the invariant holonomic system on a semisimple lie algebra on etudie la theorie geometrique des representations du groupe de weyl du point de vue des systemes holonomes sur des algebres de lie

primitive ideals and orbital integrals in complex exceptional groups in 2 two related problems were studied for complex classical groups determination of the primitive spectrum of the enveloping algebra as a set and fourier inversion of unipotent orbital integrals the first of these was solved completely extending work of joseph and others in sl n c and small groups although our techniques presumably solve the second as well up to determination of normalizing constants we carried out the calculations only for special unipotent classes see 181 we had of course tried to apply the same methods to the exceptional groups but they seem to be inadequate since that work was done however brylinski and kashiwara and beilinson and bernstein have established the kazhdan lusztig conjecture giving character formulas for irreducible highest weight modules 3 71 because of a conjecture of joseph proved in 24 this determines in principle the primitive ideals with a fixed regular integral infinitesimal character they are in one to one correspondence with what kazhdan and lusztig call left cells in the weyl group however the algorithm given by kazhdan and lusztig to compute these cells is enormously complicated requiring one to compute roughly 1 i polynomials of degrees on the order of half the number of positive roots this is very unsatisfactory however it

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

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

a highly robust estimator through partially likelihood function modeling and its application in computer vision the authors present a highly robust estimator known as the model fitting mf estimator for general regression they explain that high robustness becomes possible through partially but completely modeling the unknown log likelihood function the partial modeling takes place by taking the bayesian statistical decision rule and a number of important heuristics into consideration while maximizing the log likelihood function applications include the automatic selection of multiple thresholds single rigid motion estimation or multiple rigid motion segmentation and estimation from two perspective views it is believed that the proposed mf estimator will aid in solving many robust estimation problems that demand an estimator that is either highly robust or capable of handling contaminated gaussian mixture models

12 24 and beyond abstract we generalize the well known 12 and 24 theorems for reflexive polytopes of dimension 2 and 3 to any smooth reflexive polytope our methods apply to a wider category of objects here called reflexive gkm graphs that are associated with certain monotone symplectic manifolds which do not necessarily admit a toric action as an application we provide bounds on the betti numbers for certain monotone hamiltonian spaces which depend on the minimal chern number of the manifold

intrinsic parameter calibration procedure for a high distortion fish eye lens camera with distortion model and accuracy estimation this paper presents a calibration procedure for a fish eye lens a high distortion lens mounted on a ccd tv camera the method is designed to account for the differences in images acquired via a distortion free lens camera setup and the images obtained by a fish eye lens camera the calibration procedure essentially defines a mapping between points in the world coordinate system and their corresponding point locations in the image plane this step is important for applications in computer vision which involve quantitative measurements the objective of this mapping is to estimate the internal parameters of the camera including the effective focal length one pixel width on the image plane image distortion center and distortion coefficients the number of parameters to be calibrated is reduced by using a calibration pattern with equally spaced dots and assuming a pin hole model camera behavior for the image center thus assuming negligible distortion at the image distortion center our method employs a non linear transformation between points in the world coordinate system and their corresponding location on the image plane a lagrangian minimization method is used to determine the coefficients of the transformation the validity and effectiveness of our calibration and distortion correction procedure are confirmed by application of this procedure on real images

implicit and explicit camera calibration theory and experiments by implicit camera calibration we mean the process of calibrating a camera without explicitly computing its physical parameters implicit calibration can be used for both three dimensional 3 d measurement and generation of image coordinates in this paper we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes the back projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points a set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes under the assumption of the radial distortion model we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation by combining with any linear calibration techniques this method makes explicit the camera physical parameters extensive experimental comparison of our methods with the classic photogrammetric method and tsai s 1986 method in the aspects of 3 d measurement both absolute and relative errors the prediction of image coordinates and the effect of the number of calibration points is made using real images from 15 different depth values

irregularity of hypergeometric systems via slopes along coordinate subspaces we study the irregularity sheaves attached to the a hypergeometric d module ma introduced by gel fand et al where a z d n is pointed of full rank and c more precisely we investigate the slopes of this module along coordinate subspaces in the process we describe the associated graded ring to a positive semigroup ring for a filtration defined by an arbitrary weight vector l on torus equivariant generators to this end we introduce the a l umbrella a simplicial complex determined by a and l and identify its facets with the components of the associated graded ring we then establish a correspondence between the full a l umbrella and the components of the l characteristic variety of ma we compute in combinatorial terms the multiplicities of these components in the l characteristic cycle of the associated euler koszul complex identifying them with certain intersection multiplicities we deduce from this that slopes of ma are combinatorial independent of and in one to one correspondence with jumps of the a l umbrella this confirms a conjecture of sturmfels and gives a converse of a theorem of hotta ma is regular if and only if a defines a projective variety 1991 mathematics subject classification 13n10 14m25 16w70

invariant differential operators and an homomorphism of harish chandra let g be a reductive complex lie algebra with adjoint group g cartan subalgebra h and weyl group w then g acts naturally on the algebra of polynomial functions o g and hence on the ring of differential operators with polynomial coefficients d g similarly w acts on h and hence on d h in hc2 harish chandra defined an algebra homomorphism d g d h recently wallach proved that if g has no factors of type e6 e7 or e8 then this map is surjective wa theorem 3 1 the significance of wallach s result is that it enables him to give an easy proof of an important theorem of harish chandra about invariant distributions and to give an elegant new approach to the springer correspondence the main aim of this paper is to give an elementary proof of wa theorem 3 1 that also works for all reductive lie algebras set

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

nonmetric calibration of camera lens distortion differential methods and robust estimation this paper addresses the problem of calibrating camera lens distortion which can be significant in medium to wide angle lenses our approach is based on the analysis of distorted images of straight lines we derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines unlike the other existing approaches we also provide fast closed form solutions to the distortion coefficients we prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm our approach provides a way to get around this and at the same time it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise robust results in addition while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another we present a robust approach to distortion calibration based on the least median of squares estimator our approach is thus able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three dimensional linear segments experiments to evaluate the performance of this approach on synthetic and real data are reported

orbits invariants and representations associated to involutions of reductive groups by an involution of an algebraic group or lie algebra we mean an automorphism 0 such that 0 2 is the identity automorphism let 0 be an involution of a complex reductive lie algebra q and let p denote the 1 eigenspace of 0 on q get g be the adjoint group of q and let k g glog go kostant and rallis 10 have made a detailed study of the action of k on p in particular they obtain very precise information concerning the orbits of k on p and the representation of k on c p the algebra of polynomial functions on p in this paper we consider a global analogue of the problem studied by kostant and rallis let g be a reductive affine algebraic group over an algebraically closed field k of characteristic 2 let 0 be an involution of g and let k gegi0 g g if g is semisimple and the base field is c then g k is the complexification of a riemannian symmetric space we study the action of k and of groups closely related to k by left translation on the coset space g k for technical reasons it is convenient to study a slightly different but equivalent problem let r g g be defined by r g g0 g i then z g p is a closed subvariety of g furthermore z is constant on left cosets of g modulo k and induces an isomorphism o g k p we have o k g k k o g k for k e k and geg thus p is stable under conjugation by k and a is a k isomorphism of affine k varieties we consider the action of k on p by conjugation let x e g have jordan decomposition x x x then we show that x e p if and only if both x and x are in p thus we have a jordan decomposition for elements of p this will play a key role in our results a torus s of g is o anisotropic if o s s 1 for every ses it is known that any two maximal 0 anisotropic tori of g are k let a be a maximal 0 anisotropic torus of g the following result characterizes semisimple elements of p

characteristic cycles for the loop grassmannian and nilpotent orbits x which is a linear combination of closures of conormal bundles to submanifolds of x intuitively the microlocal multiplicities c me asurethesingularity of at in settings related to representation theory a group g acts on x is g equivariant and the microlocal multiplicities play a significant but only partially understood role in representation theory see ro sv abv and kasa e g in this paper we compute microlocal multiplicities for certain cases of interest in representation theory let g be a connected reductive group with loop group lg and let p bethesubgroup of lg consisting of loops with positive fourier coefficients then p orbits on theloop grassmannian lg p correspond to the irreducible representations l of thedual re ductivegroup g for dominant weights and of a torus of

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

camera calibration with distortion models and accuracy evaluation a camera model that accounts for major sources of camera distortion namely radial decentering and thin prism distortions is presented the proposed calibration procedure consists of two steps 1 the calibration parameters are estimated using a closed form solution based on a distribution free camera model and 2 the parameters estimated in the first step are improved iteratively through a nonlinear optimization taking into account camera distortions according to minimum variance estimation the objective function to be minimized is the mean square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters the authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems the validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele and wide angle lenses

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

closed formulae for a b function associated with a weighted homogeneous isolated complete intersection singularity abstract following ideas of b malgrange we give explicit formulae for a b function associated with a weighted homogeneous polynomial morphism which defines an isolated complete intersection singularity

robust metric calibration of non linear camera lens distortion camera lens distortion is crucial to obtain the best performance cameral model up to now different techniques exist which try to minimize the calibration error using different lens distortion models or computing them in different ways some compute lens distortion camera parameters in the camera calibration process together with the intrinsic and extrinsic ones others isolate the lens distortion calibration without using any template and basing the calibration on the deformation in the image of some features of the objects in the scene like straight lines or circles these lens distortion techniques which do not use any calibration template can be unstable if a complete camera lens distortion model is computed they are named non metric calibration or self calibration methods traditionally a camera has been always best calibrated if metric calibration is done instead of self calibration this paper proposes a metric calibration technique which computes the camera lens distortion isolated from the camera calibration process under stable conditions independently of the computed lens distortion model or the number of parameters to make it easier to resolve this metric technique uses the same calibration template that will be used afterwards for the calibration process therefore the best performance of the camera lens distortion calibration process is achieved which is transferred directly to the camera calibration process

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

nonmetric calibration of wide angle lenses and polycameras images taken with wide angle cameras tend to have severe distortions which pull points towards the optical center this paper proposes a simple method for recovering the distortion parameters without the use of any calibration objects since distortions cause straight lines in the scene to appear as curves in the image our algorithm seeks to find the distortion parameters that map the image curves to straight lines the user selects a small set of points along the image curves recovery of the distortion parameters is formulated as the minimization of an objective function which is designed to explicitly account for noise in the selected image points experimental results are presented for synthetic data as well as real images we also present the idea of a polycamera which is defined as a tightly packed camera cluster possible configurations are proposed to capture very large fields of view such camera clusters tend to have a nonsingle viewpoint we therefore provide analysis of what we call the minimum working distance for such clusters finally we present results for a polycamera consisting of four wide angle sensors having a minimum working distance of about 4 m on undistorting the acquired images using our proposed technique we create real time high resolution panoramas

true multi image alignment and its application to mosaicing and lens distortion correction multiple images of a scene are related through 2d 3d view transformations and linear and nonlinear camera transformations we present an algorithm for true multi image alignment that does not rely on the measurements of a reference image being distortion free the algorithm is developed to specifically align and mosaic images using parametric transformations in the presence of lens distortion when lens distortion is present none of the images can be assumed to be ideal in our formulation all the images are modeled as intensity measurements represented in their respective coordinate systems each of which is related to an ideal coordinate system through an interior camera transformation and an exterior view transformation the goal of the accompanying algorithm is to compute an image in the ideal coordinate system while solving for the transformations that relate the ideal system with each of the data images key advantages of the technique presented in this paper are i no reliance on one distortion free image ii ability to register images and compute coordinate transformations even when the multiple images are of an extended scene with no overlap between the first and last frame of the sequence and iii ability to handle linear and nonlinear transformations within the same framework results of applying the algorithm are presented for the correction of lens distortion and creation of video mosaics

when should we consider lens distortion in camera calibration abstract this work investigates the effect of neglecting lens distortion in camera calibration and presents a theoretical analysis of the calibration accuracy we derived an approximate upper envelope for the 2d prediction error which is a function of a few factors including the number of calibration points the observation error of 2d image points the radial lens distortion coefficient the image size and resolution this error envelope provides a guide line for selecting both a proper camera calibration configuration and an appropriate camera model while satisfying the desired accuracy experimental results from both computer simulations and real experiments are included in this paper