compatibility of local and global langlands correspondences we prove the compatibility of local and global langlands correspondences for gln which was proved up to semisimplification in ht more precisely for the ndimensional l adic representation rl of the galois group of an imaginary cm field l attached to a conjugate self dual regular algebraic cuspidal automorphic representation of gln al which is square integrable at some finite place we show that frobenius semisimplification of the restriction of rl to the decomposition group of a place v of l not dividing l corresponds to v by the local langlands correspondence if v is square integrable for some finite place v 6 l we deduce that rl is irreducible we also obtain conditional results in the case v l

fuzzy edge detection for omnidirectional images the use of omnidirectional vision has increased during these past years it provides a very large field of view nevertheless omnidirectional images contain significant radial distortions and conventional image processing is not adapted to these specific images this paper presents an edge detector adapted to the image geometry fuzzy sets will be used to take into account all imprecisions introduced by the sampling process the prewitt filter applied to omnidirectional image will be studied to illustrate this paper

correspondence free structure from motion we present a novel approach for the estimation of 3d motion directly from two images using the radon transform the feasibility of any camera motion is computed by integrating over all feature pairs that satisfy the epipolar constraint this integration is equivalent to taking the inner product of a similarity function on feature pairs with a dirac function embedding the epipolar constraint the maxima in this five dimensional motion space will correspond to compatible rigid motions the main novelty is in the realization that the radon transform is a filtering operator if we assume that the similarity and dirac functions are defined on spheres and the epipolar constraint is a group action of rotations on spheres then the radon transform is a correlation integral we propose a new algorithm to compute this integral from the spherical fourier transform of the similarity and dirac functions generating the similarity function now becomes a preprocessing step which reduces the complexity of the radon computation by a factor equal to the number of feature pairs processed the strength of the algorithm is in avoiding a commitment to correspondences thus being robust to erroneous feature detection outliers and multiple motions

lyapunov based range identification for paracatadioptric systems many applications require the interpretation of the euclidean coordinates of features of a 3 d object through 2 d images in this paper the relative range and the euclidean coordinates of an object or camera undergoing general affine motion are determined for paracatadioptric imaging systems via a nonlinear observer the nonlinear observer asymptotically determines the range information provided that the motion parameters are known the observer is developed through a lyapunov based design and stability analysis and simulation results are provided that illustrate the performance of the state estimator the contributions of this paper are that the developed observer 1 can be applied to both affine and nonaffine systems 2 can be used for both the fixed and moving camera configurations 3 is continuous and 4 yields an asymptotic result

prinjective modules reflection functors quadratic forms and auslander reiten sequences let a b be artinian rings and let a m b be an a b bimodule which is a finitely generated left a module and a finitely generated right b module a right a m b prinjective module is a finitely genrated module x r x a x b x a a m b x b over the triangular matrix ring r a o a m b b such that x a is a projective a module x b is an injective b module and is a b homomorphism we study the category prin r b a of right a m b prinjective modules it is an additive krull schmidt subcategory of mod r closed under extensions

the buzzard diamond jarvis conjecture for unitary groups let p 2 be prime we prove the weight part of serre s conjecture for rank two unitary groups for mod p representations in the unramified case that is the buzzard diamond jarvis conjecture for unitary groups by proving that any serre weight which occurs is a predicted weight our methods are purely local using the theory of modules to determine the possible reductions of certain two dimensional crystalline representations

moduli of finite flat group schemes and modularity we prove that under some mild conditions a two dimensional p adic galois representation which is residually modular and potentially barsotti tate at p is modular this provides a more conceptual way of establishing the shimura taniyama weil conjecture especially for elliptic curves which acquire good reduction over a wildly ramified extension of 3 the main ingredient is a new technique for analyzing flat deformation rings it involves resolving them by spaces which parametrize finite flat group scheme models of galois representations introduction

serre weights for rank two unitary groups we study the weight part of a generalisation of serre s conjecture for mod l galois representations associated to automorphic representations on rank two unitary groups for odd primes l we propose a conjectural set of serre weights agreeing with all conjectures in the literature and under a mild assumption on the image of the mod l galois representation we are able to show that any modular representation is modular of each conjectured weight we make no assumptions on the ramification or inertial degrees of l our main innovations are the use of outer forms of text gl 2 to avoid the parity difficulties with inner forms and the use of the lifting techniques and change of weight results introduced in barnet lamb et al j am math soc 24 2 411 469 2011 duke math j 161 8 1521 1580 2012 potential automorphy and change of weight preprint 2010

galois representations arising from some compact shimura varieties our aim is to establish some new cases of the global langlands correspondence for glm along the way we obtain a new result on the description of the cohomology of some compact shimura varieties let f be a cm eld with complex conjugation c and

catadioptric camera calibration using geometric invariants central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint in this paper we propose a novel method for the calibration of central catadioptric cameras using geometric invariants lines and spheres in space are all projected into conics in the catadioptric image plane we prove that the projection of a line can provide three invariants whereas the projection of a sphere can only provide two from these invariants constraint equations for the intrinsic parameters of catadioptric camera are derived therefore there are two kinds of variants of this novel method the first one uses projections of lines and the second one uses projections of spheres in general the projections of two lines or three spheres are sufficient to achieve catadioptric camera calibration one important conclusion in this paper is that the method based on projections of spheres is more robust and has higher accuracy than that based on projections of lines the performances of our method are demonstrated by both the results of simulations and experiments with real images

a fisher rao metric for paracatadioptric images of lines in a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror a 360 field of view is obtained but the image is severely distorted in particular straight lines in the scene project to circles in the image these distortions make it difficult to detect projected lines using standard image processing algorithms the distortions are removed using a fisher rao metric which is defined on the space of projected lines in the paracatadioptric image the space of projected lines is divided into subsets such that on each subset the fisher rao metric is closely approximated by the euclidean metric each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform the result is a set of digital images to which standard image processing algorithms can be applied the effectiveness of this approach to line detection is illustrated using two algorithms both of which are based on the sobel edge operator the task of line detection is reduced to the task of finding isolated peaks in a sobel image an experimental comparison is made between these two algorithms and third algorithm taken from the literature and based on the hough transform

calibration of ultrawide fisheye lens cameras by eigenvalue minimization we present a new technique for calibrating ultrawide fisheye lens cameras by imposing the constraint that collinear points be rectified to be collinear parallel lines to be parallel and orthogonal lines to be orthogonal exploiting the fact that line fitting reduces to an eigenvalue problem in 3d we do a rigorous perturbation analysis to obtain a practical calibration procedure doing experiments we point out that spurious solutions exist if collinearity and parallelism alone are imposed our technique has many desirable properties for example no metric information is required about the reference pattern or the camera position and separate stripe patterns can be displayed on a video screen to generate a virtual grid eliminating the grid point extraction processing

rotation recovery from spherical images without correspondences this paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence the method is particularly useful for the alignment of large rotations and has potential impact on 3d shape alignment the foundation of the method lies in the fact that the spherical harmonic coefficients undergo a unitary mapping when the original image is rotated the correlation between two images is a function of rotations and we show that it has an so 3 fourier transform equal to the pointwise product of spherical harmonic coefficients of the original images the resolution of the rotation space depends on the bandwidth we choose for the harmonic expansion and the rotation estimate is found through a direct search in this 3d discretized space a refinement of the rotation estimate can be obtained from the conservation of harmonic coefficients in the rotational shift theorem a novel decoupling of the shift theorem with respect to the euler angles is presented and exploited in an iterative scheme to refine the initial rotation estimates experiments show the suitability of the method for large rotations and the dependence of the method on bandwidth and the choice of the spherical harmonic coefficients

the sato tate conjecture for hilbert modular forms we prove the sato tate conjecture for hilbert modular forms more precisely we prove the natural generalisation of the sato tate conjecture for regular algebraic cuspidal automorphic representations of gl2 af f a totally real field which are not of cm type the argument is based on the potential automorphy techniques developed by taylor et al but makes use of automorphy lifting theorems over ramified fields together with a topological argument with local deformation rings in particular we give a new proof of the conjecture for modular forms which does not make use of potential automorphy theorems for non ordinary n dimensional galois representations

fast geodesic active fields for image registration based on splitting and augmented lagrangian approaches in this paper we present an efficient numerical scheme for the recently introduced geodesic active fields gaf framework for geometric image registration this framework considers the registration task as a weighted minimal surface problem hence the data term and the regularization term are combined through multiplication in a single parametrization invariant and geometric cost functional the multiplicative coupling provides an intrinsic spatially varying and data dependent tuning of the regularization strength and the parametrization invariance allows working with images of nonflat geometry generally defined on any smoothly parametrizable manifold the resulting energy minimizing flow however has poor numerical properties here we provide an efficient numerical scheme that uses a splitting approach data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented lagrangian approach our approach is more flexible than standard gaussian regularization since one can interpolate freely between isotropic gaussian and anisotropic tv like smoothing in this paper we compare the geodesic active fields method with the popular demons method and three more recent state of the art algorithms nl optical flow mrf image registration and landmark enhanced large displacement optical flow thus we can show the advantages of the proposed fastgaf method it compares favorably against demons both in terms of registration speed and quality over the range of example applications it also consistently produces results not far from more dedicated state of the art methods illustrating the flexibility of the proposed framework

scale invariant features and polar descriptors in omnidirectional imaging we propose a method to compute scale invariant features in omnidirectional images we present a formulation based on the riemannian geometry for the definition of differential operators on non euclidian manifolds that adapt to the mirror and lens structures in omnidirectional imaging these operators lead to a scale space analysis that preserves the geometry of the visual information in omnidirectional images we then build a novel scale invariant feature detection framework for omnidirectional images that can be mapped on the sphere we further present a new descriptor and feature matching solution for these omnidirectional images the descriptor builds on the log polar planar descriptors and adapts the descriptor computation to the specific geometry and the nonuniform sampling density of omnidirectional images we also propose a rotation invariant matching method that eliminates the orientation computation during the feature detection phase and thus decreases the computational complexity experimental results demonstrate that the new feature computation method combined with the adapted descriptors offers promising detection and matching performance i e it improves on the common scale invariant feature transform sift features computed on the unwrapped omnidirectional images as well as spherical sift features finally we show that the proposed framework also permits to match features between images with different native geometry

a reduction functor tameness and tits form for a class of orders abstract let d be a complete discrete valuation domain which is an algebra over an algebraically closed field k we study in the paper a class of suborders of tiled d orders by means of a rational quadratic form q associated to and a finite poset i having exactly two maximal elements and criteria for finite lattice type and for tame lattice type of are given in terms of the form q and of the category i spr of socle projective k linear representations of the poset i the shape of auslander reiten quiver latt is described in corollary 3 2 a reduction functor h latt i spr preserving representation types is constructed it is shown in corollary 2 10 that for any poset i having exactly two maximal elements there exists a d order in our class an additive functor latt i spr preserving representation types and a poset isomorphism i i

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

scale invariant feature transform on the sphere theory and applications a sift algorithm in spherical coordinates for omnidirectional images is proposed this algorithm can generate two types of local descriptors local spherical descriptors and local planar descriptors with the first ones point matching between two omnidirectional images can be performed and with the second ones the same matching process can be done but between omnidirectional and planar images furthermore a planar to spherical mapping is introduced and an algorithm for its estimation is given this mapping allows to extract objects from an omnidirectional image given their sift descriptors in a planar image several experiments confirming the promising and accurate performance of the system are conducted

optimal estimation and detection in homogeneous spaces this paper presents estimation and detection techniques in homogeneous spaces that are optimal under the squared error loss function the data is collected on a manifold which forms a homogeneous space under the transitive action of a compact lie group signal estimation problems are addressed by formulating wiener hopf equations for homogeneous spaces the coefficient functions of these equations are the signal correlations which are assumed to be known the resulting coupled integral equations on the manifold are converted to wiener hopf convolutional integral equations on the group these are solved using the peter weyl theory of fourier transform on compact lie groups the computational complexity of this algorithm is reduced using the bi invariance of the correlations with respect to a stabilizer subgroup the theory of matched filtering for isotropic signal fields is developed for signal classification where given a set of template signals on the manifold and a noisy test signal the objective is to optimally detect the template buried in the test signal this is accomplished by designing a filter on the manifold that maximizes the signal to noise ratio snr of the filtered output an expression for the snr is obtained as a ratio of quadratic forms expressed as haar integrals over the transformation group these integrals are expressed in the fourier domain as infinite sums over the irreducible representations simplification of these sums is achieved by invariance properties of the signal function and the noise correlation function the wiener filter and matched filter are developed for an abstract homogeneous space and then specialized to the case of spherical signals under the action of the rotation group applications of these algorithms to denoising of 3d surface data visual navigation with omnidirectional camera and detection of compact embedded objects in the stochastic background are discussed with experimental results

local global compatibility and the action of monodromy on nearby cycles we strengthen the local global compatibility of langlands correspondences for gln in the case when n is even and l 6d p let l be a cm field and let be a cuspidal automorphic representation of gln al which is conjugate self dual assume that 1 is cohomological and not slightly regular as defined by shin in this case chenevier and harris constructed an l adic galois representationrl and proved the local global compatibility up to semisimplification at primes v not dividing l we extend this compatibility by showing that the frobenius semisimplification of the restriction of rl to the decomposition group at v corresponds to the image of v via the local langlands correspondence we follow the strategy of taylor and yoshida where it was assumed that is square integrable at a finite place to make the argument work we study the action of the monodromy operator n on the complex of nearby cycles on a scheme which is locally etale over a product of strictly semistable schemes and we derive a generalization of the weight spectral sequence in this case we also prove the ramanujan petersson conjecture for as above

a peak reduction functor for socle projective representations throughout this paper k is a fixed algebraically closed field given a finite poset i e partially ordered set j with the partial order u we denote by max j the set of all maximal elements of j with respect to the order u and we set jys j max j the poset j is said to be an r peak poset provided max j s r throughout this paper we suppose that j s 4 4 1 n p p and max j s p p without loss of generality 1 r 1 r we can assume that the partial order u in j is such that i u j implies 4 i f j in the natural order for all i j g 1 n w x we recall from 18 that the category j spr of peak j spaces or socle projective representations of j over the field k is defined as follows the objects of j spr are systems m s m of finite dimensional k vector j jg j spaces m such that j

a reduced tits quadratic form and tameness of three partite subamalgams of tiled orders let d be a complete discrete valuation domain with the unique maximal ideal p we suppose that d is an algebra over an algebraically closed field k and d p k subamalgam d suborders of a tiled d order are studied in the paper by means of the integral tits quadratic form q zn1 2n3 2 z a criterion for a subamalgam d order to be of tame lattice type is given in terms of the tits quadratic form q and a forbidden list 1 17 of minor d suborders of presented in the tables

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

geometric properties of central catadioptric line images and their application in calibration in central catadioptric systems lines in a scene are projected to conic curves in the image this work studies the geometry of the central catadioptric projection of lines and its use in calibration it is shown that the conic curves where the lines are mapped possess several projective invariant properties from these properties it follows that any central catadioptric system can be fully calibrated from an image of three or more lines the image of the absolute conic the relative pose between the camera and the mirror and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected this result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors moreover it is proven that systems with a hyperbolic elliptical mirror can be calibrated from the image of two lines if both the shape and the pose of the mirror are known then two line images are enough to determine the image of the absolute conic encoding the camera s intrinsic parameters the sensitivity to errors is evaluated and the approach is used to calibrate a real camera

automorphic lifts of prescribed types we prove a variety of results on the existence of automorphic galois representations lifting a residual automorphic galois representation we prove a result on the structure of deformation rings of local galois representations and deduce from this and the method of khare and wintenberger a result on the existence of modular lifts of specified type for galois representations corresponding to hilbert modular forms of parallel weight 2 we discuss some conjectures on the weights of n dimensional mod p galois representations finally we use recent work of taylor to prove level raising and lowering results for n dimensional automorphic galois representations

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

potentially semi stable deformation rings let k qp be a finite extension and gk gal k k the galois group of an alge braic closure k let f be a finite field of characteristic p and vf a finite dimensional f vector space equipped with a continuous action of gkthe study of the defor mation theory of galois representations was initiated by mazur ma who showed that if vf has no non trivial endomorphisms then it admits a universal deformation ring ryw after the work of wiles wi and the conjectures of fontaine mazur fm it became clear that for arithmetic applications it was important to understand cer tain quotients of ry corresponding to deformations satisfying certain conditions for example wiles uses deformations which arise from finite flat group schemes and the corresponding quotient of ryw was constructed by ramakrishna ra suppose that l k is a finite extension and let a b be integers it seems to be a kind of folklore conjecture that there should be a quotient of ry whose points in finite extensions of w f l p correspond to deformations of vf which become semi stable over l and have hodge tate weights in the interval a b this is closely related to the final conjecture of fo 3 special cases of this when vf is 2 dimensional are conjectured in the papers of fontaine mazur fm p 191 breuil conrad diamond taylor bcdt conj 1 1 1 and breuil m zard bm 2 2 2 4 the purpose of this paper is to prove such a result

variable structuring element based fuzzy morphological operations for single viewpoint omnidirectional images morphological tools can provide transformations suitable for real projective images but the camera and objects to be analyzed have to be positioned in such a manner that a regular mesh on the objects projects a regular mesh on the image a morphological modification of the image is thus the projection of an equivalent operation on the object otherwise due to perspective effects a morphological operation on the image is not the projection of an equivalent operation on the objects to be analyzed with catadioptric omnidirectional images it is almost impossible to place the sensor such that a regular mesh on the scene projects a regular mesh on the image nevertheless with proper calibration of a central catadioptric system the projection of a regular structuring element in a scene can be determined for each point on the image the aim of this paper is to present new morphological operators that use this projective property these operators make use of a structuring element of varying shape since this varying shape cannot be represented as a binary union of pixels we propose to use a fuzzy extension of the classical gray level morphology to account for this phenomenon this fuzzy extension is performed via fuzzy integrals

generalized camera calibration including fish eye lenses a method is described for accurately calibrating cameras including radial lens distortion by using known points such as those measured from a calibration fixture both the intrinsic and extrinsic parameters are calibrated in a single least squares adjustment but provision is made for including old values of the intrinsic parameters in the adjustment the distortion terms are relative to the optical axis which is included in the model so that it does not have to be orthogonal to the image sensor plane these distortion terms represent corrections to the basic lens model which is a generalization that includes the perspective projection and the ideal fish eye lens as special cases the position of the entrance pupil point as a function of off axis angle also is included in the model the complete camera model including all of these effects often is called cahvore a way of adding decentering distortion also is described a priori standard deviations can be used to apply weight to given initial approximations which can be zero for the distortion terms for the difference between the optical axis and the perpendicular to the sensor plane and for the terms representing movement of the entrance pupil so that the solution for these is well determined when there is insufficient information in the calibration data for the other parameters initial approximations needed for the nonlinear least squares adjustment are obtained in a simple manner from the calibration data and other known information weight can be given to these also if desired outliers among the calibration points that disagree excessively with the other data are removed by means of automatic editing based on analysis of the residuals the use of the camera model also is described including partial derivatives for propagating both from object space to image space and vice versa these methods were used to calibrate the cameras on the mars exploration rovers

catadioptric projective geometry catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera central catadioptric sensors are the class of these devices having a single effective viewpoint in this paper we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications we show that a central catadioptric projection is equivalent to a two step mapping via the sphere the second step is equivalent to a stereographic projection in the case of parabolic mirrors conventional lens based perspective cameras are also central catadioptric devices with a virtual planar mirror and are thus covered by the unifying model we prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images conics it turns out that planar and parabolic mirrors build a dual catadioptric projection pair as a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system

paracatadioptric camera calibration catadioptric sensors refer to the combination of lens based devices and reflective surfaces these systems are useful because they may have a field of view which is greater than hemispherical providing the ability to simultaneously view in any direction configurations which have a unique effective viewpoint are of primary interest among these is the case where the reflective surface is a parabolic mirror and the camera is such that it induces an orthographic projection and which we call paracatadioptric we present an algorithm for the calibration of such a device using only the images of lines in space in fact we show that we may obtain all of the intrinsic parameters from the images of only three lines and that this is possible without any metric information we propose a closed form solution for focal length image center and aspect ratio for skewless cameras and a polynomial root solution in the presence of skew we also give a method for determining the orientation of a plane containing two sets of parallel lines from one uncalibrated view such an orientation recovery enables a rectification which is impossible to achieve in the case of a single uncalibrated view taken by a conventional camera we study the performance of the algorithm in simulated setups and compare results on real images with an approach based on the image of the mirror s bounding circle

on the weights of mod p hilbert modular forms we prove many cases of a conjecture of buzzard diamond and jarvis on the possible weights of mod p hilbert modular forms by making use of modularity lifting theorems and computations in p adic hodge theory

geometry based distributed scene representation with omnidirectional vision sensors this paper addresses the problem of efficient representation of scenes captured by distributed omnidirectional vision sensors we propose a novel geometric model to describe the correlation between different views of a 3 d scene we first approximate the camera images by sparse expansions over a dictionary of geometric atoms since the most important visual features are likely to be equivalently dominant in images from multiple cameras we model the correlation between corresponding features in different views by local geometric transforms for the particular case of omnidirectional images we define the multiview transforms between corresponding features based on shape and epipolar geometry constraints we apply this geometric framework in the design of a distributed coding scheme with side information which builds an efficient representation of the scene without communication between cameras the wyner ziv encoder partitions the dictionary into cosets of dissimilar atoms with respect to shape and position in the image the joint decoder then determines pairwise correspondences between atoms in the reference image and atoms in the cosets of the wyner ziv image in order to identify the most likely atoms to decode under epipolar geometry constraints experiments demonstrate that the proposed method leads to reliable estimation of the geometric transforms between views in particular the distributed coding scheme offers similar rate distortion performance as joint encoding at low bit rate and outperforms methods based on independent decoding of the different images

identical projective geometric properties of central catadioptric line images and sphere images with applications to calibration central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint lines and spheres in space are all projected into conics in the central catadioptric image planes and such conics are called line images and sphere images respectively we discovered that there exists an imaginary conic in the central catadioptric image planes defined as the modified image of the absolute conic miac and by utilizing the miac the novel identical projective geometric properties of line images and sphere images may be exploited each line image or each sphere image is double contact with the miac which is an analogy of the discovery in pinhole camera that the image of the absolute conic iac is double contact with sphere images note that the iac also exists in the central catadioptric image plane but it does not have the double contact properties with line images or sphere images this is the main reason to propose the miac from these geometric properties with the miac two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework note that there are many linear approaches to central catadioptric camera calibration using line images it seems that to use the properties that line images are tangent to the miac only leads to an alternative geometric construction for calibration however for sphere images there are only some nonlinear calibration methods in literature therefore to propose linear methods for sphere images may be the main contribution of this paper our new algorithms have been tested in extensive experiments with respect to noise sensitivity

automorphy of some residually s_5 galois representations let f be a totally real field and p an odd prime we prove an automorphy lifting theorem for geometric representations rho g f rightarrow mathrm gl 2 overline mathbb q p which lift irreducible residual representations overline rho that arise from hilbert modular forms the new result is that we allow the case p 5 overline rho has projective image s 5 cong mathrm pgl 2 mathbb f 5 and the fixed field of the kernel of the projective representation contains zeta 5 the usual taylor wiles method does not work in this case as there are elements of dual selmer that cannot be killed by allowing ramification at taylor wiles primes these elements arise from our hypothesis and the non vanishing of h 1 mathrm pgl 2 mathbb f 5 mathrm ad 1 where mathrm ad 1 is the adjoint of the natural representation of mathrm gl 2 mathbb f 5 twisted by the quadratic character of mathrm pgl 2 mathbb f 5

lattices in the cohomology of shimura curves we prove the main conjectures of breuil j reine angew math 2012 including a generalisation from the principal series to the cuspidal case and dembele j reine angew math 2012 subject to a mild global hypothesis that we make in order to apply certain r mathbb t theorems more precisely we prove a multiplicity one result for the mod p cohomology of a shimura curve at iwahori level and we show that certain apparently globally defined lattices in the cohomology of shimura curves are determined by the corresponding local p adic galois representations we also indicate a new proof of the buzzard diamond jarvis conjecture in generic cases our main tools are the geometric breuil mezard philosophy developed in emerton and gee j inst math jussieu 2012 and a new and more functorial perspective on the taylor wiles kisin patching method along the way we determine the tamely potentially barsotti tate deformation rings of generic two dimensional mod p representations generalising a result of breuil and mezard bull soc math de france 2012 in the principal series case

on weakly non negative unit forms and tame algebras in this paper we consider integral quadratic forms q ip z of the form q x 2i x i jqijx xj and call them unit forms such a unit form q is said to be weakly non negative if q x q whenever jt2 0 that is whenever x o for i 1 n our main purpose is to formulate a criterion for weak non negativity of unit forms this question arises in various areas of representation theory in connection with the characterization of tame representation type in the representation theory of quivers 17 6 partially ordered sets 18 19 certain classes of bimodules 8 23 1 3 and certain classes of algebras 20 14 24 16 for each of these structures q there is a unit form qn naturally attached to q such that the weak non negativity of qn is an equivalent or at least a necessary condition for q to be of tame representation type a class of algebras for which tame representation type is equivalent to the weak non negativity of the associated unit form is described in the last section of this paper a general criterion for weak non negativity using determinants was given by zeldich 28 see also 21 another criterion was obtained by de la pena 21 our approach is similar to that in 11 where we gave a characterization of weakly positive unit forms based on the classification of the critical forms let us recall some notions given a unit form q ip tl and a non empty subset ix im of 1 n we denote by qt the quadratic form qd where d z it maps the cth natural basis vector ek onto eik such a unit form q is called the restriction of q to we call a unit form q on ip a hypercritical form if q is weakly non negative for every proper subset 1 n though q itself is not in these terms a unit form q is weakly non negative if and only if q admits no hypercritical restriction so we have to classify the hypercritical forms in 1 we show that they can be obtained by certain elementary transformations from the unit forms naturally attached to the hyperbolic graphs of fig 1 on p 50 in particular there are only finitely many hypercritical forms however their number is large by a simple process we reduce the problem to the classification of the stretched hypercritical forms in 2 we show that except for a few of them these are of the shape q x q x xn xn ixn where q q n d is critical in a similar way the unit forms attached to the hyperbolic graphs am dm em correspond to those

structure from motion with wide circular field of view cameras this paper presents a method for fully automatic and robust estimation of two view geometry autocalibration and 3d metric reconstruction from point correspondences in images taken by cameras with wide circular field of view we focus on cameras which have more than 180deg field of view and for which the standard perspective camera model is not sufficient e g the cameras equipped with circular fish eye lenses nikon fc e8 183deg sigma 8 mm f4 ex 180deg or with curved conical mirrors we assume a circular field of view and axially symmetric image projection to autocalibrate the cameras many wide field of view cameras can still be modeled by the central projection followed by a nonlinear image mapping examples are the above mentioned fish eye lenses and properly assembled catadioptric cameras with conical mirrors we show that epipolar geometry of these cameras can be estimated from a small number of correspondences by solving a polynomial eigenvalue problem this allows the use of efficient ransac robust estimation to find the image projection model the epipolar geometry and the selection of true point correspondences from tentative correspondences contaminated by mismatches real catadioptric cameras are often slightly noncentral we show that the proposed autocalibration with approximate central models is usually good enough to get correct point correspondences which can be used with accurate noncentral models in a bundle adjustment to obtain accurate 3d scene reconstruction noncentral camera models are dealt with and results are shown for catadioptric cameras with parabolic and spherical mirrors

tame prinjective type and tits form of two peak posets ii throughout this paper we use the terminology and notation introduced w x in 5 7 11 13 in particular k is an algebraically closed field and we denote by i u a finite poset i e partially ordered set with respect to the partial order u we shall write i j if i u j and i j for the sake of simplicity we write i instead of i u we denote by max i the set of all maximal elements of i and i will be called an n peak poset if max i s n let ki be the incidence k algebra of the poset i that is ki is the k subalgebra of the full i i matrix algebra m k consisting of all i w x matrices l in m k such that l s 0 if i uu j in i u we recall from i j i i j w x 13 that the socle soc ki of the right ki module ki is projective and the global dimension of the algebra ki is finite we denote by mod ki the category of finitely generated right ki mod ules and by prin ki the full subcategory of mod ki consisting of all prinjective modules that is modules x in mod ki having a projective resolution of the form

weight elimination in serre type conjectures we prove the weight elimination direction of the serre weight conjectures as formulated by herzig for forms of u n which are compact at infinity and split at places dividing p in generic situations that is we show that all modular weights for a mod p galois representation are contained in the set predicted by herzig under some additional hypotheses we also show modularity of all the obvious weights

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

joint registration and super resolution with omnidirectional images this paper addresses the reconstruction of high resolution omnidirectional images from multiple low resolution images with inexact registration when omnidirectional images from low resolution vision sensors can be uniquely mapped on the 2 sphere such a reconstruction can be described as a transform domain super resolution problem in a spherical imaging framework we describe how several spherical images with arbitrary rotations in the so 3 rotation group contribute to the reconstruction of a high resolution image with help of the spherical fourier transform sft as low resolution images might not be perfectly registered in practice the impact of inaccurate alignment on the transform coefficients is analyzed we then cast the joint registration and super resolution problem as a total least squares norm minimization problem in the sft domain a l1 regularized total least squares problem is considered and solved efficiently by interior point methods experiments with synthetic and natural images show that the proposed methods lead to effective reconstruction of high resolution images even when large registration errors exist in the low resolution images the quality of the reconstructed images also increases rapidly with the number of low resolution images which demonstrates the benefits of the proposed solution in super resolution schemes finally we highlight the benefit of the additional regularization constraint that clearly leads to reduced noise and improved reconstruction quality

automatic line extraction in uncalibrated omnidirectional cameras with revolution symmetry revolution symmetry is a realistic assumption for modelling the majority of catadioptric and dioptric cameras in central systems it can be described by a projection model based on radially symmetric distortion in these systems straight lines are projected on curves called line images these curves have in general more than two degrees of freedom and their shape strongly depends on the particular camera configuration therefore the existing line extraction methods for this kind of omnidirectional cameras require the camera calibration by contrast with the perspective case where the calibration is not involved in the shape of the projected line image however this drawback can be considered as an advantage because the shape of the line images can be used for self calibration in this paper we present a novel method to extract line images in uncalibrated omnidirectional images which is valid for radially symmetric central systems in this method we propose using the plumb line constraint to find closed form solutions for different types of camera systems dioptric or catadioptric the inputs of the proposed method are points belonging to the line images and their intensity gradient the gradient information allows to reduce the number of points needed in the minimal solution improving the result and the robustness of the estimation the scheme is used in a line image extraction algorithm to obtain lines from uncalibrated omnidirectional images without any assumption about the scene the algorithm is evaluated with synthetic and real images showing good performance the results of this work have been implemented in an open source matlab toolbox for evaluation and research purposes

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

scale space analysis and active contours for omnidirectional images a new generation of optical devices that generate images covering a larger part of the field of view than conventional cameras namely catadioptric cameras is slowly emerging these omnidirectional images will most probably deeply impact computer vision in the forthcoming years provided that the necessary algorithmic background stands strong in this paper we propose a general framework that helps define various computer vision primitives we show that geometry which plays a central role in the formation of omnidirectional images must be carefully taken into account while performing such simple tasks as smoothing or edge detection partial differential equations pdes offer a very versatile tool that is well suited to cope with geometrical constraints we derive new energy functionals and pdes for segmenting images obtained from catadioptric cameras and show that they can be implemented robustly using classical finite difference schemes various experimental results illustrate the potential of these new methods on both synthetic and natural images

potentially crystalline deformation rings and serre weight conjectures shapes and shadows we prove the weight part of serre s conjecture in generic situations for forms of u 3 which are compact at infinity and split at places dividing p as conjectured by herzig duke math j 149 1 37 116 2009 we also prove automorphy lifting theorems in dimension three the key input is an explicit description of tamely potentially crystalline deformation rings with hodge tate weights 2 1 0 for k mathbb q p unramified combined with patching techniques our results show that the geometric breuil mezard conjectures hold for these deformation rings

potential automorphy and change of weight we prove an automorphy lifting theorem for l adic representations where we impose a new condition at l which we call potentential diagonalizability this result allows for change of weight and seems to be substantially more exible than previous theorems along the same lines we derive several applications for instance we show that any irreducible totally odd essentially self dual regular weakly compatible system of l adic representations of the absolute galois group of a totally real eld is potentially automorphic and hence is pure and its l function has meromorphic continuation to the whole complex plane and satises the expected functional equation

structure from motion with line segments under relaxed endpoint constraints we present a novel structure from motion pipeline which estimates motion and wiry 3d structure from imaged line segments across multiple views although the position and orientation of line segments can be determined more accurately than point features the instability of their endpoints and the fact that lines are not constrained by epipolar geometry diverted most research focus away to point based methods in our approach we tackle the problem of instable endpoints by utilizing relaxed constraints on their positions both during matching and as well in the following bundle adjustment stage furthermore we gain efficiency in estimating trifocal image relations by decoupling rotation and translation to this end a novel linear solver for relative translation estimation given rotations from five line correspondences in three views is introduced extensive experiments on long image sequences show that our line based structure from motion pipeline advantageously complements point based methods giving more meaningful 3d representation for indoor scenarios

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

visual attention on the sphere human visual system makes an extensive use of visual attention in order to select the most relevant information and speed up the vision process inspired by visual attention several computer models have been developed and many computer vision applications rely today on such models however the actual algorithms are not suitable to omnidirectional images which contain a significant amount of geometrical distorsion in this paper we present a novel computational approach that performs in spherical geometry and thus is suitable for omnidirectional images following one of the actual models of visual attention the spherical saliency map is obtained by fusing together intensity chromatic and orientation spherical cue conspicuity maps that are themselves obtained through multiscale analysis on the sphere finally the consecutive maxima in the spherical saliency map represent the spots of attention on the sphere in the experimental part the proposed method is then compared to the standard one using a synthetic image also we provide examples of spots detection in real omnidirectional scenes which show its advantages finally an experiment illustrates the homogeneity of the detected visual attention in omnidirectional images

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

on the universal mod p supersingular quotients for gl2 f over f p for a general f qp abstract let f q p be a finite extension we explore the universal supersingular mod p representations of gl 2 f by computing a basis for their spaces of invariants under the pro p iwahori subgroup this generalizes works of breuil and schein from q p and the totally ramified cases to an arbitrary extension f q p using these results we then construct for an unramified f q p quotients of the universal supersingular modules which have as quotients all the supersingular representations of gl 2 f with a gl 2 o f socle that is expected to appear in the mod p local langlands correspondence a construction in the case of an extension of q p with inertia degree 2 and suitable ramification index is also presented