multiple motion scene reconstruction with uncalibrated cameras in this paper we describe a reconstruction method for multiple motion scenes which are scenes containing multiple moving objects from uncalibrated views assuming that the objects are moving with constant velocities the method recovers the scene structure the trajectories of the moving objects the camera motion and the camera intrinsic parameters except skews simultaneously we focus on the case where the cameras have unknown and varying focal lengths while the other intrinsic parameters are known the number of the moving objects is automatically detected without prior motion segmentation the method is based on a unified geometrical representation of the static scene and the moving objects it first performs a projective reconstruction using a bilinear factorization algorithm and then converts the projective solution to a euclidean one by enforcing metric constraints experimental results on synthetic and real images are presented

untwisting a projective reconstruction a method for upgrading a projective reconstruction to metric is presented the method compares favourably to state of the art algorithms and has been found extremely reliable for both large and small reconstructions in a large number of experiments on real data the notion of a twisted pair is generalized to the uncalibrated case the reconstruction is first transformed by considering cheirality so that it does not contain any twisted pairs it is argued that this is essential since the method then proceeds by local perturbation as is preferrable we utilize a cost function that reflects the prior likelihood of calibration matrices well it is shown that with any such cost function there is little hope of untwisting a twisted pair by local perturbation the results show that in practice it is most often sufficient to start with a reconstruction that is free from twisted pairs provided that the minimized objective function is a geometrically meaningful quantity when subjected to the common degeneracy of little or no rotation between the views the proposed method still yields a very reasonable member of the family of possible solutions furthermore the method is very fast and therefore suitable for the purpose of viewing reconstructions

boundedness of automorphic l functions in vertical strips the purpose of this paper is to prove the boundedness in vertical strips of finite width for all the l functions that appear in constant terms of eisenstein series under a certain natural assumption on local normalized intertwining operators as a corollary we prove the boundedness for a number of important l functions among them the symmetic cube and triple product l functions attached to cusp forms on gl 2 as well as several rankin selberg product l functions where the local assumption was alredy proved to be valid in each case under the same assumption the finiteness of poles on all of c for all of these l functions is also proved a necessary step in the proof of boundedness in vertical strips

regularized bundle adjustment to model heads from image sequences without calibration data we address the structure from motion problem in the context of head modeling from video sequences for which calibration data is not available this task is made challenging by the fact that correspondences are difficult to establish due to lack of texture and that a quasi euclidean representation is required for realism we have developed an approach based on regularized bundle adjustment it takes advantage of our rough knowledge of the head s shape in the form of a generic face model it allows us to recover relative head motion and epipolar geometry accurately and consistently enough to exploit a previously developed stereo based approach to head modeling in this way complete and realistic head models can be acquired with a cheap and entirely passive sensor such as an ordinary video camera with minimal manual intervention we chose to demonstrate and evaluate our technique mainly in the context of head modeling we do so because it is the application for which all the tools required to perform the complete reconstruction are available to us we will however argue that the approach is generic and could be applied to other tasks such as body modeling for which generic facetized models exist

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy this paper presents a consistent theory for describing indeterminacy and uncertainty of three dimensional 3 d reconstruction from a sequence of images first we give a group theoretical analysis of gauges and gauge transformations we then discuss how to evaluate the reliability of the solution that has indeterminacy and extend the cramer rao lower bound to incorporate internal indeterminacy we also introduce the free gauge approach and define the normal form of a covariance matrix that is independent of particular gauges finally we show simulated and real image examples to illustrate the effect of gauge freedom on uncertainty description

self calibration with varying focal length from two images obtained by a stereo head the self calibration approach based on the absolute conic or its dual the absolute dual quadric has the merit of allowing the intrinsic camera parameters to vary in image sequence in this paper we show that certain linear equations resulting from the infinity homography can be added to a system of originally undetermined linear equations to find the absolute dual quadric for a stereo head the special stereo configurations considered here allow one camera to rotate around either one or two of the coordinate axes defined by another camera experiments with synthetic images show that satisfactory results can be obtained with only the proposed linear methods for real images obtained with non ideal stereo configurations and possibly with measurement noises results obtained from the proposed linear methods may serve as reasonable initial guesses for some non linear optimization procedure

stabilizing the focal length computation for 3 d reconstruction from two uncalibrated views in order to reconstruct 3 d shape from two uncalibrated views one needs to resolve two problems i the computed focal lengths can be imaginary ii the computation fails for fixated images we present a practical remedy for these by subsampling feature points and fixing the focal length we first summarize theoretical backgrounds and then do simulations which reveal a rather surprising fact that when the focal length is actually fixed not using that knowledge yields better results for non fixated images we give an explanation to this seeming paradox and derive a hybrid method switching the computation by judging whether or not the images are fixated doing simulations and real image experiments we demonstrate the effectiveness of our method

generalised correlation for multi feature correspondence computing correspondences between pairs of images is fundamental to all structures from motion algorithms correlation is a popular method to estimate similarity between patches of images in the standard formulation the correlation function uses only one feature such as the gray level values of a small neighbourhood research has shown that different features such as colour edge strength corners texture measures work better under di0erent conditions we propose a framework of generalized correlation that can compute a real valued similarity measure using a feature vector whose components can be dissimilar the framework can combine the e0ects of di0erent image features such as multi spectral features edges corners texture measures etc into a single similarity measure in a 3exible manner additionally it can combine results of di0erent window sizes used for correlation with proper weighting for each relative importances of the features can be estimated from the image itself for accurate correspondence in this paper we present the framework of generalised correlation provide a few examples demonstrating its power as well as discuss the implementation issues 2002 published by elsevier science ltd on behalf of pattern recognition society

cuspidality of symmetric powers with applications the purpose of this paper is to prove that the symmetric fourth power of a cusp form on rm gl 2 whose existence was proved earlier by the first author is cuspidal unless the corresponding automorphic representation is of dihedral tetrahedral or octahedral type as a consequence we prove a number of results toward the ramanujan petersson and sato tate conjectures in particular we establish the bound q sp 1 9 sb v for unramified hecke eigenvalues of cusp forms on rm gl 2 over an arbitrary number field this is the best bound available at present

on moments of twisted l functions we study the average of the product of the central values of two l functions of modular forms f and g twisted by dirichlet characters to a large prime modulus q as our principal tools we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of q and we use the theory of deligne and katz to prove new bounds on bilinear forms in kloosterman sums with power savings when both variables are near the square root of q when at least one of the forms f and g is non cuspidal we obtain an asymptotic formula for the mixed second moment of twisted l functions with a power saving error term in particular when both are non cuspidal this gives a significant improvement on m young s asymptotic evaluation of the fourth moment of dirichlet l functions in the general case the asymptotic formula with a power saving is proved under a conjectural estimate for certain bilinear forms in kloosterman sums

three dimensional unstructured mesh generation part 1 fundamental aspects of triangulation and point creation abstract the present paper introduces an alternative approach for delaunay triangulation in which the triangulation is mapped from an equivalent convex hull in a higher dimension furthermore some fundamental aspects of a point creation algorithm for unstructured mesh generation have been addressed based on numerical experiments a point spacing tensor and point insertion criterion have been introduced aiming to deal with anisotropic meshes

globally convergent autocalibration using interval analysis we address the problem of autocalibration of a moving camera with unknown constant intrinsic parameters existing autocalibration techniques use numerical optimization algorithms whose convergence to the correct result cannot be guaranteed in general to address this problem we have developed a method where an interval branch and bound method is employed for numerical minimization thanks to the properties of interval analysis this method converges to the global solution with mathematical certainty and arbitrary accuracy and the only input information it requires from the user are a set of point correspondences and a search interval the cost function is based on the huang faugeras constraint of the essential matrix a recently proposed interval extension based on bernstein polynomial forms has been investigated to speed up the search for the solution finally experimental results are presented

quasi perspective projection model theory and application to structure and motion factorization from uncalibrated image sequences this paper addresses the problem of factorization based 3d reconstruction from uncalibrated image sequences previous studies on structure and motion factorization are either based on simplified affine assumption or general perspective projection the affine approximation is widely adopted due to its simplicity whereas the extension to perspective model suffers from recovering projective depths to fill the gap between simplicity of affine and accuracy of perspective model we propose a quasi perspective projection model for structure and motion recovery of rigid and nonrigid objects based on factorization framework the novelty and contribution of this paper are as follows firstly under the assumption that the camera is far away from the object with small lateral rotations we prove that the imaging process can be modeled by quasi perspective projection which is more accurate than affine model from both geometrical error analysis and experimental studies secondly we apply the model to establish a framework of rigid and nonrigid factorization under quasi perspective assumption finally we propose an extended cholesky decomposition to recover the rotation part of the euclidean upgrading matrix we also prove that the last column of the upgrading matrix corresponds to a global scale and translation of the camera thus may be set freely the proposed method is validated and evaluated extensively on synthetic and real image sequences and improved results over existing schemes are observed

on the local langlands conejcture mathrm gl n the cyclic case let f be a locally compact nonarchimedean field and p its residue characteristic let f be a separable algebraic closure of f wf the weil group of f over f e a character of fx of order n and e the corresponding character of wf then there exists a canonical map from the set of equivalence classes a of irreducible degree n representations of wf such that e a a to the set of equivalence classes 7r of admissible irreducible supercuspidal representations of gl n f verifying odet x 7t this map is shown to be bijective and to preserve e factors for pairs

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

camera calibration using symmetric objects this paper proposes a novel method for camera calibration using images of a mirror symmetric object assuming unit aspect ratio and zero skew we show that interimage homographies can be expressed as a function of only the principal point by minimizing symmetric transfer errors we thus obtain an accurate solution for the camera parameters we also extend our approach to a calibration technique using images of a 1 d object with a fixed pivoting point unlike existing methods that rely on orthogonality or pole polar relationship our approach utilizes new interimage constraints and does not require knowledge of the 3 d coordinates of feature points to demonstrate the effectiveness of the approach we present results for both synthetic and real images

an analogue of the bombieri vinogradov theorem for fourier coefficients of cusp forms we prove analogues of the bombieri vinogradov theorem and the barban davenport halberstam theorem on primes in arithmetic progressions for fourier coefficients of cusp forms

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

an improved algorithm for two image camera self calibration and euclidean structure recovery using absolute quadric we present an improved algorithm for two image camera self calibration and euclidean structure recovery where the effective focal lengths of both cameras are assumed to be the only unknown intrinsic parameters by using the absolute quadric it is shown that the effective focal lengths can be computed linearly from two perspective images without imposing scene or motion constraints moreover a quadratic equation derived from the absolute quadric is proposed for solving the parameters of the plane at infinity from two images which upgrades a projective reconstruction to a euclidean reconstruction

tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions the input to the method consists of the boundary faces of the polyhedral region and possibly internal and hole interfaces plus the desired number of tetrahedra and other scalar parameters the region is decomposed into convex polyhedra in two stages so that tetrahedra of one length scale can be generated in each subregion a mesh distribution function which is either automatically constructed from the first stage convex polyhedron decomposition or supplied by the user is used to determine the tetrahedron sizes in the subregions then a boundary constrained triangulation is constructed in each convex polyhedron with local transformations being used to improve the quality of the tetahedra

an efficient solution to the five point relative pose problem an efficient algorithmic solution to the classical five point relative pose problem is presented the problem is to find the possible solutions for relative camera pose between two calibrated views given five corresponding points the algorithm consists of computing the coefficients of a tenth degree polynomial in closed form and subsequently finding its roots it is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem we investigate the numerical precision of the algorithm we also study its performance under noise in minimal as well as overdetermined cases the performance is compared to that of the well known 8 and 7 point methods and a 6 point scheme the algorithm is used in a robust hypothesize and test framework to estimate structure and motion in real time with low delay the real time system uses solely visual input and has been demonstrated at major conferences

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

a geometric approach for the analysis and computation of the intrinsic camera parameters the authors of this paper adopted the projected characteristics of the absolute conic in terms of the pascal s theorem to propose an entirely new camera calibration method based on purely geometric thoughts the use of this theorem in the geometric algebra framework allows us to compute a projective invariant using the conics of only two images which expressed using brackets helps us to set enough equations to solve the calibration problem the method requires restricted controlled camera movements our method is less sensitive to noise as the kruppa s equation based methods experiments with simulated and real images con rm that the performance of the algorithm is reliable 2001pattern recognition society published by elsevier science ltd all rights reserved

radial multi focal tensors the 1d radial camera maps all points on a plane containing the principal axis onto the radial line which is the intersection of that plane and the image plane it is a sufficiently general model to express both central and non central cameras since the only assumption it makes is of known center of distortion in this paper we study the multi focal tensors arising out of 1d radial cameras there exist no two view constraints like the fundamental matrix for 1d radial cameras however the 3 view and 4 view cases are interesting for the 4 view case we have the radial quadrifocal tensor which has 15 d o f and 2 internal constraints for the 3 view case we have the radial trifocal tensor which has 7 d o f and no internal constraints under the assumption of a purely rotating central camera this can be used to do a non parametric estimation of the radial distortion of a 1d camera even in the case of a non rotating camera it can be used to do parametric estimation assuming a planar scene finally we examine the mixed trifocal tensor which models the case of two 1d radial cameras and one standard pin hole camera of the above radial multifocal tensors only the radial trifocal tensor is useful practically since it doesn t require any knowledge of the scene and is extremely robust we demonstrate results based on real images for this for the quadrifocal tensor too we present a way to do a metric reconstruction of the scene and to undistort the image given a sufficiently dense set of point correspondences we also show results on synthetic images however it must be noted that currently the quadrifocal and mixed trifocal tensors are useful only from a theoretical stand point

initialization method for self calibration using 2 views recently 3d structure recovery through self calibration of camera has been actively researched traditional calibration algorithm requires known 3d coordinates of the control points while self calibration only requires the corresponding points of images thus it has more flexibility in real application in general self calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera thus it requires initial value for the nonlinear minimization traditional approaches get the initial values assuming they have the same intrinsic parameters while they are dealing with the situation where the intrinsic parameters of the camera may change in this paper we propose new initialization method using the minimum 2 images proposed method is based on the assumption that the least violation of the camera s intrinsic parameter gives more stable initial value synthetic and real experiment shows this result

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

simple algorithm for adaptive refinement of three dimensional finite element tetrahedral meshes a simple strategy to adaptively refine three dimensional tetrahedral meshes has been implemented the procedure adaptively refines a crude initial mesh using solution error indicators or other suitable measures in this paper example problems were remeshed using a refinement ratio determined from an a posteriori error indicator obtained from the finite element solution or the problem the resulting finite element meshes are round to have a smooth gradient in element size aspect ratios are calculated to determine the quality or each element and a smoothing procedure is employed to improve the element aspect ratio example meshes are included to show the adaptive nature or the remesher when applied over several solution cycles

sweepline algorithm for unstructured grid generation on two dimensional non convex domains the sweepline algorithm has been modified to triangulate a set of nodes on a non convex domain the new method is based on a fragile sweepline which is split and rejoined in a manner which ensures that boundaries are preserved both the original and the modified algorithms are introduced using simple examples it is shown that a set of n nodes is triangulated in o n log n time the validity of the new method has been confirmed through testing on a variety of problems and two test cases are presented in this paper

camera calibration from surfaces of revolution this paper addresses the problem of calibrating a pinhole camera from images of a surface of revolution camera calibration is the process of determining the intrinsic or internal parameters i e aspect ratio focal length and principal point of a camera and it is important for both motion estimation and metric reconstruction of 3d models in this paper a novel and simple calibration technique is introduced which is based on exploiting the symmetry of images of surfaces of revolution traditional techniques for camera calibration involve taking images of some precisely machined calibration pattern such as a calibration grid the use of surfaces of revolution which are commonly found in daily life e g bowls and vases makes the process easier as a result of the reduced cost and increased accessibility of the calibration objects in this paper it is shown that two images of a surface of revolution will provide enough information for determining the aspect ratio focal length and principal point of a camera with fixed intrinsic parameters the algorithms presented in this paper have been implemented and tested with both synthetic and real data experimental results show that the camera calibration method presented is both practical and accurate

a normal offsetting technique for automatic mesh generation in three dimensions a technique based on a normal offsetting procedure for the fully automatic generation of meshes suitable for finite element analysis in three dimensions is presented the method is completely automatic requiring no user intervention in the process and no special modelling procedures the method is applied to three dimensional solid geometries the procedure positions nodes in the interior domain of an object by offsetting an initial set of nodes on the object boundary along vectors normal to the boundary to define a layer of new interior point locations the offset points are processed to ensure good nodal spacing appropriate for generating well shaped elements following processing the offset points become a new boundary surrounding the remaining unmeshed region in the interior of the geometric domain the offsetting procedure is applied again to this new boundary layer to form another offset layer farther into the domain interior the offset process offset cycle is repeated until the entire region is filled with nodes tetrahedral elements are then formed by triangulation of the nodes the boundary based technique ensures good quality element shapes for analysis in critical boundary regions and facilitates applications involving integration of mesh generation with design geometry databases calculation of nodal locations are based on local parameters avoiding the higher order time complexities associated with global calculations

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

robust multi view feature matching from multiple unordered views this paper explores the problem of multi view feature matching from an unordered set of widely separated views a set of local invariant features is extracted independently from each view first we propose a new view ordering algorithm that organizes all the unordered views into clusters of related i e the same scene views by efficiently computing the view similarity values of all view pairs by reasonably selecting part of extracted features to match second a robust two view matching algorithm is developed to find initial matches then detect the outliers and finally incrementally find more reliable feature matches under the epipolar constraint between two views from dense to sparse based on an assumption that changes of both motion and feature characteristics of one match are consistent with those of neighbors third we establish the reliable multi view matches across related views by reconstructing missing matches in a neighboring triple of views and efficiently determining the states of matches between view pairs finally the reliable multi view matches thus obtained are used to automatically track all the views by using a self calibration method the proposed methods were tested on several sets of real images experimental results show that it is efficient and can track a large set of multi view feature matches across multiple widely separated views

self calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters in this paper the theoretical and practical feasibility of self calibration in the presence of varying intrinsic camera parameters is under investigation the paper s main contribution is to propose a self calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming focusing cameras the feasibility of the approach is illustrated on real and synthetic examples besides this a theoretical proof is given which shows that the absence of skew in the image plane is sufficient to allow for self calibration a counting argument is developed which depending on the set of constraints gives the minimum sequence length for self calibration and a method to detect critical motion sequences is proposed

a fully automatic three dimensional mesh generator for complex geometries this paper gives a detailed description of an algorithm for the automatic generation of 3 d linear unstructured tetrahedral meshes for complex geometries although the algorithm has been tailored for internal boundaries a brief description is given on how the code can be modified to treat complex exterior geometries

invariant distributions and time averages for horocycle flows there are infinitely many obstructions to existence of smooth solutions of the cohomological equation uu f where u is the vector field generating the horocycle flow on the unit tangent bundle sm of a riemann m surface of finite area and f is a given function on sm we study the sobolev regularity of these obstructions construct smooth solutions of the cohomological equation and derive asymptotics for the ergodic averages of horocycle flows

visual modeling with a hand held camera in this paper a complete system to build visual models from camera images is presented the system can deal with uncalibrated image sequences acquired with a hand held camera based on tracked or matched features the relations between multiple views are computed from this both the structure of the scene and the motion of the camera are retrieved the ambiguity on the reconstruction is restricted from projective to metric through self calibration a flexible multi view stereo matching scheme is used to obtain a dense estimation of the surface geometry from the computed data different types of visual models are constructed besides the traditional geometry and image based approaches a combined approach with view dependent geometry and texture is presented as an application fusion of real and virtual scenes is also shown

modularity of the rankin selberg l series and multiplicity one for sl 2 let f g be primitive cusp forms holomorphic or otherwise on the upper half plane h of levels n m respectively with unitarily normalized l functions l s f equation and l s g equation when p does not divide n resp m the inverse roots p p resp p p are nonzero with sum ap resp bp for every p prime to nm set lp s f g 1 p pp s 1 p pp s 1 p pp s 1 p pp s 1 let l s f g denote the incomplete euler product of lp s f g over all p not dividing nm this is closely related to the convolution l series sum over n 1 a sub n b sub n n s whose miraculous properties were first studied by rankin and selberg

real zeros and size of rankin selberg l functions in the level aspect in this paper some asymptotic formulas are proved for the harmonic mollified second moment of a family of rankin selberg l functions one of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average a first consequence is a new subconvexity bound for rankin selberg l functions in the level aspect moreover infinitely many rankin selberg l functions having at most eight non trivial real zeros are produced and some new non trivial estimates for the analytic rank of the family studied are obtained

generation of oriented three dimensional delaunay grids suitable for the control volume integration method a fully automatic algorithm for three dimensional mesh generation is presented the algorithm preserves the robustness and time efficiency of the finite octree technique replacing octrees by more general 2 4 8 trees it is capable of generating oriented meshes in a post processing step meshes are transformed in order to satisfy the delaunay criterion and so that non overlapping closed control volumes can be defined for each mesh point through edge bisectors the method is shown to be appropriate for modelling semiconductor devices where the control volume scheme is the method of choice due to the peculiarities of the partial differential equations involved and where locally refined and oriented meshes are essential to describe the relevant internal physical quantities adequately while keeping the number of mesh points practical

affine approximation for direct batch recovery of euclidian structure and motion from sparse data we present a batch method for recovering euclidian camera motion from sparse image data the main purpose of the algorithm is to recover the motion parameters using as much of the available information and as few computational steps as possible the algorithm thus places itself in the gap between factorisation schemes which make use of all available information in the initial recovery step and sequential approaches which are able to handle sparseness in the image data euclidian camera matrices are approximated via the affine camera model thus making the recovery direct in the sense that no intermediate projective reconstruction is made using a little known closure constraint the fa closure we are able to formulate the camera coefficients linearly in the entries of the affine fundamental matrices the novelty of the presented work is twofold firstly the presented formulation allows for a particularly good conditioning of the estimation of the initial motion parameters but also for an unprecedented diversity in the choice of possible regularisation terms secondly the new autocalibration scheme presented here is in practice guaranteed to yield a least squares estimate of the calibration parameters as a bi product the affine camera model is rehabilitated as a useful model for most cameras and scene configurations e g wide angle lenses observing a scene at close range experiments on real and synthetic data demonstrate the ability to reconstruct scenes which are very problematic for previous structure from motion techniques due to local ambiguities and error accumulation

constrained structure and motion from multiple uncalibrated views of a piecewise planar scene this paper is about multi view modeling of a rigid scene we merge the traditional approaches of reconstructing image extractable features and of modeling via user provided geometry we use features to obtain a first guess for structure and motion fit geometric primitives correct the structure so that reconstructed features lie exactly on geometric primitives and optimize both structure and motion in a bundle adjustment manner while enforcing the underlying constraints we specialize this general scheme to the point features and the plane geometric primitives the underlying geometric relationships are described by multi coplanarity constraints we propose a minimal parameterization of the structure enforcing these constraints and use it to devise the corresponding maximum likelihood estimator the recovered primitives are then textured from the input images the result is an accurate and photorealistic model experimental results using simulated data confirm that the accuracy of the model using the constrained methods is of clearly superior quality compared to that of traditional methods and that our approach performs better than existing ones for various scene configurations in addition we observe that the method still performs better in a number of configurations when the observed surfaces are not exactly planar we also validate our method using real images

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

image interpolation using enhanced multiresolution critical point filters there are increasing demands for image interpolation in various fields such as virtual reality computer animation and video transmission the critical point filters cpf we have proposed previously enable completely automatic matching of two images in our previous method however it has taken a long time to compute the optimal parameter values by iterative searches this paper proposes an improved algorithm called the enhanced critical point filters ecpf where the parameters are stably computed using together the inverse mapping from the destination to the source it takes only a second to match images whose size is 64 64 the algorithm is also improved in its precision by directly handling color images while the previous algorithm has taken only the intensity value into account we apply ecpf to keyframe interpolation of video sequences we also apply ecpf to interpolating two different views of an object to generate any intermediate views in this case there are many constraints that can be used to determine the mapping between the images we propose a method to use such constraints to improve the accuracy of the mappings as the results image based pseudo 3d models are easily created from a set of views without any special devices

a case against kruppa s equations for camera self calibration we consider the self calibration problem for perspective cameras and especially the classical kruppa equation approach it is known that for several common types of camera motion self calibration is degenerate which manifests itself through the existence of ambiguous solutions the author previously 1997 1999 studied these critical motion sequences and showed their importance for practical applications here we reveal a type of camera motion that is not critical for the generic self calibration problem but for which the kruppa equation approach fails this is the case if the optical centers of all cameras lie on a sphere and if the optical axes pass through the sphere s center a very natural situation for 3d object modeling from images results of simulated experiments demonstrate the instability of numerical self calibration algorithms in near degenerate configurations

twisted endoscopy and reducibility of induced representations for p adic groups 1 introduction this is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the levi factors ofmaximal parabolic subgroups of p adic groups on the unitary axis the problem is equivalent to determining certain local langlands l functions which are of arithmetic significance by themselves one of the main aims of this paper is to interpret our results in the direction of the parametrization problem by means of the theory of twisted endoscopy for which our method seems to be very suitable when the representation is supercuspidal we also study the reducibility of the induced representations off the unitary axis let f be a p adic field of characteristic zero fix a positive integer n 1 and let g be either of the groups sp2n s02n or s02n l in all three cases there is a conjugacy class of maximal parabolic subgroups which has gl as its levi factor let p mn be the standard parabolic subgroup ofg in this conjugacy class then m gl let tr be a discrete series representation of m gln f and given s c let i s tr be the representation of g g f induced from tr r idet ls let i tr i 0 tr

camera self calibration from unknown planar structures enforcing the multiview constraints between collineations in this paper we describe an efficient method to impose the constraints existing between the collineations between images which can be computed from a sequence of views of a planar structure these constraints are usually not taken into account by multiview techniques in order not to increase the computational complexity of the algorithms however imposing the constraints is very useful since it allows a reduction of geometric errors in the reprojected features and provides a consistent set of collineations which can be used for several applications such as mosaicing reconstruction and self calibration in order to show the validity of our approach this paper focus on self calibration from unknown planar structures proposing a method exploiting the consistent set of collineations our method can deal with an arbitrary number of views and an arbitrary number of planes and varying camera internal parameters however for simplicity this papers will only discuss the case with one plane in several views the results obtained with synthetic and real data are very accurate and stable even when using only few images

efficient focus sampling through depth of field calibration due to the limited depth of field dof of conventional digital cameras only the objects within a certain distance range from the camera are in focus objects outside the dof are observed with different amounts of defocus depending on their position focus sampling consists of capturing different images of the same scene by changing the focus configuration of the camera in order to alternately bring objects at different depths into focus focus sampling is an important part of different focus related applications such as autofocus focus stacking and depth estimation this work proposes a calibration procedure for modeling the depth of field of conventional cameras in order to perform an efficient focus sampling the method is simple in terms of repeatability and can be easily implemented in different imaging devices experimental tests are presented in order to illustrate the effectiveness of the proposed approach in autofocus results demonstrate that a significant reduction in the number of frames required to capture during autofocusing can be achieved by means of the proposed methodology