rigidity theorems for submetries in positive curvature abstract we derive general structure and rigidity theorems for submetries f m x where m is a complete riemannian manifold with sectional curvature sec m 1 when applied to a non trivial riemannian submersion it follows that diam x 2 in case of equality there is a riemannian submersion s m from a unit sphere and as a consequence f is known up to metric congruence a similar rigidity theorem also holds in the general context of riemannian foliations

near field acoustic source localization and beamforming in spherical harmonics domain in this paper we address the issue of near field source localization using spherical microphone array the spherical array has been widely used for far field source localization due to ease of array processing in spherical harmonics domain various methods for far field source localization has been reformulated in spherical harmonics domain however near field source localization that involves joint estimation of range and bearing of the sources has hitherto not been investigated in this paper the near field data model is developed in spherical harmonics domain in particular three methods that jointly estimate the range and bearing of multiple sources in the spherical array framework are proposed two subspace based methods called the spherical harmonic multiple signal classification sh music and the spherical harmonics music group delay sh mgd for near field source localization are first presented in addition a method for near field source localization and beamforming using spherical harmonic mvdr sh mvdr is also formulated formulation and analysis of cramer rao bound for near field sources is presented in spherical harmonics domain various source localization experiments were conducted on simulated and signal acquired over spherical microphone array in an anechoic chamber root mean square error and probability of resolution are utilized as measures to evaluate the proposed methods the significance and practical application of the proposed methods is discussed using experiment on interference suppression the near field sh mvdr beamforming is utilized in this context

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

homeomorphism classification of positively curved manifolds with almost maximal symmetry rank we show that a closed simply connected 8 manifold 9 manifold of positive sectional curvature on which a 3 torus 4 torus acts isometrically is homeomorphic to a sphere a complex projective space or a quaternionic projective plane sphere we show that a closed simply connected 2m manifold m 5 of positive sectional curvature on which an m 1 torus acts isometrically is homeomorphic to a complex projective space if and only if its euler characteristic is not 2 by wi these results imply a homeomorphism classification for positively curved n manifolds n 8 of almost maximal symmetry rank open image in new window

triangulation in random refractive distortions random refraction occurs in turbulence and through a wavy water air interface it creates distortion that changes in space time and with viewpoint localizing objects in three dimensions 3d despite this random distortion is important to some predators and also to submariners avoiding the salient use of periscopes we take a multiview approach to this task refracted distortion statistics induce a probabilistic relation between any pixel location and a line of sight in space measurements of an object s random projection from multiple views and times lead to a likelihood function of the object s 3d location the likelihood leads to estimates of the 3d location and its uncertainty furthermore multiview images acquired simultaneously in a wide stereo baseline have uncorrelated distortions this helps reduce the acquisition time needed for localization the method is demonstrated in stereoscopic video sequences both in a lab and a swimming pool

concavity and rigidity in non negative curvature we show that for a manifold with non negative curvature one obtains a collection of concave functions special cases of which are the concavity of the length of a jacobi field in dimension 2 and the concavity of the volume in general we use these functions to show that there are many cohomogeneity one manifolds which do not carry an analytic invariant metric with non negative curvature this implies in particular that one of the candidates in positively curved cohomogeneity one manifolds and 3 sasakian geometry does not carry an invariant metric with positive curvature

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

removing atmospheric turbulence via space invariant deconvolution to correct geometric distortion and reduce space and time varying blur a new approach is proposed in this paper capable of restoring a single high quality image from a given image sequence distorted by atmospheric turbulence this approach reduces the space and time varying deblurring problem to a shift invariant one it first registers each frame to suppress geometric deformation through b spline based nonrigid registration next a temporal regression process is carried out to produce an image from the registered frames which can be viewed as being convolved with a space invariant near diffraction limited blur finally a blind deconvolution algorithm is implemented to deblur the fused image generating a final output experiments using real data illustrate that this approach can effectively alleviate blur and distortions recover details of the scene and significantly improve visual quality

symmetric data attachment terms for large deformation image registration nonrigid medical image registration between images that are linked by an invertible transformation is an inherently symmetric problem the transformation that registers the image pair should ideally be the inverse of the transformation that registers the pair with the order of images interchanged this property is referred to as symmetry in registration or inverse consistent registration however in practical estimation the available registration algorithms have tended to produce inverse inconsistent transformations when the template and target images are interchanged in this paper we propose two novel cost functions in the large deformation diffeomorphic framework that are inverse consistent these cost functions have symmetric data attachment terms in the first the matching error is measured at all points along the flow between template and target and in the second matching is enforced only at the midpoint of the flow between the template and target we have implemented these cost functions and present experimental results to validate their inverse consistent property and registration accuracy

cohomogeneity one topological manifolds revisited we prove a structure theorem for closed topological manifolds of cohomogeneity one this result corrects an oversight in the literature we complete the equivariant classification of closed simply connected cohomogeneity one topological manifolds in dimensions 5 6 and 7 and obtain topological characterizations of these spaces in these dimensions these manifolds are homeomorphic to smooth manifolds

lifting group actions and nonnegative curvature we examine the question when a group acting by cohomogeneity one on the base of a principal g bundle can be lifted to the total space and commutes with the action by g we answer this question completely when the base of the principle bundle is 4 dimensional

cohomogeneity one riemannian manifolds of even dimension with strictly positive curvature i we classify compact positively curved riemannian manifolds of even dimension acted on by a semisimple but not simple group with a codimension one orbit

tits geometry and positive curvature there is a well known link between maximal polar representations and isotropy representations of symmetric spaces provided by dadok moreover the theory by tits and burns spatzier provides a link between irreducible symmetric spaces of non compact type of rank at least 3 and irreducible topological spherical buildings of rank at least 3 we discover and exploit a rich structure of a connected chamber system of finite coxeter type mathsf m associated with any polar action of cohomogeneity at least 2 on any simply connected closed positively curved manifold although this chamber system is typically not a tits geometry of type mathsf m its universal tits cover indeed is a building in all but two exceptional cases we construct a topology on this universal cover making it into a compact spherical building in the sense of burns and spatzier using this structure we classify up to equivariant diffeomorphism all polar actions on simply connected positively curved manifolds of cohomogeneity at least 2

strongly nonnegative curvature we prove that all currently known examples of manifolds with nonnegative sectional curvature satisfy a stronger condition their curvature operator can be modified with a 4 form to become positive semidefinite

isometric actions on spheres with an orbifold quotient we classify representations of compact connected lie groups whose induced action on the unit sphere has the orbit space isometric to a riemannian orbifold

avoiding symmetry breaking spatial non uniformity in deformable image registration via a quasi volume preserving constraint the choice of a reference image typically influences the results of deformable image registration thereby making it asymmetric this is a consequence of a spatially non uniform weighting in the cost function integral that leads to general registration inaccuracy the inhomogeneous integral measure which is the local volume change in the transformation thus varying through the course of the registration causes image regions to contribute differently to the objective function more importantly the optimization algorithm is allowed to minimize the cost function by manipulating the volume change instead of aligning the images the approaches that restore symmetry to deformable registration successfully achieve inverse consistency but do not eliminate the regional bias that is the source of the error in this work we address the root of the problem the non uniformity of the cost function integral we introduce a new quasi volume preserving constraint that allows for volume change only in areas with well matching image intensities and show that such a constraint puts a bound on the error arising from spatial non uniformity we demonstrate the advantages of adding the proposed constraint to standard asymmetric and symmetrized demons and diffeomorphic demons algorithms through experiments on synthetic images and real x ray and 2d 3d brain mri data specifically the results show that our approach leads to image alignment with more accurate matching of manually defined neuroanatomical structures better tradeoff between image intensity matching and registration induced distortion improved native symmetry and lower susceptibility to local optima in summary the inclusion of this space and time varying constraint leads to better image registration along every dimension that we have measured it

new extremal problems for the riemannian recognition program via alexandrov geometry in its most general form the recognition problem in riemannian geometry asks for the identification of an unknown riemannian manifold via measurements of metric invariants on the manifold optimally one wants to recognize a manifold having made as few measurements as possible many results in riemannian geometry including pinching theorems can be viewed this way here we are only interested in measurements that assign real numbers to each complete riemannian manifold typical examples of such invariants are diameter volume curvature bounds etc when viewing one or several invariants i ii ii of this type as a map on a suitable class l of riemannian manifolds the following problems pose themselves

high dimensional image registration using symmetric priors this paper is about warping a brain image from one subject the object image so that it matches another the template image a high dimensional model is used whereby a finite element approach is employed to estimate translations at the location of each voxel in the template image bayesian statistics are used to obtain a maximum a posteriori map estimate of the deformation field the validity of any registration method is largely based upon the constraints or in this instance priors incorporated into the model describing the transformations in this approach we assume that the priors should have some form of symmetry in that priors describing the probability distribution of the deformations should be identical to those for the inverses i e warping brain a to brain b should not be different probabilistically from warping b to a the fundamental assumption is that the probability of stretching a voxel by a factor of n is considered to be the same as the probability of shrinking n voxels by a factor of n 1 in the bayesian framework adopted here the priors are assumed to have a gibbs form where the gibbs potential is a penalty function that embodies this symmetry the penalty function of choice is based upon the singular values of the jacobian having a lognormal distribution this enforces a continuous one to one mapping a gradient descent algorithm is presented that incorporates the above priors in order to obtain a map estimate of the deformations we demonstrate this approach for the two dimensional case but the principles can be extended to three dimensions a number of examples are given to demonstrate how the method works

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

homogeneous randers spaces with isotropic s curvature and positive flag curvature in this paper we will give a complete classification of homogeneous randers spaces with isotropic s curvature and positive flag curvature this results in a large class of finsler spaces with non constant positive flag curvature at the final part of the paper we prove a rigidity result asserting that a homogeneous randers space with almost isotropic s curvature and negative ricci scalar must be riemannian

compact differentiable transformation groups on exotic spheres 0 introduction 355 1 statement of the main results 357 2 higher dimensional subgroups of o n 1 358 3 higher dimensional transformation groups on homology spheres geometric weight systems and orbit structures 360 4 higher dimensional transformation groups on homotopy spheres and the proof of theorem b 375 5 degree of symmetry of exotic spheres revisited 381 6 large transformation groups on exotic spheres in bp 1 384

on the orbit structures ofsu n actions on manifolds of the type of euclidean spherical or projective spaces on etudie les structures d orbites des actions su n sur des espaces test qui sont du type cohomologique des espaces euclidiens spheriques ou projectifs

knots in riemannian manifolds in this paper we study submanifolds with nonpositive extrinsic curvature in a positively curved manifold among other things we prove that if k subset s n g is a totally geodesic submanifold of codimension 2 in a riemannian sphere with positive sectional curvature where n 5 then k is homeomorphic to sn 2 and the fundamental group of the knot complement pi 1 s n k cong mathbb z

revisiting bayesian blind deconvolution blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation because this problem is fundamentally ill posed strong priors on both the sharp image and blur kernel are required to regularize the solution space while this naturally leads to a standard map estimation framework performance is compromised by unknown trade off parameter settings optimization heuristics and convergence issues stemming from non convexity and or poor prior selections to mitigate some of these problems a number of authors have recently proposed substituting a variational bayesian vb strategy that marginalizes over the high dimensional image space leading to better estimates of the blur kernel however the underlying cost function now involves both integrals with no closed form solution and complex function valued arguments thus losing the transparency of map beyond standard bayesian inspired intuitions it thus remains unclear by exactly what mechanism these methods are able to operate rendering understanding improvements and extensions more difficult to elucidate these issues we demonstrate that the vb methodology can be recast as an unconventional map problem with a very particular penalty prior that conjoins the image blur kernel and noise level in a principled way this unique penalty has a number of useful characteristics pertaining to relative concavity local minima avoidance normalization and scale invariance that allow us to rigorously explain the success of vb including its existing implementational heuristics and approximations it also provides strict criteria for learning the noise level and choosing the optimal image prior that perhaps counter intuitively need not reflect the statistics of natural scenes in so doing we challenge the prevailing notion of why vb is successful for blind deconvolution while providing a transparent platform for introducing enhancements and extensions moreover the underlying insights carry over to a wide variety of other bilinear models common in the machine learning literature such as independent component analysis dictionary learning sparse coding and non negative matrix factorization

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

the optimal template effect in hippocampus studies of diseased populations we evaluate the impact of template choice on template based segmentation of the hippocampus in epilepsy four dataset specific strategies are quantitatively contrasted the closest to average individual template the average shape version of the closest to average template a best appearance template and the best appearance and shape template proposed here and implemented in the open source toolkit advanced normalization tools ants the cross correlation similarity metric drives the correspondence model and is used consistently to determine the optimal appearance minimum shape distance in the diffeomorphic space determines optimal shape our evaluation results show that with respect to gold standard manual labeling of hippocampi in epilepsy optimal shape and appearance template construction outperforms the other strategies for gaining data derived templates our results also show the improvement is most significant on the diseased side and insignificant on the healthy side thus the importance of the template increases when used to study pathology and may be less critical for normal control studies furthermore explicit geometric optimization of the shape component of the unbiased template positively impacts the study of diseased hippocampi

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

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

s curvature of cohomogeneity one randers spaces abstract in this paper we study s curvature of cohomogeneity one randers spaces with orbit space s 1 in particular we present an explicit coordinate free formula of s curvature in terms of some quantities which is determined by the metric and the structure of the manifold as an application we give a sufficient and necessary condition for a cohomogeneity one randers space to have almost isotropy s curvature furthermore we give some simple criterions for a cohomogeneity one randers space to be a berwald space or a douglas space

collapsed 5 manifolds with pinched positive sectional curvature abstract let m be a closed 5 manifold of pinched curvature 0 sec m 1 we prove that m is homeomorphic to a spherical space form if one of the following conditions holds i the center of the fundamental group has index w a constant depending on ii 1 4 1 10 6 2 and the fundamental group is a non cyclic group of order c a constant iii the volume is less than and the fundamental group is either isomorphic to a spherical 5 space group or has an odd order and it has a center of index w a constant

multiframe selective information fusion from robust error estimation theory a dynamic procedure for selective information fusion from multiple image frames is derived from robust error estimation theory the fusion rate is driven by the anisotropic gain function defined to be the difference between the gaussian smoothed edge maps of a given input frame and of an evolving synthetic output frame the gain function achieves both selection and rapid fusion of relatively sharper features from each input frame compared to the synthetic frame effective applications are demonstrated for image sharpening in imaging through atmospheric turbulence for multispectral fusion of the rgb spectral components of a scene for removal of blurred visual obstructions from in front of a distant focused scene and for high resolution two dimensional display of three dimensional objects in microscopy

on the topology of positively curved 4 manifolds with symmetry soit m une variete compacte a courbure positive orientable a 4 dimensions si m a un champ de vecteurs de killing non trivial alors m est homeomorphe a s 4 ou cp 2

a new look to multichannel blind image deconvolution the aim of this paper is to propose a new look to mbid examine some known approaches and provide a new mc method for restoring blurred and noisy images first the direct image restoration problem is briefly revisited then a new method based on inverse filtering for perfect image restoration in the noiseless case is proposed the noisy case is addressed by introducing a regularization term into the objective function in order to avoid noise amplification second the filter identification problem is considered in the mc context a new robust solution to the degradation matrix filter is then derived and used in conjunction with a total variation approach to restore the original image simulation results and performance evaluations using recent image quality metrics are provided to assess the effectiveness of the proposed methods

on the fundamental groups of manifolds of positive sectional curvature let m be an n manifold with sectional curvature 0 6 k 1 the main result asserts that the fundamental group of m has a finite normal cyclic subgroup with index less than w n 8 oc a constant depending on n and 8

seven dimensional cohomogeneity one manifolds with nonnegative curvature we show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature unless it admits one with positive curvature as a consequence the classification of nonnegatively curved cohomogeneity one manifolds in dimension seven is reduced to only one further family of candidates

torus actions on homotopy complex projective spaces we prove that an effective action of a torus t on a homotopy open image in new windowpm is linear if m 4 rk t 1 examples show that the bound is optimal combining this with a theorem of hattori we conclude that the total pontrjagin class of such a manifold is given by the usual formula 1 x2 m 1

fundamental groups of positively curved manifolds with symmetry we obtain a classification for the fundamental groups of closed n manifolds of positive sectional curvature which admit an isometric t k action with k ge frac n 6 1 n ne 11 15

positively curved manifolds with maximal discrete symmetry rank let m be a closed simply connected n manifold of positive sectional curvature we determine its homeomorphism or homotopic type if m also admits an isometric elementary p group action of large rank our main results are there exists a constant p n 0 such that 1 if m 2 n admits an effective isometric inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i action for a prime p p n then k n and implies that m 2 n is homeomorphic to a sphere or a complex projective space 2 if m 2 n 1 admits an isometric s 1 inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i action for a prime p p n then k n and implies that m is homeomorphic to a sphere 3 for m in 1 or 2 if n 7 and k 3 n 4 2 then m is homeomorphic to a sphere or homotopic to a complex projective space

near field multiple source localization by passive sensor array the localization of multiple near field sources in a spatially white gaussian noise environment is studied a modified two dimensional 2 d version of the multiple signal classification music algorithm is used to localize the signal sources range and bearing a global optimum maximum likelihood searching approach to localize these sources is discussed it is shown that in the single source situation the covariances of both the 2 d music estimator and the maximum likelihood estimator mle approach the cramer rao lower bound as the number of snapshots increases to infinity in the multiple source situation it is observed that for a high signal to noise ratio snr and a large number of snapshots the root mean square errors rmses of both localization techniques are relatively small however for low snr and or small number of snapshots the performance of the mle is much superior that of the modified 2 d music

blind identification of multichannel fir blurs and perfect image restoration despite its practical importance in image processing and computer vision blind blur identification and blind image restoration have so far been addressed under restrictive assumptions such as all pole stationary image models blurred by zero or minimum phase point spread functions relying upon diversity availability of a sufficient number of multiple blurred images we develop blind fir blur identification and order determination schemes apart from a minimal persistence of the excitation condition also present with nonblind setups the inaccessible input image is allowed to be deterministic or random and of unknown color of distribution with the blurs satisfying a certain co primeness condition in addition we establish existence and uniqueness results which guarantee that single input multiple output fir blurred images can be restored blindly though perfectly in the absence of noise using linear fir filters results of simulations employing the blind order determination blind blur identification and blind image restoration algorithms are presented when the snr is high direct image restoration is found to yield better results than indirect image restoration which employs the estimated blurs in low snr indirect image restoration performs well while the direct restoration results vary with the delay but improve with larger equalizer orders

cohomogeneity one disk bundles with normal homogeneous collars we consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved1 invariant metric with normal collar i e such that near the boundary the metric is the product of an interval and a normal homogeneous space if such a bundle is not the quotient of a trivial bundle then we show that its rank has to be in 2 3 4 6 8 moreover we give a complete classification of such bundles of rank 6 and 8 and a partial classification for rank 3

simultaneous multi scale registration using large deformation diffeomorphic metric mapping in the framework of large deformation diffeomorphic metric mapping lddmm we present a practical methodology to integrate prior knowledge about the registered shapes in the regularizing metric our goal is to perform rich anatomical shape comparisons from volumetric images with the mathematical properties offered by the lddmm framework we first present the notion of characteristic scale at which image features are deformed we then propose a methodology to compare anatomical shape variations in a multi scale fashion i e at several characteristic scales simultaneously in this context we propose a strategy to quantitatively measure the feature differences observed at each characteristic scale separately after describing our methodology we illustrate the performance of the method on phantom data we then compare the ability of our method to segregate a group of subjects having alzheimer s disease and a group of controls with a classical coarse to fine approach on standard 3d mr longitudinal brain images we finally apply the approach to quantify the anatomical development of the human brain from 3d mr longitudinal images of pre term babies results show that our method registers accurately volumetric images containing feature differences at several scales simultaneously with smooth deformations

diffeomorphism type of the berger space so 5 so 3 we compute the eells kuiper invariant of the berger manifold so 5 so 3 and determine that it is diffeomorphic to the total space of an s 3 bundle over s 4 this answers a question raised by k grove and w ziller

plane wave decomposition of the sound field on a sphere by spherical convolution spherical microphone arrays have been recently studied for sound analysis and sound recordings which have the advantage of spherical symmetry facilitating three dimensional analysis this paper complements the recent microphone array design studies by presenting a theoretical analysis of plane wave decomposition given the sound pressure on a sphere the analysis uses the spherical fourier transform and the spherical convolution where it is shown that the amplitudes of the incident plane waves can be calculated as a spherical convolution between the pressure on the sphere and another function which depends on frequency and the sphere radius the spatial resolution of plane wave decomposition given limited bandwidth in the spherical fourier domain is formulated and ways to improve the computation efficiency of plane wave decomposition are introduced the paper concludes with a simulation example of plane wave decomposition

obstructions to positive curvature and symmetry we discuss new obstructions to positive sectional curvature and symmetry the main result asserts that the index of the dirac operator twisted with the tangent bundle vanishes on a 2 connected manifold of dimension 8 if the manifold admits a metric of positive sectional curvature and isometric effective s1 action the proof relies on the rigidity theorem for elliptic genera and properties of totally geodesic submanifolds

curvature and symmetry of milnor spheres since milnor s discovery of exotic spheres mi one of the most intriguing problems in riemannian geometry has been whether there are exotic spheres with positive curvature it is well known that there are exotic spheres that do not even admit metrics with positive scalar curvature hi on the other hand there are many examples of exotic spheres with positive ricci curvature cf ch1 he po and na and this work recently culminated in wr where it is shown that every exotic sphere that bounds a parallelizable manifold has a metric of positive ricci curvature this includes all exotic spheres in dimension 7 so far however no example of an exotic sphere with positive sectional curvature has been found in fact until now only one example of an exotic sphere with nonnegative sectional curvature was known the so called gromoll meyer sphere gm in dimension 7 as one of our main results we prove

finite isometry groups of 4 manifolds with positive sectional curvature let m be an oriented compact riemannian 4 manifold with positive sectional curvature let g be a finite subgroup of the isometry group of m we prove that if g is a finite group of order g ge 3 10 500 then i g is isomorphic to a subgroup of pu 3 if g is odd ii g contains an index at most 2 normal subgroup which is isomorphic to a subgroup of so 5 or pu 3 if g is even and m is not homeomorphic to s4 moreover m is homeomorphic to mathbb c p 2 if g is non abelian of odd order

new examples of manifolds with strictly positive curvature berger 3 wallach 10 and berard bergery 2 have classified all simply connected smooth manifolds which allow a homogeneous riemannian metric of strictly positive curvature besides the rank one symmetric spaces there exist five exceptional manifolds and an infinite series of 7 manifolds of distinct homotopy type which have been studied by aloft and wallach 1 these are diffeomorphic to mpq su 3 upq where p q are positive integers and upq is the one parameter subgroup of diagonal matrices

harmonic self maps of cohomogeneity one manifolds we develop the theory of equivariant harmonic self maps of compact cohomogeneity one manifolds and construct new harmonic self maps of the compact lie groups mathrm so 4 ell 2 ell ge 1 with degree 3 of mathrm so 8 mathrm so 14 and mathrm so 26 with degree 5 each of mathrm so 10 with degree 7 and of mathrm so 14 with degree 11 by exhibiting linear solutions to non linear singular boundary value problems

index parity of closed geodesics and rigidity of hopf fibrations the diameter rigidity theorem of gromoll and grove 1987 states that a riemannian manifold with sectional curvature 1 and diameter 2 is either homeomorphic to a sphere locally isometric to a rank one symmetric space or it has the cohomology ring of the cayley plane ca the reason that they were only able to recognize the cohomology ring of ca is due to an exceptional case in another theorem gromoll and grove 1988 a riemannian submersion m b b with connected fibers that is defined on the euclidean sphere m is metrically congruent to a hopf fibration unless possibly m b 15 8 we will rule out the exceptional cases in both theorems our argument relies on a rather unusal application of morse theory for that purpose we give a general criterion which allows to decide whether the morse index of a closed geodesic is even or odd

kreck stolz invariants for quaternionic line bundles we generalise the kreck stolz invariants s2 and s3 by defining a new invariant the t invariant for quaternionic line bundles over closed spin manifolds m of dimension 4k 1 with h 3 m q h 4 m q 0 the t invariant classifies closed smooth oriented 2 connected rational homology 7 spheres up to almost diffeomorphism and detects exotic homeomorphisms between such manifolds the t invariant also provides information about quaternionic line bundles over a fixed manifold and we use it to give a new proof of a theorem of feder and gitler about the values of the second chern classes of quaternionic line bundles over hp k the t invariant for s 4k 1 is closely related to the adams e invariant on the 4k 5 stem

cohomogeneity one einstein sasaki 5 manifolds we consider hypersurfaces in einstein sasaki 5 manifolds which are tangent to the characteristic vector field we introduce evolution equations that can be used to reconstruct the 5 dimensional metric from such a hypersurface analogous to the nearly hypo and half flat evolution equations in higher dimensions we use these equations to classify einstein sasaki 5 manifolds of cohomogeneity one

curvatures of homogeneous randers spaces abstract we study curvatures of homogeneous randers spaces after deducing the coordinate free formulas of the flag curvature and ricci scalar of homogeneous randers spaces we give several applications we first present a direct proof of the fact that a homogeneous randers space is ricci quadratic if and only if it is a berwald space we then prove that any left invariant randers metric on a non commutative nilpotent lie group must have three flags whose flag curvature is positive negative and zero respectively this generalizes a result of j a wolf on riemannian metrics we prove a conjecture of j milnor on the characterization of central elements of a real lie algebra in a more generalized sense finally we study homogeneous finsler spaces of positive flag curvature and particularly prove that the only compact connected simply connected lie group admitting a left invariant finsler metric with positive flag curvature is su 2

spline based image registration the problem of image registration subsumes a number of problems and techniques in multiframe image analysis including the computation of optic flow general pixel based motion stereo correspondence structure from motion and feature tracking we present a new registration algorithm based on spline representations of the displacement field which can be specialized to solve all of the above mentioned problems in particular we show how to compute local flow global parametric flow rigid flow resulting from camera egomotion and multiframe versions of the above problems using a spline based description of the flow removes the need for overlapping correlation windows and produces an explicit measure of the correlation between adjacent flow estimates we demonstrate our algorithm on multiframe image registration and the recovery of 3d projective scene geometry we also provide results on a number of standard motion sequences

cohomogeneity two torus actions on non negatively curved manifolds of low dimension let mathrm m n n in 4 5 6 be a compact simply connected n manifold which admits some riemannian metric with non negative curvature and an isometry group of maximal possible rank then any smooth effective action on mathrm m n by a torus mathrm t n 2 is equivariantly diffeomorphic to an isometric action on a normal biquotient furthermore it follows that any effective isometric circle action on a compact simply connected non negatively curved four dimensional manifold is equivariantly diffeomorphic to an effective isometric action on a normal biquotient

the identification of multiple outliers abstract one approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations in this article we define outliers in terms of their position relative to the model for the good observations the outlier identification problem is then the problem of identifying those observations that lie in a so called outlier region methods based on robust statistics and outward testing are shown to have the highest possible breakdown points in a sense derived from donoho and huber but a more detailed analysis shows that methods based on robust statistics perform better with respect to worst case behavior a concrete outlier identifier based on a suggestion of hampel is given

positively curved manifolds with symmetry there are very few examples of riemannian manifolds with positive sectionalcurvature known in fact in dimensions above 24 all known examplesare diffeomorphic to locally rank one symmetric spaces we give a partialexplanation of this phenomenon by showing that a positively curved simplyconnected compact manifold m g is up to homotopy given by a rank onesymmetric space provided that its isometry group iso m g is large moreprecisely we prove first that if dim iso m g i 2 dim m 6 then m is tangentially homotopically equivalent to a rank one symmetric space or m is homogeneous secondly we show that in dimensions above 18 k 1 2 each m is tangentially homotopically equivalent to a rank one symmetric space where k 0 denotes the cohomogeneity k dim m iso m g