a continuous interior penalty method for viscoelastic flows in this paper we consider a finite element discretization of the oldroyd b model of viscoelastic flows the method uses standard continuous polynomial finite element spaces for velocities pressures and stresses inf sup stability and stability for convection dominated flows are obtained by adding a term penalizing the jump of the solution gradient over element faces to increase robustness when the deborah number is high we add a nonlinear artificial viscosity of shock capturing type the method is analyzed on a linear model problem and optimal a priori error estimates are proven that are independent of the solvent viscosity eta s finally we demonstrate the performance of the method on some known benchmark cases

geometric exponents and kleinian groups suppose lambda is the limit set of an analytically finite kleinian group and that omega j is an enumeration of the components of omega s 2 setminus lambda then sum j diam omega j 2 infty this had been conjectured by maskit we also define a number of different geometric critical exponents associated to a compact set in the plane which generalize the index of besicovitch and taylor on the line although these exponents may differ for general sets we show that they are all equal when lambda is the limit set of a non elementary analytically finite kleinian group and they agree with the classical poincare exponent

galkerkin least squares finite element methods for the three field stokes system in 3 abstract in this work two new finite element methods for solving the three field stokes system associated with viscoelastic flow problems in three dimensional space are introduced both methods are based on a galerkin least squares formulation and complete first and second order convergence proofs of the corresponding approximations are given

tractable constraints on ordered domains abstract finding solutions to a constraint satisfaction problem is known to be an np complete problem in general but may be tractable in cases where either the set of allowed constraints or the graph structure is restricted in this paper we identify a restricted set of contraints which gives rise to a class of tractable problems this class generalizes the notion of a horn formula in propositional logic to larger domain sizes we give a polynomial time algorithm for solving such problems and prove that the class of problems generated by any larger set of constraints is np complete

linear time algorithms for testing the realisability of line drawings of curved objects this paper shows that the semantic labelling of line drawings of curved objects with piecewise c 3 surfaces is solvable in linear time this result is robust to changes in the assumptions on object shape when all vanishing points are known a different linear time algorithm exists to solve the labelling problem furthermore in both cases all legally labelled line drawings of curved objects are shown to be physically realisable however when some but not all of the vanishing points are known when the drawing is an orthographic projection of a scene containing parallel lines or when we wish to minimise the number of phantom junctions the labelling problem becomes np hard the introduction of collinearity constraints also renders the labelling problem np complete except in the case when all vanishing points are known 1999 elsevier science b v all rights reserved

planar formulae and their uses we define the set of planar boolean formulae and then show that the set of true quantified planar formulae is polynomial space complete and that the set of satisfiable planar formulae is np complete using these results we are able to provide simple and nearly uniform proofs of np completeness for planar node cover planar hamiltonian circuit and line geometric connected dominating set and of polynomial space completeness for planar generalized geography the np completeness of planar node cover and planar hamiltonian circuit and line were first proved elsewhere m r garey and d s johnson the rectilinear steiner tree is np complete siam j appl math 32 1977 pp 826 834 and m r garey d s johnson and r e tarjan the planar hamilton circuit problem is np complete siam j comp 5 1976 pp 704 714

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

study of a finite element method for the time dependent generalized stokes system associated with viscoelastic flow a three field finite element scheme designed for solving systems of partial differential equations governing time dependent viscoelastic flows is studied once a classical backward euler time discretization is performed the resulting three field system of equations allows for a stable approximation of velocity pressure and extra stress tensor by means of continuous piecewise linear finite elements in both two and three dimensional space this is proved to hold for the linearized form of the system an advantage of the new formulation is the fact that it provides an algorithm for the explicit iterative resolution of system nonlinearities convergence in an appropriate sense applying to these three flow fields is demonstrated

constraints between distant lines in the labelling of line drawings of polyhedral scenes the machine interpretation of line drawings has applications both in vision and geometric modelling this paper extends the classic technique of assigning semantic labels to lines subject to junction constraints by introducing new constraints often between distant lines these include generic constraints between lines lying on a path in the drawing as well as preference constraints between the labellings of pairs of junctions lying on parallel lines such constraints are essential to avoid an exponential number of legal labellings of drawings of objects with non trihedral vertices the strength of these constraints is demonstrated by their ability to identify the unique correct labelling of many drawings of polyhedral objects with tetrahedral vertices these new constraints also allowed us to deduce a general polyhedral junction constraint for the case when there is no limit on the number of faces which can meet at a junction

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

arc and path consistence revisited mackworth and freuder have analyzed the time complexity of several constraint satisfaction algorithms 5 we present here new algorithms for arc and path consistency and show that the arc consistency algorithm is optimal in time complexity and of the same order space complexity as the earlier algorithms a refined solution for the path consistency problem is proposed however the space complexity of the path consistency algorithm makes it practicable only for small problems these algorithms are the result of the synthesis techniques used in image a general constraint satisfaction system and local consistency methods 3

identification of faces in line drawings by edge decomposition this paper presents a method to find the faces of objects in 2d line drawings using an approach totally different from existing ones it consists of two stages decomposition and face forming in decomposition a drawing is decomposed into chains of connected edges each chain belongs to one face only but may not yet form a closed loop the decomposition is local to a vertex and takes no account of the overall structure of the drawing the algorithm ensures that there is a chain for every face in the object the face forming stage completes the loop for each chain to form a face our method can deliver both the real faces and the internal faces separately it depends only on the topology of the drawing and not on the geometry and is therefore applicable to line drawings with curves and straight lines and 3d wireframes we implemented our algorithm and tested it with hundreds of objects including objects used in previous publications it always delivers the correct result comparison with the latest methods shows that it is faster often by tens of times and in some cases hundreds of times decompose a drawing into sub loops of edges that belong to only one face form face by finding the missing edges of a sub loop in a limited search space low computational complexity more efficient than all existing methods handle manifolds and non manifolds handle line drawings and 3d wireframes with straight and curved edges

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

nonconforming finite element methods for the equations of linear elasticity in the adaptation of nonconforming finite element methods to the equations of elasticity with traction boundary conditions the main difficulty in the analysis is to prove that an appropriate discrete version of korn s second inequality is valid such a result is shown to hold for nonconforming piecewise quadratic and cubic finite elements and to be false for nonconforming piecewise linears optimal order error estimates uniform for poisson ratio v e 0 1 2 are then derived for the corresponding p2 and p3 methods this contrasts with the use of c finite elements where there is a deterioration in the convergence rate as v 1 2 for piecewise polynomials of degree 3 modifications of the continuous methods and the nonconforming linear method which also give uniform optimal order error estimates are discussed

error analysis of some galerkin least squares methods for the elasticity equations the recent technique of stabilizing mixed finite element methods by augmenting the galerkin formulation with least squares terms calculated separately on each element is considered the error analysis is performed in a unified manner yielding improved results for some methods introduced earlier in addition a new formulation is introduced and analyzed method is used within two different contexts the first is in connection with the plain strain or three dimensional problems near the incompressible limit for which the poisson ratio equals one half it is well known that for these problems a standard lower order displacement finite element method will break down by now it is also well known how a working method can be obtained a new unknown the pressure is introduced and discretized with a finite element space different from that used for the displacements the finite element method obtained falls into the class of saddlepoint problems for which there is a general theory developed by brezzi and babuska 5 7 the application of this theory shows that the method converges optimally if the discrete spaces for the displacement and pressure satisfy a stability condition for a particular choice of displacement and pressure approximations it can be a difficult task to verify this babuska brezzi or inf sup condition during the last decade this problem has been intensively studied and the performances of many combinations are now known cf 18 and 23 26 for some recent extensions in addition there exists a general technique utilizing bubble functions by which a stable method can

the patterson measure for geometrically finite groups with parabolic elements new and old we study the patterson measure on the limit set of a geometrically finite kleinian group with parabolic elements using the conformality of the patterson measure in combination with basic hyperbolic geometry a global shadow lemma is obtained this macroscopic measure estimate is exploited to derive a khintchine type theorem which is then used for a finer analysis of the density of the limit set in terms of hausdorff measure

fundamental properties of neighbourhood substitution in constraint satisfaction problems in combinatorial problems it is often worthwhile simplifying the problem using operations such as consistency before embarking on an exhaustive search for solutions neighbourhood substitution is such a simplification operation whenever a value x for a variable is such that it can be replaced in all constraints by another value y then x is eliminated this paper shows that neighbourhood substitutions are important whether the aim is to find one or all solutions it is proved that the result of a convergent sequence of neighbourhood substitutions is invariant modulo isomorphism an efficient algorithm is given to find such a sequence it is also shown that to combine consistency of any order and neighbourhood substitution we only need to establish consistency once

a new family of stable elements for nearly incompressible elasticity based on a mixed petrov galerkin finite element formulation adding to the classical hellinger reissner formulation another residual form of the equilibrium equation a new petrov galerkin finite element method is derived it fits within the framework of a mixed finite element method and is proved to be stable for rather general combinations of stress and displacement interpolations including equal order discontinuous stress and continuous displacement interpolations which are unstable within the galerkin approach error estimates are presented using the babuska brezzi theory and numerical results confirm these estimates as well as the good accuracy and stability of the method

cyclic consistency a local reduction operation for binary valued constraints valued constraint satisfaction provides a general framework for optimisation problems over finite domains it is a generalisation of crisp constraint satisfaction allowing the user to express preferences between solutions consistency is undoubtedly the most important tool for solving crisp constraints it is not only a family of simplification operations on problem instances it also lies at the heart of intelligent search techniques g kondrak p van beek artificial intelligence 89 1997 365 387 and provides the key to solving certain classes of tractable constraints p g jeavons d a cohen m c cooper artificial intelligence 101 1998 251 265 arc consistency was generalised to valued constraints by sacrificing the uniqueness of the arc consistency closure m c cooper t schiex artificial intelligence in press the notion of 3 cyclic consistency introduced in this paper again sacrifices the unique closure property in order to obtain a generalisation of path consistency to valued constraints which is checkable in polynomial time in max csp 3 cyclic consistency can be established in polynomial time and even guarantees a local form of optimality the space complexity of 3 cyclic consistency is optimal since it creates no new constraints

recovering three dimensional shape from a single image of curved objects an algorithm to recover three dimensional shape i e surface orientation and relative depth from a single segmented image is presented it is assumed that the scene is composed of opaque regular solid objects bounded by piecewise smooth surfaces with no markings or textures it is also assumed that the reflectance map r n is known for the canonical case of lambertian surfaces illuminated by a point light source this implies knowing the light source direction a variational formulation of line drawing and shading constraints in a common framework is developed the global constraints are partitioned into constraint sets corresponding to the faces edges and vertices in the scene for a face the constraints are given by horn s image irradiance equation a variational formulation of the constraints at an edge both from the known direction of the image curve corresponding to the edge and shading is developed at a vertex the constraints are modeled by a system of nonlinear equations an algorithm is presented to solve this system of constraints

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

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

related aspects of positivity in riemannian geometry pour une variete de riemann on etudie le lien entre le point 0 du l 2 spectre le plus proche de zero pour l extension de friedrich d un operateur semi defini symetrique et le taux exponentiel de transition d un operateur de markoff conservant la positivite

arc consistency and arc consistency again abstract there is no need to show the importance of arc consistency in constraint networks mohr and henderson 9 have proposed ac 4 an algorithm with optimal worst case time complexity but it has two drawbacks its space complexity and average time complexity in problems with many solutions where constraints are large these drawbacks become so important that users often replace ac 4 by ac 3 8 a non optimal algorithm in this paper we propose a new algorithm ac 6 which keeps the optimal worst case time complexity of ac 4 while working out the drawback of space complexity moreover the average time complexity of ac 6 is optimal for constraint networks where nothing is known about the constraint semantics

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

empirically derived estimates of the complexity of labeling line drawings of polyhedral scenes abstract several results have been obtained in the past about the complexity of understanding line drawings of polyhedral scenes kirousis and papadimitriou 1988 have shown that the problem of labeling line drawings of trihedral scenes is np complete the human brain however seems to grasp at a glance the 3d structure associated with a line drawing a possible explanation of this discrepancy offered by kirousis and papadimitriou themselves is that the worst case complexity does not reflect the real difficulty of labeling line drawings which might be far less in the average or in typical cases however no statistical analysis has ever been carried out to test this conjecture the core of this paper is an algorithm for the generation of random instances of polyhedral scenes random instances of line drawings are then obtained as perspective projections of these scenes and can be used as an input to standard labeling algorithms so as to derive experimental estimates of the complexity of these algorithms the results indicate that the median case complexity is linear in the number of junctions this substantiates the conjecture that typical instances of line drawings are easy to label and may help explain the ease by which the brain is able to solve the problem

linear constraints for the interpretation of line drawings of curved objects abstract drawings of curved objects often contain many linear features straight lines colinear or coplanar points parallel lines and vanishing points these linear features give rise to linear constraints on the 3d position of scene points the resulting problem can be solved by standard linear programming techniques an important characteristic of this approach is that instead of making a strong assumption such as all surfaces are planar only a very weak assumption which disallows coincidences and highly improbable objects needs to be made to be able to deduce planarity the linear constraints combined with junction labelling constraints are a powerful means of discriminating between possible and impossible line drawings they provide an important tool for the machine reconstruction of a 3d scene from a human entered line drawing

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

revisiting the siegel upper half plane i in this paper we study the automorphisms of siegel upper half plane of complex dimension 3 we give the normal forms and classify the set of fixed points of such transformations

on the complexity of labeling perspective projections of polyhedral scenes abstract this paper investigates the computational time complexity of the labeling problem for line drawings of trihedral scenes it is shown that the class of problems having polynomial complexity is larger than the simple case of line drawings of legoland scenes kirousis and papadimitriou 1988 once the location of the vanishing points in the image plane is known the labeling problem can be solved in time o nn where n is the number of segments and n is the number of vanishing points the vanishing points can be given a priori otherwise can in many cases be detected by standard techniques from the line drawing itself the np completeness of the labeling problem for line drawings of trihedral scenes kirousis and papadimitriou 1988 is then due to the lack of knowledge about the vanishing points which is equivalent to the knowledge of the possible directions for the edges these results help draw a more accurate boundary between the problems in the interpretation of line drawings that are polynomially solvable and those that are np complete

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

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

finite element approximation of the three field formulation of the stokes problem using arbitrary interpolations the stress displacement pressure formulation of the elasticity problem may suffer from two types of numerical instabilities related to the finite element interpolation of the unknowns the first is the classical pressure instability that occurs when the solid is incompressible whereas the second is the lack of stability in the stresses to overcome these instabilities there are two options the first is to use different interpolation for all the unknowns satisfying two inf sup conditions whereas there are several displacement pressure interpolations that render the pressure stable less possibilities are known for the stress interpolation the second option is to use a stabilized finite element formulation instead of the plain galerkin approach if this formulation is properly designed it is possible to use arbitrary interpolation for all the unknowns the purpose of this paper is precisely to present one of such formulations in particular it is based on the decomposition of the unknowns into their finite element component and a subscale which will be approximated and whose goal is to yield a stable formulation a singular feature of the method to be presented is that the subscales will be considered orthogonal to the finite element space we describe the design of the formulation and present the results of its numerical analysis