quasifinite highest weight modules over the super w 1 algebra we study quasifinite highest weight modules over the supersymmetric extension of thew1 algebra on the basis of the analysis by kac and radul we find that the quasifiniteness of the modules is again characterized by polynomials and obtain the differential equations for highest weights the spectral flow free field realization over the b c system and the embedding into widehat gl are also presented

on the cuspidal cohomology of arithmetic groups it is the main objective of this paper to show a vanishing result for cuspidal cohomology of arithmetic groups in classical groups g defined over some number field k our approach relies on the fact that cuspidal automorphic forms are nonsingular in the sense of howe this result puts a strong constraint on the archimedean components of irreducible cuspidal automorphic representations of g that can possibly contribute to the cuspidal cohomology combining this with the classification of vogan zuckerman of unitary representations with nonzero cohomology provides a constant r 0 g k only depending on g k below which the cuspidal cohomology vanishes we will give a formula for this constant for each classical group of type i in the classification scheme due to weil we conclude with making this result explicit for some split classical groups over a totally real algebraic number field

quantum reduction for affine superalgebras we extend the homological method of quantization of generalized drinfeld sokolov reductions to affine superalgebras this leads in particular to a unified representation theory of superconformal algebras

a tower of coverings of quasi projective varieties abstract the main goal of this article is to relate asymptotic geometric properties on a tower of coverings of a non compact kahler manifold of finite volume with reasonable geometric assumptions to its universal covering examples to which our findings are applicable include moduli spaces of hyperbolic punctured riemann surfaces and hermitian locally symmetric spaces of finite volume

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

poincare series for non riemannian locally symmetric spaces abstract we initiate the spectral analysis of pseudo riemannian locally symmetric spaces g h beyond the classical cases where h is compact automorphic forms or is trivial analysis on symmetric spaces for any non riemannian reductive symmetric space x g h on which the discrete spectrum of the laplacian is nonempty and for any discrete group of isometries whose action on x is sufficiently proper we construct l 2 eigenfunctions of the laplacian on x x for an infinite set of eigenvalues these eigenfunctions are obtained as generalized poincare series i e as projections to x of sums over the orbits of eigenfunctions of the laplacian on x we prove that the poincare series we construct still converge and define nonzero l 2 functions after any small deformation of inside g for a large class of groups thus the infinite set of eigenvalues we construct is stable under small deformations this contrasts with the classical setting where the nonzero discrete spectrum varies on the teichmuller space of a compact riemann surface we actually construct joint l 2 eigenfunctions for the whole commutative algebra of invariant differential operators on x

algebra algebra and friedan martinec shenker bosonization we show that the vertex algebra with central charge 1 is isomorphic to a tensor product of the simple algebra with central charge 2 and a heisenberg vertex algebra generated by a free bosonic field we construct a family of irreducible modules of the algebra with central charge 2 in terms of free fields and calculate the full character formulas of these modules with respect to the full cartan subalgebra of the algebra

s duality for the large n 4 superconformal algebra we prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric langlands program in particular we present the conjectural kernel vertex algebra for the s t 2 s duality transformation in su 2 gauge theory we find a surprising coincidence which gives a powerful hint about the nature of the corresponding duality wall concretely we determine the branching rules for the small n 4 superconformal algebra at central charge 9 as well as for the generic large n 4 superconformal algebra at central charge 6 moreover we obtain the affine vertex superalgebra of mathfrak osp 1 2 and the n 1 superconformal algebra times a free fermion as quantum hamiltonian reductions of the large n 4 superconformal algebras at c 6

wireframe projections physical realisability of curved objects and unambiguous reconstruction of simple polyhedra the reconstruction of an object from a single 2d projection of a 3d wireframe model is a vision problem with applications in cad cam and computer graphics we propose an algorithm for the interpretation of wireframe projections based on assigning semantic and numerical depth labels to lines this method allows us to state necessary and sufficient conditions for the physical realisability of a wireframe projection of a curved object the presence of linear features provides further constraints on the positions of object vertices for example each straight line gives rise to a coplanarity constraint between a set of object vertices we show that extra information such as vanishing points parallel lines or user entered depth parity information is sufficient to uniquely determine the face circuits in wireframe projections of polyhedra with simple trihedral vertices in fact a polyhedron with simple trihedral vertices can be unambiguously reconstructed from its 3d wireframe model

on existence of generic cusp forms on semisimple algebraic groups in this paper we discuss the existence of certain classes of cuspidal automorphic representations having non zero fourier coefficients for a general semisimple algebraic group g defined over a number field k such that its archimedean group g infty is not compact when g is quasi split over k we obtain a result on existence of generic cuspidal automorphic representations which generalize results of vigneras henniart and shahidi we also discuss i the existence of cuspidal automorphic forms with non zero fourier coefficients for congruence of subgroups of g infty and ii applications related to the work of bushnell and henniart on generalized whittaker models

on a construction of certain classes of cuspidal automorphic forms via poincare series in this paper we give a construction and study non vanishing of a class of cusp forms using poincare series for a semisimple algebraic group over a number field

with central charge n we study representations of the central extension of the lie algebra of differential operators on the circle the algebra we obtain complete and specialized character formulas for a large class of representations which we call primitive these include all quasi finite irreducible unitary representations we show that any primitive representation with central chargen has a canonical structure of an irreducible representation of the with the same central charge and that all irreducible representations of with central chargen arise in this way we also establish a duality between integral modules of and finite dimensional irreducible modules ofgl n and conjecture their fusion rules

overcoming superstrictness in line drawing interpretation presents an algorithm for correcting incorrect line drawings incorrect projections of a polyhedral scene such incorrect drawings arise e g when an image of a polyhedral world is taken the edges and vertices are extracted and a drawing is synthesized along the way the true positions of the vertices in the 2d projection are perturbed due to digitization errors and the preprocessing as most available algorithms for interpreting line drawings are superstrict they judge these noisy inputs as incorrect and fail to reconstruct a three dimensional scene from them the presented method overcomes this problem by moving the positions of all vertices until a very close correct drawing is found the closeness criterion is to minimize the sum of squared distances from each vertex in the input drawing to its corrected position with this tool any superstrict method for line drawing interpretation is now practical as it can be applied to the corrected version of the input drawing

limit formulas of period integrals for a certain symmetric pair abstract let g be the unitary group of a non degenerate hermitian space and h the stabilizer of a one dimensional positive definite subspace of the hermitian space for a uniform lattice in g such that h is a uniform lattice of h we introduce the averaged h period integrals of automorphic forms on g we study their behavior as shrinks to the identity along a tower of lattices in g and prove a limit formula of the h period integrals

vertex algebras for s duality we define new deformable families of vertex operator algebras mathfrak a mathfrak g psi sigma associated to a large set of s duality operations in four dimensional supersymmetric gauge theory they are defined as algebras of protected operators for two dimensional supersymmetric junctions which interpolate between a dirichlet boundary condition and its s duality image the mathfrak a mathfrak g psi sigma vertex operator algebras are equipped with two mathfrak g affine vertex subalgebras whose levels are related by the s duality operation they compose accordingly under a natural convolution operation and can be used to define an action of the s duality operations on a certain space of vertex operator algebras equipped with a mathfrak g affine vertex subalgebra we give a self contained definition of the s duality action on that space of vertex operator algebras the space of conformal blocks in the derived sense i e chiral homology for mathfrak a mathfrak g psi sigma is expected to play an important role in a broad generalization of the quantum geometric langlands program namely we expect the s duality action on vertex operator algebras to extend to an action on the corresponding spaces of conformal blocks this action should coincide with and generalize the usual quantum geometric langlands correspondence the strategy we use to define the mathfrak a mathfrak g psi sigma vertex operator algebras is of broader applicability and leads to many new results and conjectures about deformable families of vertex operator algebras

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

universal two parameter even spin w algebra abstract we construct the unique two parameter vertex algebra which is freely generated of type w 2 4 6 and generated by the weights 2 and 4 fields subject to some mild constraints all vertex algebras of type w 2 4 2 n for some n can be obtained as quotients of this universal algebra this includes the b and c type principal w algebras the z 2 orbifolds of the d type principal w algebras and many others which arise as cosets of affine vertex algebras inside larger structures as an application we classify all coincidences among the simple quotients of the b and c type principal w algebras as well as the z 2 orbifolds of the d type principal w algebras finally we use our classification to give new examples of principal w algebras of b c and d types which are lisse and rational

the dimensions of spaces of siegel cusp forms of general degree abstract in this paper we give a dimension formula for spaces of siegel cusp forms of general degree with respect to neat arithmetic subgroups the formula was conjectured before by several researchers cf 40 43 45 75 the dimensions are expressed by special values of shintani zeta functions for spaces of symmetric matrices at non positive integers this formula was given by shintani for only a small part of the geometric side of the trace formula see 64 to be precise it is the contribution of unipotent elements corresponding to the partitions 2 j 1 2 n 2 j where n denotes the degree and 0 j n hence our work is to show that all the other contributions vanish therefore one finds that shintani s formula means the dimension itself combining our formula and an explicit formula of the shintani zeta functions which was discovered by ibukiyama and saito cf 44 42 61 we can derive an explicit dimension formula for the principal congruence subgroups of level greater than two cf 43 45 in this explicit dimension formula the dimensions are described by degree n weight k level n and the bernoulli numbers b m

asymptotique des nombres de betti des varietes arithmetiques we study the question of the growth of betti numbers of certain arithmetic varieties in tower of congruence coverings in fact our results are about siegel varieties and varieties associated to orthogonal groups we explain how a theorem of waldspurger can be used to obtain lower and upper bound our results are in the direction of conjectures made by sarnak and xue

the basic stratum of some simple shimura varieties under simplifying hypotheses we prove a relation between the ell adic cohomology of the basic stratum of a shimura variety of pel type modulo a prime of good reduction of the reflex field and the cohomology of the complex shimura variety in particular we obtain explicit formulas for the number of points in the basic stratum over finite fields we obtain our results using the trace formula and truncation of the formula of kottwitz for the number of points on a shimura variety over a finite fields

plane based optimization for 3d object reconstruction from single line drawings in previous optimization based methods of 3d planar faced object reconstruction from single 2d line drawings the missing depths of the vertices of a line drawing and other parameters in some methods are used as the variables of the objective functions a 3d object with planar faces is derived by finding values for these variables that minimize the objective functions these methods work well for simple objects with a small number tv of variables as n grows however it is very difficult for them to find the expected objects this is because with the nonlinear objective functions in a space of large dimension the search for optimal solutions can easily get trapped into local minima in this paper we use the parameters of the planes that pass through the planar faces of an object as the variables of the objective function this leads to a set of linear constraints on the planes of the object resulting in a much lower dimensional null space where optimization is easier to achieve we prove that the dimension of this null space is exactly equal to the minimum number of vertex depths that define the 3d object since a practical line drawing is usually not an exact projection of a 3d object we expand the null space to a larger space based on the singular value decomposition of the projection matrix of the line drawing in this space robust 3d reconstruction can be achieved compared with the two most related methods our method not only can reconstruct more complex 3d objects from 2d line drawings but also is computationally more efficient

fourier coefficients of automorphic forms and integrable discrete series abstract let g be the group of r points of a semisimple algebraic group g defined over q assume that g is connected and noncompact we study fourier coefficients of poincare series attached to matrix coefficients of integrable discrete series we use these results to construct explicit automorphic cuspidal realizations which have appropriate fourier coefficients 0 of integrable discrete series in families of congruence subgroups in the case of g sp 2 n r we relate our work to that of li 14 for g quasi split over q we relate our work to the result about poincare series due to khare larsen and savin 12

l2 index and the selberg trace formula abstract a method is developed for computing the l 2 index of a locally symmetric elliptic differential operator d acting on a locally symmetric manifold m g k with g semisimple of real rank one and of finite co volume based on applying the selberg trace formula to the difference of the two heat kernels associated to d the applications include an extension of the osborne warner multiplicity formula to certain non integrable discrete series derived from the l 2 spinor formula and showing the existence in some cases of non invariant l 2 cohomology classes in the middle dimension via the l 2 signature formula

on a theorem of osborne and warner multiplicities in the cuspidal spectrum osborne and warner have given a formula for the multiplicity of an integrable discrete series representation in l2 g when g is real rank one semi simple lie group and is a discrete subgroup of co finite volume we simplify and evaluate this formula to show that for most g as above the multiplicity is the formal degree of the representation times the volume of g when it is not we give a simple interpretation of the difference

level raising and symmetric power functoriality iii we apply automorphy lifting techniques to establish new cases of symmetric power functoriality for hilbert modular forms of regular algebraic weight the proof is based on a novel application of an automorphy lifting theorem for residually reducible galois representations

a proof of the breuil schneider conjecture in the indecomposable case this paper contains a proof of a conjecture of breuil and schneider on the existence of an invariant norm on any locally algebraic representation of gl n with integral central character whose smooth part is given by a generalized steinberg representation in fact we prove the analogue for any connected reductive group g this is done by passing to a global setting using the trace formula for an r anisotropic model of g the ultimate norm comes from classical p adic modular forms

strong limit multiplicity for arithmetic hyperbolic surfaces and 3 manifolds we show that every sequence of torsion free arithmetic congruence lattices in mathrm pgl 2 mathbb r or mathrm pgl 2 mathbb c satisfies a strong quantitative version of the limit multiplicity property we deduce that for r 0 in certain range growing linearly in the degree of the invariant trace field the volume of the r thin part of any congruence arithmetic hyperbolic surface or congruence arithmetic hyperbolic 3 manifold m is of order at most mathrm vol m 11 12 as an application we prove gelander s conjecture on homotopy type of arithmetic hyperbolic 3 manifolds we show that there are constants a b such that every such manifold m is homotopy equivalent to a simplicial complex with at most a mathrm vol m vertices all of degrees bounded by b

characters l 2 betti numbers and an equivariant approximation theorem let g be a group with a finite subgroup h we define the l 2 multiplicity of an irreducible representation of h in the l 2 homology of a proper g cw complex these invariants generalize the l 2 betti numbers our main results are approximation theorems for l 2 multiplicities which extend the approximation theorems for l 2 betti numbers of luck farber and elek szabo respectively the main ingredient is the theory of characters of infinite groups and a method to induce characters from finite subgroups we discuss applications to the cohomology of arithmetic groups

smooth cuspidal automorphic forms and integrable discrete series in this paper we construct smooth cuspidal automorphic forms related to integrable discrete series of a connected semisimple lie group with finite center for classical and adelic situation as an application of the theory of schwartz spaces for automorphic forms developed by casselman in the classical situation smooth cuspidal automorphic forms are constructed via an explicit continuous map from the frechet space of smooth vectors of a banach realization inside l 1 g of an integrable discrete series into the space of smooth vectors of a strong topological dual of an appropriate schwartz space

on limit multiplicites of discrete series representations in spaces of automorphic forms of course the groups f are then arithmetic subgroups of g in this situation it seems natural to assume that as n the spectral decomposition of l2 f g will approximate that of g in particular let 3 be a discrete series representation of g if f is a subgroup of g let re f 6 be the multiplicity of 3 in the representation of g by right translations on l2 f g choose a haar measure dg on g if f is arithmetic let v f g be the finite volume of f g for the measure induced by dg let d 3 be the formal degree of 3 for the measure dg

sato tate theorem for families and low lying zeros of automorphic l functions we consider certain families of automorphic representations over number fields arising from the principle of functoriality of langlands let g be a reductive group over a number field f which admits discrete series representations at infinity let l g widehat g rtimes mathrm gal bar f f be the associated l group and r l g rightarrow mathrm gl d mathbb c a continuous homomorphism which is irreducible and does not factor through mathrm gal bar f f the families under consideration consist of discrete automorphic representations of g mathbb a f of given weight and level and we let either the weight or the level grow to infinity we establish a quantitative plancherel and a quantitative sato tate equidistribution theorem for the satake parameters of these families this generalizes earlier results in the subject notably of sarnak prog math 70 321 331 1987 and serre j am math soc 10 1 75 102 1997 as an application we study the distribution of the low lying zeros of the associated family of l functions l s pi r assuming from the principle of functoriality that these l functions are automorphic we find that the distribution of the 1 level densities coincides with the distribution of the 1 level densities of eigenvalues of one of the unitary symplectic and orthogonal ensembles in accordance with the katz sarnak heuristics we provide a criterion based on the frobenius schur indicator to determine this symmetry type if r is not isomorphic to its dual r vee then the symmetry type is unitary otherwise there is a bilinear form on mathbb c d which realizes the isomorphism between r and r vee if the bilinear form is symmetric resp alternating then r is real resp quaternionic and the symmetry type is symplectic resp orthogonal

a shape from shading method of polyhedral objects using prior information we propose a new method for recovering the 3d shape of a polyhedral object from its single 2d image using the shading information contained in the image and the prior information on the object in a strict sense we cannot recover the shape of a polyhedron from an incorrect line drawing even if it is practically almost correct in order to overcome this problem we propose a flexible face positioning method that can permit inconsistencies in the recovered shape that arise from vertex position errors contained in incorrect line drawings also we propose to use prior information about the horizontality and verticality of special faces and the convex and concave properties of the edges in order to attain good solutions and present a method of formulating such prior information as physical constraints the shape from shading method is formulated as a minimization problem of a nonlinear cost function with the nonlinear constraints and its solution is searched by a global optimization algorithm in the experiments with a synthetic image and three kinds of real images shapes that are similar to those of the actual objects were recovered in all cases as a result the proposed method has proven to be effective in the shape recovery of simple shape polyhedral objects

asymptotic behavior of supercuspidal representations and sato tate equidistribution for families abstract we establish properties of families of automorphic representations as we vary prescribed supercuspidal representations at a given finite set of primes for the tame supercuspidals constructed by j k yu we prove the limit multiplicity property with error terms thereby we obtain a sato tate equidistribution for the hecke eigenvalues of these families the main new ingredient is to show that the orbital integrals of matrix coefficients of tame supercuspidal representations with increasing formal degree on a connected reductive p adic group tend to zero uniformly for every noncentral semisimple element

evolutionary search for faces from line drawings single 2d line drawing is a straightforward method to illustrate 3d objects the faces of an object depicted by a line drawing give very useful information for the reconstruction of its 3d geometry two recently proposed methods for face identification from line drawings are based on two steps finding a set of circuits that may be faces and searching for real faces from the set according to some criteria the two steps however involve two combinatorial problems the number of the circuits generated in the first step grows exponentially with the number of edges of a line drawing these circuits are then used as the input to the second combinatorial search step when dealing with objects having more faces the combinatorial explosion prevents these methods from finding solutions within feasible time this paper proposes a new method to tackle the face identification problem by a variable length genetic algorithm with a novel heuristic and geometric constraints incorporated for local search the hybrid ga solves the two combinatorial problems simultaneously experimental results show that our algorithm can find the faces of a line drawing having more than 30 faces much more efficiently in addition simulated annealing for solving the face identification problem is also implemented for comparison

the interpretation of line drawings with contrast failure and shadows in line drawings derived from real images lines may be missing due to contrast failure and objects with curved surfaces may cast shadows from multiple light sources this paper shows that it is the presence of shadows rather than contrast failure that renders the line drawing labelling problem np complete however shadows are a valuable visual cue since their presence is formally shown to reduce the average ambiguity of drawings this is especially true when constraints concerning shadow formation are employed to differentiate shadow and non shadow lines the extended junction constraint concerning straight lines colinear with junctions compensates the loss of information caused by contrast failure in fact we observe the contrast failure paradox a drawing is sometimes less ambiguous when lines are partly missing due to contrast failure it is known that the coplanarity of sets of object vertices can be deduced from the presence of straight lines in the drawing this paper shows that these coplanarity constraints are robust to the presence of contrast failure

weyl s law for the cuspidal spectrum of sln let r be a principal congruence subgroup of sl n z and let be an irreducible unitary representation of so n let n cus be the counting function of the eigenvalues of the casimir operator acting in the space of cusp forms for which transform under so n according to a in this paper we prove that the counting function n cus satisfies weyl s law especially this implies that there exist infinitely many cusp forms for the full modular group sl n z

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

self dual representations of division algebras and weil groups a contrast irreducible selfdual representations of any group fall into two classes those which carry a symmetric bilinear form and the others which carry an alternating bilinear form the langlands correspondence which matches the irreducible representations of the weil group of a local field k of dimension n with the irreducible representations of the invertible elements of a division algebra d over k of index n takes selfdual representations to selfdual representations in this paper we use global methods to study how the langlands correspondence behaves relative to this distinction among selfdual representations we prove in particular that for n even is symplectic if and only if is orthogonal more generally we treat the case of gl m b for b a division algebra over k of index r and n mr

on the growth of l 2 invariants for sequences of lattices in lie groups we study the asymptotic behaviour of betti numbers twisted torsion and other spectral invariants of sequences of locally symmetric spaces our main results are uniform versions of the degeorge wallach theorem of a theorem of delorme and various other limit multiplicity theorems a basic idea is to adapt the notion of benjamini schramm convergence bs convergence originally introduced for sequences of finite graphs of bounded degree to sequences of riemannian manifolds and analyze the possible limits we show that bs convergence of locally symmetric spaces g k implies convergence in an appropriate sense of the normalized relative plancherel measures associated to l2 g this then yields convergence of normalized multiplicities of unitary representations betti numbers and other spectral invariants on the other hand when the corresponding lie group g is simple and of real rank at least two we prove that there is only one possible bs limit i e when the volume tends to infinity locally symmetric spaces always bs converge to their universal cover g k this leads to various general uniform results when restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of bs convergence which in turn implies upper estimates on the rate of convergence of normalized betti numbers in the spirit of sarnak xue an important role in our approach is played by the notion of invariant random subgroups for higher rank simple lie groups g we exploit rigidity theory and in particular the nevo stuck zimmer theorem and kazhdan s property t to obtain a complete understanding of the space of irs s of g 2017 department of mathematics princeton university

on simplicity of vacuum modules we find necessary and sufficient conditions of irreducibility of vacuum modules over affine lie algebras and superalgebras from this we derive conditions of simplicity of minimal w algebras moreover in the case of the virasoro and neveu schwarz algebras we obtain explicit formulas for the vacuum determinants

bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms let goo be a semisimple real lie group with unitary dual goo we produce new upper bounds for the multiplicities with which representations e of cohomological type appear in certain spaces of cusp forms on goo the main new idea is to apply noncommutative iwasawa theory to certain p adic completions of the cohomology of locally symmetric spaces

identifying faces in a 2d line drawing representing a manifold object a straightforward way to illustrate a 3d model is to use a line drawing faces in a 2d line drawing provide important information for reconstructing its 3d geometry manifold objects belong to a class of common solids and most solid systems are based on manifold geometry in this paper a new method is proposed for finding faces from single 2d line drawings representing manifolds the face identification is formulated based on a property of manifolds each edge of a manifold is shared exactly by two faces the two main steps in our method are 1 searching for cycles from a line drawing and 2 searching for faces from the cycles in order to speed up the face identification procedure a number of properties most of which relate to planar manifold geometry in line drawings are presented to identify most of the cycles that are or are not real faces in a drawing thus reducing the number of unknown cycles in the second searching schemes to deal with manifolds with curved faces and manifolds each represented by two or more disjoint graphs are also proposed the experimental results show that our method can handle manifolds previous methods can handle as well as those they cannot

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner