework a multichannel optical flow warping procedure aligns these shape measures between a reference brain and a subject brain creating the desired normalization the partial differential equation that carries out the warping is implemented in a euclidean framework in order to facilitate a multiresolution strategy thereby permitting large deformations between the two surfaces the technique is demonstrated by aligning 33 normal cortical surfaces and showing both improved structural alignment in manually labeled sulci and improved functional alignment in positron emission tomography data mapped to the surfaces a quantitative comparison between our proposed surface based spatial normalization method and a leading volumetric spatial normalization method is included to show that the surface based spatial normalization performs better in matching homologous cortical anatomies

solving variational problems and partial differential equations mapping into general target manifolds a framework for solving variational problems and partial differential equations that define maps onto a given generic manifold is introduced in this paper we discuss the framework for arbitrary target manifolds while the domain manifold problem was addressed in j comput phys 174 2 2001 759 the key idea is to implicitly represent the target manifold as the level set of a higher dimensional function and then implement the equations in the cartesian coordinate system where this embedding function is defined in the case of variational problems we restrict the search of the minimizing map to the class of maps whose target is the level set of interest in the case of partial differential equations we re write all the equation s geometric characteristics with respect to the embedding function we then obtain a set of equations that while defined on the whole euclidean space are intrinsic to the implicitly defined target manifold and map into it this permits the use of classical numerical techniques in cartesian grids regardless of the geometry of the target manifold the extension to open surfaces and submanifolds is addressed in this paper as well in the latter case the submanifold is defined as the intersection of two higher dimensional hypersurfaces and all the computations are restricted to this intersection examples of the applications of the framework here described include harmonic maps in liquid crystals where the target manifold is a hypersphere probability maps where the target manifold is a hyperplane chroma enhancement texture mapping and general geometric mapping between high dimensional manifolds

cortical cartography using the discrete conformal approach of circle packings cortical flattening algorithms are becoming more widely used to assist in visualizing the convoluted cortical gray matter sheet of the brain metric based approaches are the most common but suffer from high distortions conformal or angle based algorithms are supported by a comprehensive mathematical theory the conformal approach that uses circle packings is versatile in the manipulation and display of results in addition it offers some new and interesting metrics that may be useful in neuroscientific analysis and are not available through numerical partial differential equation conformal methods in this paper we begin with a brief description of cortical flat mapping from data acquisition to map displays including a brief review of past flat mapping approaches we then describe the mathematics of conformal geometry and key elements of conformal mapping we introduce the mechanics of circle packing and discuss its connections with conformal geometry using a triangulated surface representing a cortical hemisphere we illustrate several manipulations available using circle packing methods and describe the associated ensemble conformal features ecfs we conclude by discussing current and potential uses of conformal methods in neuroscience and computational anatomy

stability analysis of interconnected systems with mixed negative imaginary and small gain properties in this letter an analytical framework is proposed to examine stability of two stable linear time invariant systems interconnected in positive feedback where the systems have mixed properties of negative imaginary and small gain using the notion of dissipativity the interconnection of systems is guaranteed to be finite gain stable under the condition that the dc loop gain is contractive this work builds on griggs and exploits a new set of frequency dependent triplets that was introduced in above reference to mix two unconditional stability statements i e small gain and passivity unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative imaginary systems are connected in a feedback loop can be mixed with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop the usefulness of the proposed analytical framework is demonstrated via a numerical example

brain surface conformal parameterization with the ricci flow in brain mapping research parameterized 3 d surface models are of great interest for statistical comparisons of anatomy surface based registration and signal processing here we introduce the theories of continuous and discrete surface ricci flow which can create riemannian metrics on surfaces with arbitrary topologies with user defined gaussian curvatures the resulting conformal parameterizations have no singularities and they are intrinsic and stable first we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves secondly we conformally parameterize each cortical surface to a parameter domain with a user designed gaussian curvature arrangement in the parameter domain a shape index based on conformal invariants is computed and inter subject cortical surface matching is performed by solving a constrained harmonic map we illustrate various target curvature arrangements and demonstrate the stability of the method using longitudinal data to map statistical differences in cortical morphometry we studied brain asymmetry in 14 healthy control subjects we used a manifold version of hotelling s t2 test applied to the jacobian matrices of the surface parameterizations a permutation test along with the cumulative distribution of p values were used to estimate the overall statistical significance of differences the results show our algorithm s power to detect subtle group differences in cortical surfaces

coordinate systems for conformal cerebellar flat maps methods quasi conformal flat maps of the human cerebellum 1 4 were created from a high resolution tl weighted mri volume 5 a topologically correct surface was produced from a cerebellar volume defined by a plane parallel to the posterior commisure obex line and orthogonal to a plane passing through the vermal midline our quasi conformal flattening procedure 2 3 was applied to this surface to produce flat maps the cortical surface was parcellated according to 6 and activations produced by a target interception task were imposed eleven readily identifiable anatomical landmarks e g the apex of the fourth ventricle and the rostral most tip of the lingula were defined for the hyperbolic coordinate system one landmark was used as the map center and a second to specify the map orientation we also used a polar coordinate system on the hyperbolic flat map with equiangular grid lines radiating from the map focus and equidistant circles surrounding the focus for the spherical coordinate system one landmark was used as the north pole one as the south pole and a third as a distinguished equatorial point we used the usual latitude and longitude coordinates similar to 7 results and conclusions a major benefit of quasi conformal flat maps is that they can be used to generate canonical surface based coordinate systems for a cortical surface since our fiat maps to the hyperbolic plane and the sphere are l l and onto the coordinate systems produced by these flat maps can be used to quantitatively localize structure and function furthermore these flat maps are mathematically unique different choices of landmarks and coordinate systems will increase the utility of flat maps for studying functional imaging dam we believe that the use of cerebellar flat maps and canonical coordinate systems based on reproducible anatomical landmarks will improve our ability to localize functional activity on the cerebellar cortex and to quantify anatomical and functional differences between individual subjects and groups of subjects

combinatorial ricci flows on surfaces we show that the analogue of hamilton s ricci flow in the combinatorial setting produces solutions which converge exponentially fast to thurston s circle packing on surfaces as a consequence a new proof of thurston s existence of circle packing theorem is obtained as another consequence ricci flow suggests a new algorithm to find circle packings

spectral generalized multi dimensional scaling multidimensional scaling mds is a family of methods that embed a given set of points into a simple usually flat domain the points are assumed to be sampled from some metric space and the mapping attempts to preserve the distances between each pair of points in the set distances in the target space can be computed analytically in this setting generalized mds is an extension that allows mapping one metric space into another that is mds into target spaces in which distances are evaluated numerically rather than analytically here we propose an efficient approach for computing such mappings between surfaces based on their natural spectral decomposition where the surfaces are treated as sampled metric spaces the resulting spectral gmds procedure enables efficient embedding by incorporating smoothness of the metric structure into the problem thereby substantially reducing the complexity involved in its solution while practically overcoming its non convex nature the method is compared to existing techniques that compute dense correspondence between shapes numerical experiments of the proposed method demonstrate its efficiency and accuracy compared to state of the art approaches especially when isometry invariance is a dominant property

ar identification of latent variable graphical models the paper proposes an identification procedure for autoregressive gaussian stationary stochastic processes under the assumption that the manifest or observed variables are nearly independent when conditioned on a limited number of latent or hidden variables the method exploits the sparse plus low rank decomposition of the inverse of the manifest spectral density and the efficient convex relaxations recently proposed for such decompositions

near isometric flattening of brain surfaces flattened representations of brain surfaces are often used to visualize and analyze spatial patterns of structural organization and functional activity here we present a set of rigorous criteria and accompanying test cases with which to evaluate flattening algorithms that attempt to preserve shortest path distances on the original surface we also introduce a novel flattening algorithm that is the first to satisfy all of these criteria and demonstrate its ability to produce accurate flat maps of human and macaque visual cortex using this algorithm we have recently obtained results showing a remarkable unexpected degree of consistency in the shape and topographic structure of visual cortical areas within humans and macaques as well as between these two species

the emerging discipline of computational functional anatomy computational functional anatomy cfa is the study of functional and physiological response variables in anatomical coordinates for this we focus on two things i the construction of bijections via diffeomorphisms between the coordinatized manifolds of human anatomy and ii the transfer group action and parallel transport of functional information into anatomical atlases via these bijections we review advances in the unification of the bijective comparison of anatomical submanifolds via point sets including points curves and surface triangulations as well as dense imagery we examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in dti as well as parallel transport of metric information across multiple templates which preserves the inner product

a multi resolution scheme for distortion minimizing mapping between human subcortical structures based on geodesic construction on riemannian manifolds in this paper we deal with a subcortical surface registration problem subcortical structures including hippocampi and caudates have a small number of salient features such as heads and tails unlike cortical surfaces therefore it is hard if not impossible to perform subcortical surface registration with only such features it is also non trivial for neuroanatomical experts to select landmarks consistently for subcortical surfaces of different subjects we therefore present a landmark free approach for subcortical surface registration by measuring the amount of mesh distortion between subcortical surfaces assuming that the surfaces are represented by meshes the input meshes can be constructed using any surface modeling tool available in the public domain since our registration method is independent of a surface modeling process given the source and target surfaces together with their representing meshes the vertex positions of the source mesh are iteratively displaced while preserving the underlying surface shape in order to minimize the distortion to the target mesh by representing each surface mesh as a point on a high dimensional riemannian manifold we define a distance metric on the manifold that measures the amount of distortion from a given source mesh to the target mesh based on the notion of isometry while penalizing triangle flipping under this metric we reduce the distortion minimization problem to the problem of constructing a geodesic curve from the moving source point to the fixed target point on the manifold while satisfying the shape preserving constraint we adopt a multi resolution framework to solve the problem for distortion minimizing mapping between the source and target meshes we validate our registration scheme through several experiments distance metric comparison visual validation using real data robustness test to mesh variations feature alignment using anatomic landmarks consistency with previous clinical findings and comparison with a surface based registration method lddmm surface

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

conformal wasserstein distances comparing surfaces in polynomial time abstract we present a constructive approach to surface comparison realizable by a polynomial time algorithm we determine the similarity of two given surfaces by solving a mass transportation problem between their conformal densities this mass transportation problem differs from the standard case in that we require the solution to be invariant under global mobius transformations we present in detail the case where the surfaces to compare are disk like we also sketch how the approach can be generalized to other types of surfaces

from understanding of color perception to dynamical systems by manifold learning let us start with a seemingly unrelated field to that described in the article by yair et al 1 in pnas the field of psychophysics deals with the relationships between physical stimuli and mental phenomena an excellent example is the scientific community s early efforts to study the human perception of color scientists have been intrigued by visual awareness of colors trying to understand our interpretation of colors and attempting to quantify human perception with simple equations roughly speaking one could divide these efforts into axiomatic ones that gave birth to the young maxwell helmholtz and later on schrodinger so called inductive color line elements and the empirical color arc lengths that reflected the effort to virtually embed measurements of human color perception into a simple often euclidean domain in fact the latter school of thought of treating the problem empirically rather than axiomatically is probably one of the earliest attempts to apply a manifold learning technique to study a psychophysical phenomenon the outcome was the insightful observation that human color perception is 3d while most birds probably have and most dinosaurs probably had a color perception manifold of higher dimensions and most other mammals share a lower dimensional space for the lack of perception of color one of the analysis tools used to arrive at this important observation is known as multidimensional scaling mds and is related to the famous principal component analysis machinery that is commonly used in big data representation for which various modern generalizations exist while axiomatic realizations of studying the color receptors in the eye lead maxwell 2 to the understanding that color images could be synthesized by a linear 1 1email ron at cs technion ac il 1 xref corresp 1 1

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

quadrilateral mesh generation ii meromorphic quartic differentials and abel jacobi condition abstract this work discovers the equivalence relation between quadrilateral meshes and meromorphic quartic differentials each quad mesh induces a conformal structure of the surface and a meromorphic quartic differential where the configuration of singular vertices corresponds to the configurations of the poles and zeros divisor of the meromorphic differential due to riemann surface theory the configuration of singularities of a quad mesh satisfies the abel jacobi condition inversely if a divisor satisfies the abel jacobi condition then there exists a meromorphic quartic differential whose divisor equals the given one furthermore if the meromorphic quartic differential is with finite trajectories then it also induces a quad mesh the poles and zeros of the meromorphic differential correspond to the singular vertices of the quad mesh besides the theoretic proofs the computational algorithm for verification of abel jacobi condition is also explained in detail furthermore constructive algorithm of meromorphic quartic differential on genus zero surfaces is proposed which is based on the global algebraic representation of meromorphic differentials our experimental results demonstrate the efficiency and efficacy of the algorithm this opens up a novel direction for quad mesh generation using algebraic geometric approach

optimal mass transport for shape matching and comparison surface based 3d shape analysis plays a fundamental role in computer vision and medical imaging this work proposes to use optimal mass transport map for shape matching and comparison focusing on two important applications including surface registration and shape space the computation of the optimal mass transport map is based on monge brenier theory in comparison to the conventional method based on monge kantorovich theory this method significantly improves the efficiency by reducing computational complexity from o n 2 to o n for surface registration problem one commonly used approach is to use conformal map to convert the shapes into some canonical space although conformal mappings have small angle distortions they may introduce large area distortions which are likely to cause numerical instability thus resulting failures of shape analysis this work proposes to compose the conformal map with the optimal mass transport map to get the unique area preserving map which is intrinsic to the riemannian metric unique and diffeomorphic for shape space study this work introduces a novel riemannian framework conformal wasserstein shape space by combing conformal geometry and optimal mass transport theory in our work all metric surfaces with the disk topology are mapped to the unit planar disk by a conformal mapping which pushes the area element on the surface to a probability measure on the disk the optimal mass transport provides a map from the shape space of all topological disks with metrics to the wasserstein space of the disk and the pullback wasserstein metric equips the shape space with a riemannian metric we validate our work by numerous experiments and comparisons with prior approaches and the experimental results demonstrate the efficiency and efficacy of our proposed approach

multivariate tensor based morphometry on surfaces application to mapping ventricular abnormalities in hiv aids here we developed a new method called multivariate tensor based surface morphometry tbm and applied it to study lateral ventricular surface differences associated with hiv aids using concepts from differential geometry and the theory of differential forms we created mathematical structures known as holomorphic one forms to obtain an efficient and accurate conformal parameterization of the lateral ventricular surfaces in the brain the new meshing approach also provides a natural way to register anatomical surfaces across subjects and improves on prior methods as it handles surfaces that branch and join at complex 3d junctions to analyze anatomical differences we computed new statistics from the riemannian surface metrics these retain multivariate information on local surface geometry we applied this framework to analyze lateral ventricular surface morphometry in 3d mri data from 11 subjects with hiv aids and 8 healthy controls our method detected a 3d profile of surface abnormalities even in this small sample multivariate statistics on the local tensors gave better effect sizes for detecting group differences relative to other tbm based methods including analysis of the jacobian determinant the largest and smallest eigenvalues of the surface metric and the pair of eigenvalues of the jacobian matrix the resulting analysis pipeline may improve the power of surface based morphometry studies of the brain

factors of the fock functional can the fields and of a representation of the ccr s be written as 1 1 1 1 2 and similarly for such that i and i satisfy the ccr s what are the possible i s and i s this is equivalent to a factorization of the corresponding generating functionals scaled by 1 generalizing this question somewhat we show a noncommutative analog of cramer s theorem of probability theory if and are fock fields then so are i i i 1 2 similarly for quasifree representations of the ccr s as an application we show that the fields of a representation of the ccr s whose generating functional differs from a fock functional by a phase factor only are just shifted fock fields

computing surface uniformization using discrete beltrami flow in this paper we propose a novel algorithm for computing surface uniformization for surfaces with arbitrary topology according to the celebrated uniformization theorem all riemann surfaces can be classified as elliptic parabolic or hyperbolic our algorithm is able to work on all these cases by first constructing an initial map onto an appropriate domain such as a sphere or a polygon in the plane mathbb r 2 or the hyperbolic disk d and then morphing the diffeomorphism based on the discrete beltrami flow algorithm for high genus surfaces both the final mapping and the target domain are unknown which presents a challenge in general each such surface can be conformally mapped onto d modulo a discrete subgroup of all fractional linear transforms on d a conformal copy of the surface which is also its uniformization domain can be visualized as a fundamental polygon in d corresponding to the discrete subgroup where the generators of the discrete subgroup map each side of the fundament

automatic construction of correspondences for tubular surfaces statistical shape modeling is an established technique and is used for a variety of tasks in medical image processing such as image segmentation and analysis a challenging task in the construction of a shape model is establishing a good correspondence across the set of training shapes especially for shapes of cylindrical topology very little work has been done this paper describes an automatic method to obtain a correspondence for a set of cylindrical shapes the method starts from an initial correspondence which is provided by cylindrical parameterization the quality of the obtained correspondence measured in terms of the description length is then improved by deforming the parameterizations using cylindrical b spline deformations and by optimization of the spatial alignment of the shapes in order to allow efficient gradient guided optimization an analytic expression is provided for the gradient of this quality measure with respect to the parameters of the parameterization deformation and the spatial alignment a comparison is made between models obtained from the correspondences before and after the optimization the results show that in comparison with parameterization based correspondences this new method establishes correspondences that generate models with significantly increased performance in terms of reconstruction error generalization ability and specificity

robust output feedback consensus for networked negative imaginary systems a robust output feedback consensus problem for networked homogeneous negative imaginary ni systems is investigated in this technical note by virtue of ni systems theory a set of reasonable yet elegant conditions are derived for output consensus under fraktur l 2 external disturbances as well as ni model uncertainty as a byproduct this technical note also reaffirms a previous result by li et al which shows the robustness of networked systems is always worse than that of single agent systems furthermore the eventual convergence sets are also characterized for several special ni systems that are commonly studied in the literature it is shown how the results in this work embed and generalize earlier results for these classes of systems we show that the natural convergence set boils down to the centroid of the initial pattern when the initial conditions of the controllers are zero numerical examples are given to showcase the main results

strictly negative imaginary state feedback control with a prescribed degree of stability abstract this paper presents conditions for the synthesis of a strictly negative imaginary closed loop system with a prescribed degree of stability under the assumption of full state feedback a perturbation method is used to ensure the closed loop system has both the strict negative imaginary property and a prescribed degree of stability this approach involves the real schur decomposition of a matrix followed by the solution to two lyapunov equations also we present and clarify the perturbation properties of strictly negative imaginary systems

trace a topological graph representation for automatic sulcal curve extraction a proper geometric representation of the cortical regions is a fundamental task for cortical shape analysis and landmark extraction however a significant challenge has arisen due to the highly variable convoluted cortical folding patterns in this paper we propose a novel topological graph representation for automatic sulcal curve extraction trace in practice the reconstructed surface suffers from noise influences introduced during image acquisition surface reconstruction in the presence of noise on the surface trace determines stable sulcal fundic regions by employing the line simplification method that prevents the sulcal folding pattern from being significantly smoothed out the sulcal curves are then traced over the connected graph in the determined regions by the dijkstra s shortest path algorithm for validation we used the state of the art surface reconstruction pipelines on a reproducibility data set the experimental results showed higher reproducibility and robustness to noise in trace than the existing method li et al 2010 with over 20 relative improvement in error for both surface reconstruction pipelines in addition the extracted sulcal curves by trace were well aligned with manually delineated primary sulcal curves we also provided a choice of parameters to control quality of the extracted sulcal curves and showed the influences of the parameter selection on the resulting curves

shape analysis of planar multiply connected objects using conformal welding shape analysis is a central problem in the field of computer vision in 2d shape analysis classification and recognition of objects from their observed silhouettes are extremely crucial but difficult it usually involves an efficient representation of 2d shape space with a metric so that its mathematical structure can be used for further analysis although the study of 2d simply connected shapes has been subject to a corpus of literatures the analysis of multiply connected shapes is comparatively less studied in this work we propose a representation for general 2d multiply connected domains with arbitrary topologies using conformal welding a metric can be defined on the proposed representation space which gives a metric to measure dissimilarities between objects the main idea is to map the exterior and interior of the domain conformally to unit disks and circle domains unit disk with several inner disks removed using holomorphic 1 forms a set of diffeomorphisms of the unit circle mathbb s 1 can be obtained which together with the conformal modules are used to define the shape signature a shape distance between shape signatures can be defined to measure dissimilarities between shapes we prove theoretically that the proposed shape signature uniquely determines the multiply connected objects under suitable normalization we also introduce a reconstruction algorithm to obtain shapes from their signatures this completes our framework and allows us to move back and forth between shapes and signatures with that a morphing algorithm between shapes can be developed through the interpolation of the beltrami coefficients associated with the signatures experiments have been carried out on shapes extracted from real images results demonstrate the efficacy of our proposed algorithm as a stable shape representation scheme

the ricci flow on the 2 sphere the classical uniformization theorem interpreted differential geomet rically states that any riemannian metric on a 2 dimensional surface ispointwise conformal to a constant curvature metric thus one can con sider the question of whether there is a natural evolution equation whichconformally deforms any metric on a surface to a constant curvature met ric the primary interest in this question is not so much to give a newproof of the uniformization theorem but rather to understand nonlinearparabolic equations better especially those arising in differential geome try a sufficiently deep understanding of parabolic equations should yieldimportant new results in riemannian geometry the question in the preceding paragraph has been studied by richardhamilton 3 and brad osgood ralph phillips and peter sarnak 6 in 3 hamilton studied the following equation which we refer to as

the implicit closest point method for the numerical solution of partial differential equations on surfaces many applications in the natural and applied sciences require the solutions of partial differential equations pdes on surfaces or more general manifolds the closest point method is a simple and accurate embedding method for numerically approximating pdes on rather general smooth surfaces however the original formulation is designed to use explicit time stepping this may lead to a strict time step restriction for some important pdes such as those involving the laplace beltrami operator or higher order derivative operators to achieve improved stability and efficiency we introduce a new implicit closest point method for surface pdes the method allows for large stable time steps while retaining the principal benefits of the original method in particular it maintains the order of accuracy of the discretization of the underlying embedding pde it works on sharply defined bands without degrading the accuracy of the method and it applies to general smooth surfaces it also is very simple and may be applied to a rather general class of surface pdes convergence studies for the in surface heat equation and a fourth order biharmonic problem are given to illustrate the accuracy of the method we demonstrate the flexibility and generality of the method by treating flows involving diffusion reaction diffusion and fourth order spatial derivatives on a variety of interesting surfaces including surfaces of mixed codimension

closed loop stability analysis of discrete time negative imaginary systems abstract we derive necessary and sufficient conditions for stability analysis of a positive feedback interconnection of a discrete time negative imaginary system and a discrete time strictly negative imaginary system general stability analysis results for continuous time negative imaginary systems connected in positive feedback have recently been proposed those recent results extend previous theorems by removing restrictive assumptions on the infinite frequency gains imposed in the earlier literature and by extending the class of negative imaginary systems for which the results are applicable to include systems with free body dynamics i e poles at the origin here we present the discrete time counterparts of the aforementioned recently developed results which specialise to simple and easy to check conditions under specific assumptions last we illustrate some of the results by several examples

a negative imaginary lemma without minimality assumptions and robust state feedback synthesis for uncertain negative imaginary systems abstract negative imaginary systems have important engineering applications for example in lightly damped flexible structures with collocated position sensors and force actuators this paper proposes a new negative imaginary lemma for generalized negative imaginary systems where the minimality assumption is relaxed the proposed lemma facilitates both analysis and synthesis for negative imaginary systems invoking this result a systematic robust static state feedback synthesis method is proposed in an lmi framework for systems with strictly negative imaginary uncertainty e g unmodeled spill over dynamics in a lightly damped flexible structure assuming all states are available for state feedback two numerical examples are given to show the usefulness of the proposed results

variational principles for circle patterns and koebe s theorem we prove existence and uniqueness results for patterns of circles with prescribed intersection angles on constant curvature surfaces our method is based on two new functionals one for the euclidean and one for the hyperbolic case we show how colin de verdiere s bragger s and rivin s functionals can be derived from ours

infinite dimensional negative imaginary systems we consider second order infinite dimensional systems with force control and collocated position measurement interconnected with finite dimensional controllers of the same type we show that under assumptions that generalize those in the finite dimensional case the theory of negative imaginary systems asymptotic stability of the closed loop system can be concluded but that the closed loop system may not be exponentially stable nor input output stable

metric optimization for surface analysis in the laplace beltrami embedding space in this paper we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research using the laplace beltrami eigen system we represent each surface with an isometry invariant embedding in a high dimensional space the key idea in our system is that we realize surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding by minimizing a distance measure in the embedding space with metric optimization our method generates a conformal map directly between surfaces with highly uniform metric distortion and the ability of aligning salient geometric features besides pairwise surface maps we also extend the metric optimization approach for group wise atlas construction and multi atlas cortical label fusion in experimental results we demonstrate the robustness and generality of our method by applying it to map both cortical and hippocampal surfaces in population studies for cortical labeling our method achieves excellent performance in a cross validation experiment with 40 manually labeled surfaces and successfully models localized brain development in a pediatric study of 80 subjects for hippocampal mapping our method produces much more significant results than two popular tools on a multiple sclerosis study of 109 subjects

necessary and sufficient conditions on negative imaginariness for interval siso transfer functions and their interconnection this article is concerned with the study of the negative imaginariness of interval transfer functions necessary and sufficient conditions for strictly negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on kharitonov s theorem then certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed finally an example is provided to illustrate the main results of the article

automatic alignment of genus zero surfaces a new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero the algorithm takes as input a pair of surfaces that are topological 2 spheres each surface given by a distinct triangulation the algorithm then constructs a map f between the two surfaces first each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm the two mappings are then composed with a mobius transformation to generate the function f the mobius transformation is chosen by minimizing an energy that measures the distance of f from an isometry we illustrate our approach using several real life data sets we show first that the algorithm allows for accurate automatic and landmark free nonrigid registration of brain surfaces we then validate our approach by comparing shapes of proteins we provide numerical experiments to demonstrate that the distances computed with our algorithm between low resolution surface based representations of proteins are highly correlated with the corresponding distances computed between high resolution atomistic models for the same proteins

discrete time negative imaginary systems abstract in this paper we introduce the notion of a discrete time negative imaginary system and we investigate its relations with discrete time positive real system theory in the framework presented here discrete time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function in analogy with the case of discrete time positive real functions as well as analogously to the continuous time case this means in particular that we do not need to restrict our notions and definitions to systems with rational transfer functions we also provide a discrete time counterpart of the different notions that have appeared so far in the literature within the framework of strictly positive real and in the more recent theory of strictly negative imaginary systems and to show how these notions are characterized and linked to each other stability analysis results for the feedback interconnection of discrete time negative imaginary systems are also derived

computing quasiconformal maps using an auxiliary metric and discrete curvature flow surface mapping plays an important role in geometric processing which induces both area and angular distortions if the angular distortion is bounded the mapping is called a quasiconformal mapping qc mapping many surface mappings in our physical world are quasiconformal the angular distortion of a qc mapping can be represented by the beltrami differentials according to qc teichmuller theory there is a one to one correspondence between the set of beltrami differentials and the set of qc surface mappings under normalization conditions therefore every qc surface mapping can be fully determined by the beltrami differential and reconstructed by solving the so called beltrami equation in this work we propose an effective method to solve the beltrami equation on general riemann surfaces the solution is a qc mapping associated with the prescribed beltrami differential the main strategy is to define an auxiliary metric am on the domain surface such that the original qc mapping becomes conformal under the auxiliary metric the desired qc mapping can then be obtained by using the conventional conformal mapping method in this paper we first formulate a discrete analogue of qc mappings on triangular meshes then we propose an algorithm to compute discrete qc mappings using the discrete yamabe flow method to the best of our knowledge it is the first work to compute the discrete qc mappings for general riemann surfaces especially with different topologies numerically the discrete qc mapping converges to the continuous solution as the mesh grid size approaches to 0 we tested our algorithm on surfaces scanned from real life with different topologies experimental results demonstrate the generality and accuracy of our auxiliary metric method

surface fluid registration of conformal representation application to detect disease burden and genetic influence on hippocampus in this paper we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1 forms inverse consistent surface fluid registration and multivariate tensor based morphometry mtbm first we conformally map a surface onto a planar rectangle space with holomorphic 1 forms second we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface third we align the feature image with a chosen template image via the fluid image registration algorithm which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization the inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images this alignment induces a corresponding deformation on the surface we tested the system on alzheimer s disease neuroimaging initiative adni baseline dataset to study ad symptoms on hippocampus in our system by modeling a hippocampus as a 3d parametric surface we nonlinearly registered each surface with a selected template surface then we used mtbm to analyze the morphometry difference between diagnostic groups experimental results show that the new system has better performance than two publicly available subcortical surface registration tools first and spharm we also analyzed the genetic influence of the apolipoprotein e 4 allele apoe4 which is considered as the most prevalent risk factor for ad our work successfully detected statistically significant difference between apoe4 carriers and non carriers in both patients of mild cognitive impairment mci and healthy control subjects the results show evidence that the apoe genotype may be associated with accelerated brain atrophy so that our work provides a new mri analysis tool that may help presymptomatic ad research

on classical properties of thermal squeezed states the authors use the formalism of thermo field dynamics and the classical cramer s theorem to show that if two quantum systems are prepared independently and their centre of mass is found to be a thermal squeezed state then both systems were prepared in thermal squeezed states this constitutes an alternative derivation of the quantum version of cramer s theorem further they consider the case of two systems that are prepared independently and their centre of mass is in a pure state in the expanded space of thermo field dynamics in this case it is shown that the system is also separable in the centre of mass and relative coordinates and again all the states involved are thermal squeezed states

thermalized displaced and squeezed number states in the coordinate representation within the framework of thermofield dynamics the wavefunctions of the thermalized displaced number and squeezed number states are given in the coordinate representation furthermore the time evolution of these wavefunctions is considered by introducing a thermal coordinate representation and we also calculate the corresponding probability densities average values and variances of the position coordinate some special cases of which are consistent with results in the literature

larger is twistier spectral analysis of gyrification spangy applied to adult brain size polymorphism abstract the description of cortical folding pattern cfp is challenging because of geometric complexity and inter subject variability on a cortical surface mesh curvature estimation provides a good scalar proxy of cfp the oscillations of this function can be studied using a fourier like analysis to produce a power spectrum representative of the spatial frequency composition of cfp first we introduce an original method for the spectral analysis of gyrication spangy which performs a spectral decomposition of the mean curvature of the grey white interface mesh based on the laplace beltrami operator eigenfunctions spangy produces an ordered 7 bands power spectrum of curvature b0 b6 and provides an anatomically relevant segmentation of cfp based on local spectral composition a spatial frequency being associated with each eigenfunction the bandwidth design assumes frequency doubling between consecutive spectral bands next we observed that the last 3 spectral bands b4 5 and 6 accounted for 93 of the analyzed spectral power and were associated with fold related variations of curvature whereas the lower frequency bands were related to global brain shape the spectral segmentation of cfp revealed 1st 2nd and 3rd order elements associated with b4 b5 and b6 respectively these elements could be related to developmentally defined primary secondary and tertiary folds finally we used allometric scaling of frequency bands power and segmentation to analyze the relationship between the spectral composition of cfp and brain size in a large adult dataset total folding power followed a positive allometric scaling which did not divide up proportionally between the bands b4 contribution was constant b5 increased like total folding power and b6 much faster besides apparition of new elements of pattern with increasing size only concerned the 3rd order hence we demonstrate that large brains are twistier than smaller ones because of an increased number of high spatial frequency folds ramifications and kinks that accommodate the allometric increase of cortical surface

brain surface conformal parameterization using riemann surface structure in medical imaging parameterized 3 d surface models are useful for anatomical modeling and visualization statistical comparisons of anatomy and surface based registration and signal processing here we introduce a parameterization method based on riemann surface structure which uses a special curvilinear net structure conformal net to partition the surface into a set of patches that can each be conformally mapped to a parallelogram the resulting surface subdivision and the parameterizations of the components are intrinsic and stable their solutions tend to be smooth functions and the boundary conditions of the dirichlet problem can be enforced conformal parameterization also helps transform partial differential equations pdes that may be defined on 3 d brain surface manifolds to modified pdes on a two dimensional parameter domain since the jacobian matrix of a conformal parameterization is diagonal the modified pde on the parameter domain is readily solved to illustrate our techniques we computed parameterizations for several types of anatomical surfaces in 3 d magnetic resonance imaging scans of the brain including the cerebral cortex hippocampi and lateral ventricles for surfaces that are topologically homeomorphic to each other and have similar geometrical structures we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other finally we present an automatic sulcal landmark location algorithm by solving pdes on cortical surfaces the landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks

weighted fourier series representation and its application to quantifying the amount of gray matter we present a novel weighted fourier series wfs representation for cortical surfaces the wfs representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions the basic properties of the representation are investigated in connection with a self adjoint partial differential equation and the traditional spherical harmonic spharm representation to reduce steep computational requirements a new iterative residual fitting irf algorithm is developed its computational and numerical implementation issues are discussed in detail the computer codes are also available at http www stat wisc edu mchung softwares weighted spharm weighted spharm html as an illustration the wfs is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects within the wfs framework cortical thickness and gray matter density are computed and compared

negative imaginary synthesis via dynamic output feedback and static state feedback a riccati approach abstract this paper is concerned with the study of strictly negative imaginary sni systems and the problem of synthesizing a controller rendering a linear fractional system sni first a set of necessary and sufficient conditions are developed for an sni lemma without imposing minimality assumptions the proposed lemma supports both the analysis and synthesis of sni systems then a set of sufficient conditions based on the solution of algebraic riccati equations is provided for the solution of the sni synthesis problem finally an illustrative example demonstrates the usefulness of the results given herein

spectral multidimensional scaling an important tool in information analysis is dimensionality reduction there are various approaches for large data simplification by scaling its dimensions down that play a significant role in recognition and classification tasks the efficiency of dimension reduction tools is measured in terms of memory and computational complexity which are usually a function of the number of the given data points sparse local operators that involve substantially less than quadratic complexity at one end and faithful multiscale models with quadratic cost at the other end make the design of dimension reduction procedure a delicate balance between modeling accuracy and efficiency here we combine the benefits of both and propose a low dimensional multiscale modeling of the data at a modest computational cost the idea is to project the classical multidimensional scaling problem into the data spectral domain extracted from its laplace beltrami operator there embedding into a small dimensional euclidean space is accomplished while optimizing for a small number of coefficients we provide a theoretical support and demonstrate that working in the natural eigenspace of the data one could reduce the process complexity while maintaining the model fidelity as examples we efficiently canonize nonrigid shapes by embedding their intrinsic metric into a method often used for matching and classifying almost isometric articulated objects finally we demonstrate the method by exposing the style in which handwritten digits appear in a large collection of images we also visualize clustering of digits by treating images as feature points that we map to a plane

ricci flow for 3d shape analysis ricci flow is a powerful curvature flow method which is invariant to rigid motion scaling isometric and conformal deformations we present the first application of surface ricci flow in computer vision previous methods based on conformal geometry which only handle 3d shapes with simple topology are subsumed by the ricci flow based method which handles surfaces with arbitrary topology we present a general framework for the computation of ricci flow which can design any riemannian metric by user defined curvature the solution to ricci flow is unique and robust to noise we provide implementation details for ricci flow on discrete surfaces of either euclidean or hyperbolic background geometry our ricci flow based method can convert all 3d problems into 2d domains and offers a general framework for 3d shape analysis we demonstrate the applicability of this intrinsic shape representation through standard shape analysis problems such as 3d shape matching and registration and shape indexing surfaces with large nonrigid anisotropic deformations can be registered using ricci flow with constraints of feature points and curves we show how conformal equivalence can be used to index shapes in a 3d surface shape space with the use of teichmuller space coordinates experimental results are shown on 3d face data sets with large expression deformations and on dynamic heart data

feedback stability of negative imaginary systems this paper extends the robust feedback stability theorem of negative imaginary systems by removing restrictive assumptions on the instantaneous gains of the systems that were imposed in the earlier literature and it further generalizes this robust analysis result into the case that allows negative imaginary systems to have poles at the origin in doing so we extend the class of negative imaginary systems for which this robust stability theorem is applicable we also show that this new generalized necessary and sufficient result specializes to the earlier theorems under the same assumptions we additionally prove that the previously known dc gain condition is not only necessary and sufficient for robust feedback stability under the earlier specified instantaneous gain assumptions but is also necessary and sufficient for robust feedback stability under new different and equally simple assumptions the general robust feedback stability theorem for negative imaginary systems with free body dynamics i e poles at the origin derived in this paper also specializes to the case that is only applicable for the negative imaginary system without poles at the origin since the results for negative imaginary systems with free body dynamics developed in this paper depend on the existence of a matrix psi with certain properties we also propose a systematic construction of this matrix psi and show that construction of one such psi is sufficient for determining the feedback stability of the closed loop system finally examples are used to demonstrate the applicability of the results

genus zero surface conformal mapping and its application to brain surface mapping we developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one forms for surfaces with or without boundaries gu and yau 2002 gu and yau 2003 for genus zero surfaces our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map in this paper we apply the algorithm to the cortical surface matching problem we use a mesh structure to represent the brain surface further constraints are added to ensure that the conformal map is unique empirical tests on magnetic resonance imaging mri data show that the mappings preserve angular relationships are stable in mris acquired at different times and are robust to differences in data triangulation and resolution compared with other brain surface conformal mapping algorithms our algorithm is more stable and has good extensibility

coherent states on the m sheeted complex plane coherent states on the m sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied operators am am which create and annihilate clusters of m particles are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the ordinary glauber coherent states with respect to a a an extended bargmann representation in the m sheeted complex plane and p and q representations with respect to our coherent states are studied applications of this formalism in the study of hamiltonians that describe m particle clustering are also considered