kernel of star product for spin tomograms the spin state tomogram is presented as the modulus squared of the matrix element of the su 2 group irreducible representation for the spin system we established explicitly a realization of the set of operators defining for spin tomograms the star product formalism in terms of irreducible tensors on the set of spin tomograms the delta function and standard and moyal like kernels of the tomogram star product are calculated explicitly in terms of clebsch gordan and racah coefficients and matrix elements of the su 2 irreducible representation in the limit of infinite spin the spin tomogram is shown to become the tomogram of the harmonic oscillator state

robust recovery of shapes with unknown topology from the dual space in this paper we address the problem of reconstructing an object surface from silhouettes previous works by other authors have shown that based on the principle of duality surface points can be recovered theoretically as the dual to the tangent plane space of the object in practice however the identification of tangent basis in the tangent plane space is not trivial given a set of discretely sampled data this problem is further complicated by the existence of bitangents to the object surface the key contribution of this paper is the introduction of epipolar parameterization in identifying a well defined local tangent basis this extends the applicability of existing dual space reconstruction methods to fairly complicated shapes without making any explicit assumption on the object topology we verify our approach with both synthetic and real world data and compare it both qualitatively and quantitatively with other popular reconstruction algorithms experimental results demonstrate that our proposed approach produces more accurate estimation while maintaining reasonable robustness toward shapes with complex topologies

integration of geometric elements euclidean relations and motion curves for parametric shape and motion estimation this paper presents an approach to shape and motion estimation that integrates heterogeneous knowledge into a unique model based framework we describe the observed scenes in terms of structured geometric elements points line segments rectangles 3d corners sharing explicitly euclidean relationships orthogonality parallelism colinearity coplanarity camera trajectories are represented with adaptative models which account for the regularity of usual camera motions two different strategies of automatic model building lead us to reduced models for shape and motion estimation with a minimal number of parameters these models increase the robustness to noise and occlusions improve the reconstruction and provide a high level representation of the observed scene the parameters are optimally computed within a sequential bayesian estimation procedure that gives accurate and reliable results on synthetic and real video imagery

surface shape from the deformation of apparent contours the spatiotemporal analysis of deforming silhouettes apparent contours is here extended using the mathematics of perspective projections and tools from differential geometry analysis of the image motion of a silhouette or apparent contour enables computation of local surface curvature along the corresponding contour generator on the surface assuming viewer motion is known to perform the analysis a spatiotemporal parameterization of image curve motion is needed but is underconstrained a manifestation of the well known aperture problem it is shown that an epipolar parameterization is most naturally matched to the recovery of surface curvature

automatic model construction and pose estimation from photographs using triangular splines this paper addresses the automatic construction of complex spline object models from a few photographs our approach combines silhouettes from registered images to construct a g sup 1 continuous triangular spline approximation of an object with unknown topology we apply a similar optimization procedure to estimate the pose of a modeled object from a single image experimental examples of model construction and pose estimation are presented for several complex objects

invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

camera calibration from images of spheres this paper introduces a novel approach for solving the problem of camera calibration from spheres by exploiting the relationship between the dual images of spheres and the dual image of the absolute conic iac it is shown that the common pole and polar with regard to the conic images of two spheres are also the pole and polar with regard to the iac this provides two constraints for estimating the iac and hence allows a camera to be calibrated from an image of at least three spheres experimental results show the feasibility of the proposed approach

an extreme form of superactivation for quantum zero error capacities the zero error capacity of a channel is the rate at which it can send information perfectly with zero probability of error and has long been studied in classical information theory we show that the zero error capacity of quantum channels exhibits an extreme form of nonadditivity one which is not possible for classical channels or even for the usual capacities of quantum channels by combining probabilistic arguments with algebraic geometry we prove that there exist channels and with no zero error classical capacity whatsoever but whose joint zero error quantum capacity is positive this striking effect is an extreme form of the superactivation phenomenon as it implies that both the classical and quantum zero error capacities of these channels can be superactivated simultaneously while being a strictly stronger property of capacities superactivation of the quantum zero error capacity was not previously known

motion estimation in image sequences using the deformation of apparent contours the problem of determining the camera motion from apparent contours or silhouettes of a priori unknown curved 3d surfaces is considered in a sequence of images it is shown how to use the generalized epipolar constraint on apparent contours one such constraint is obtained for each epipolar tangency point in each image pair an accurate algorithm for computing the motion is presented based on a maximum likelihood estimate it is shown how to generate initial estimates on the camera motion using only the tracked contours it is also shown that in theory the motion can be calculated from the deformation of a single contour the algorithm has been tested on several real image sequences for both euclidean and projective reconstruction the resulting motion estimate is compared to motion estimates calculated independently using standard feature based methods the motion estimate is also used to classify the silhouettes as curves or apparent contours the statistical evaluation shows that the technique gives accurate and stable results

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

full volumetric descriptions from three intensity images we address the problem of recovering high level volumetric and segmented or part based descriptions of objects from intensity images as input we use three closely spaced images of an object and recover descriptions based on generalized cylinders gcs we start by extracting a hierarchy of groups from contour images in the three views grouping is based on proximity parallelism and symmetry the groups in the three views are matched and their contours are labeled as true edges we then infer the gc axis its cross section and the scaling function the cross section is recovered if seen in the images else it is inferred using the visible surfaces and gc properties we consider groups with true edges limb edges or a combination of both the coarse volumetric descriptions obtained are refined to include surface details as seen in the intensity images we demonstrate results on real images of moderately complex objects with texture and shadows

a stratified approach for camera calibration using spheres this paper proposes a stratified approach for camera calibration using spheres previous works have exploited epipolar tangents to locate frontier points on spheres for estimating the epipolar geometry it is shown in this paper that other than the frontier points two additional point features can be obtained by considering the bitangent envelopes of a pair of spheres a simple method for locating the images of such point features and the sphere centers is presented an algorithm for recovering the fundamental matrix in a plane plus parallax representation using these recovered image points and the epipolar tangents from three spheres is developed a new formulation of the absolute dual quadric as a cone tangent to a dual sphere with the plane at infinity being its vertex is derived this allows the recovery of the absolute dual quadric which is used to upgrade the weak calibration to a full calibration experimental results on both synthetic and real data are presented which demonstrate the feasibility and the high precision achieved by our proposed algorithm

introducing a new problem shape from silhouette when the relative positions of the viewpoints is unknown 3d shapes can be reconstructed from 2d silhouettes by back projecting them from the corresponding viewpoints and intersecting the resulting solid cones however in many practical cases as observing an aircraft or an asteroid the positions of the viewpoints with respect to the object are not known in these cases the relative position of the solid cones is not known and the intersection cannot be performed the purpose of this paper is introducing and stating in a theoretical framework the problem of understanding 3d shapes from silhouettes when the relative positions of the viewpoints are unknown the results presented provide a first insight into the problem in particular the case of orthographic viewing directions parallel to the same plane is thoroughly discussed and sets of inequalities are presented which allow determining objects compatible with the silhouettes

free form object reconstruction from silhouettes occluding edges and texture edges a unified and robust operator based on duality in this paper the duality in differential form is developed between a 3d primal surface and its dual manifold formed by the surface s tangent planes that is each tangent plane of the primal surface is represented as a four dimensional vector that constitutes a point on the dual manifold the iterated dual theorem shows that each tangent plane of the dual manifold corresponds to a point on the original 3d surface that is the dual of the dual goes back to the primal this theorem can be directly used to reconstruct 3d surface from image edges by estimating the dual manifold from these edges in this paper we further develop the work in our original conference papers resulting in the robust differential dual operator we argue that the operator makes good use of the information available in the image data by using both points of intensity discontinuity and their edge directions we provide a simple physical interpretation of what the abstract algorithm is actually estimating and why it makes sense in terms of estimation accuracy our algorithm operates on all edges in the images including silhouette edges self occlusion edges and texture edges without distinguishing their types thus resulting in improved accuracy and handling locally concave surface estimation if texture edges are present the algorithm automatically handles various degeneracies and the algorithm incorporates new methodologies for implementing the required operations such as appropriately relating edges in pairs of images evaluating and using the algorithm s sensitivity to noise to determine the accuracy of an estimated 3d point experiments with both synthetic and real images demonstrate that the operator is accurate robust to degeneracies and noise and general for reconstructing free form objects from occluding edges and texture edges detected in calibrated images or video sequences

generalised epipolar constraints in this paper we will discuss structure and motion problems for curved surfaces these will be studied using the silhouettes or apparent contours in the images the problem of determining camera motion from the apparent contours of curved three dimensional surfaces is studied it will be shown how special points called epipolar tangency points or frontier points can be used to solve this problem a generalised epipolar constraint is introduced which applies to points curves as well as to apparent contours of surfaces the theory is developed for both continuous and discrete motion known and unknown orientation calibrated and uncalibrated perspective weak perspective and orthographic cameras results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces is presented a statistical evaluation is performed to estimate the stability of the solution it is also shown how the motion of the camera from a sequence of images can be obtained from the relative motion between image pairs

visually guided ranging from observations of points lines and curves via an identifier based nonlinear observer abstract in this paper we consider the problem of estimating the range information of features on an affine plane in r 3 by observing its image with the aid of a ccd camera wherein we assume that the camera is undergoing a known motion the features considered are points lines and planar curves located on planar surfaces of static objects the dynamics of the moving projections of the features on the image plane have been described as a suitable differential equation on an appropriate feature space this dynamics is used to estimate feature parameters from which the range information is readily available in this paper the proposed identification has been carried out via a newly introduced identifier based observer performance of the observer has been studied via simulation

epipolar parameterization for reconstructing 3d rigid curve abstract this paper describes a new method for reconstructing a 3d rigid curve from a sequence of uncalibrated images using 31 epipolar parameterization the approach can be divided into the following two steps first a nonlinear discrete method is presented for point by point reconstruction of the curve instead of whole curve reconstruction projective and euclidean geometric tools are used second the parametric representation of the curve is defined by 31 b spline curves a linear method is proposed to interpolate the reconstructed points to obtain a complete curve thus it is proved that the 31 curve interpolation is equivalent to determining a set of control points of 3d regularized b spline curves it is shown that the 3d epipolar parameterization is an efficient method for reconstructing a 31 curve from image sequences experimental results are presented for real data

what s next an interactive next best view approach shape from silhouettes algorithms use either a surface or a volumetric approach a problem with the volumetric approach is that in general we know neither the accuracy of the reconstruction nor where to locate new viewpoints for improving the accuracy in this paper we present a general approach to interactive object specific volumetric algorithms based on a necessary condition for the best possible reconstruction to have been performed the outlined approach can be applied to any class of objects as an example of this approach an interactive algorithm has been implemented for convex polyhedra

quantum zero error source channel coding and non commutative graph theory alice and bob receive a bipartite state possibly entangled from some finite collection or from some subspace alice sends a message to bob through a noisy quantum channel such that bob may determine the initial state with zero chance of error this framework encompasses for example teleportation dense coding entanglement assisted quantum channel capacity and one way communication complexity of function evaluation with classical sources and channels this problem can be analyzed using graph homomorphisms we show this quantum version can be analyzed using homomorphisms on non commutative graphs an operator space generalization of graphs previously the lovasz vartheta number has been generalized to non commutative graphs we show this to be a homomorphism monotone thus providing bounds on quantum source channel coding we generalize the schrijver and szegedy numbers and show these to be monotones as well as an application we construct a quantum channel whose entanglement assisted zero error one shot capacity can only be unlocked using a non maximally entangled state these homomorphisms allow definition of a chromatic number for non commutative graphs many open questions are presented regarding the possibility of a more fully developed theory

epipolar geometry from profiles under circular motion addresses the problem of motion estimation from profiles apparent contours of an object rotating on a turntable in front of a single camera a practical and accurate technique for solving this problem from profiles alone is developed it is precise enough to reconstruct the shape of the object no correspondences between points or lines are necessary symmetry of the surface of revolution swept out by the rotating object is exploited to obtain the image of the rotation axis and the homography relating epipolar lines in two views robustly and elegantly these together with geometric constraints for images of rotating objects are used to obtain first the image of the horizon which is the projection of the plane that contains the camera centers and then the epipoles thus fully determining the epipolar geometry of the image sequence the estimation of this geometry by this sequential approach avoids many of the problems found in other algorithms the search for the epipoles by far the most critical step is carried out as a simple 1d optimization parameter initialization is trivial and completely automatic at all stages after the estimation of the epipolar geometry the euclidean motion is recovered using the fixed intrinsic parameters of the camera obtained either from a calibration grid or from self calibration techniques finally the spinning object is reconstructed from its profiles using the motion estimated in the previous stage results from real data are presented demonstrating the efficiency and usefulness of the proposed methods

robust structure and motion from outlines of smooth curved surfaces this paper addresses the problem of estimating the motion of a camera as it observes the outline or apparent contour of a solid bounded by a smooth surface in successive image frames in this context the surface points that project onto the outline of an object depend on the viewpoint and the only true correspondences between two outlines of the same object are the projections of frontier points where the viewing rays intersect in the tangent plane of the surface in turn the epipolar geometry is easily estimated once these correspondences have been identified given the apparent contours detected in an image sequence a robust procedure based on ransac and a voting strategy is proposed to simultaneously estimate the camera configurations and a consistent set of frontier point projections by enforcing the redundancy of multiview epipolar geometry the proposed approach is in principle applicable to orthographic weak perspective and affine projection models experiments with nine real image sequences are presented for the orthographic projection case including a quantitative comparison with the ground truth data for the six data sets for which the latter information is available sample visual hulls have been computed from all image sequences for qualitative evaluation

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

separation between quantum lovasz number and entanglement assisted zero error classical capacity quantum lovasz number is a quantum generalization of the lovasz number in graph theory it is the best known efficiently computable upper bound of the entanglement assisted zero error classical capacity of a quantum channel however it remains an intriguing open problem whether quantum entanglement can always enhance the zero error capacity to achieve the quantum lovasz number in this paper by constructing a particular class of qutrit to qutrit channels we show that there exists a strict gap between the entanglement assisted zero error capacity and the quantum lovasz number interestingly for this class of quantum channels the quantum generalization of fractional packing number is strictly larger than the zero error capacity assisted with feedback or no signaling correlations which differs from the case of classical channels

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

3d surface reconstruction using occluding contours this paper addresses the problem of 3d surface reconstruction using image sequences it has been shown that shape recovery from three or more occluding contours of the surface is possible given a known camera motion several algorithms which have been recently proposed allow such a reconstruction under the assumption of a linear camera motion a new approach is presented which deals with the reconstruction problem directly from a discrete point of view first a theoretical study of the epipolar correspondence between occluding contours is achieved a correct depth formulation is then derived from a local approximation of the surface up to order two this allows the local shape to be estimated given three consecutive contours without any constraints on the camera motion experimental results are presented for both synthetic and real data

efficient surface reconstruction from contours based on two dimensional delaunay triangulation this paper introduces an efficient method for surface reconstruction from sectional contours the surface between neighbouring sections is reconstructed based on the consistent utilization of the two dimensional constrained delaunay triangulation the triangulation is used to extract the parametric domain and to solve the problems associated with correspondence tiling and branching in a general framework natural distance interpolations are performed in order to complete the mapping of the added intermediate points surface smoothing and remeshing are conducted to optimize the initial surface triangulations several examples are presented to demonstrate the effectiveness and efficiency of the proposed approach

tracking non rigid objects using probabilistic hausdorff distance matching this paper proposes a new method of extracting and tracking a non rigid object moving against a cluttered background while allowing camera movement for object extraction we first detect an object using watershed segmentation technique and then extract its contour points by approximating the boundary using the idea of feature point weighting for object tracking we take the contour to estimate its motion in the next frame by the maximum likelihood method the position of the object is estimated using a probabilistic hausdorff measurement while the shape variation is modelled using a modified active contour model the proposed method is highly tolerant to occlusion unless an object is fully occluded during tracking the result is stable and the method is robust enough for practical application

motion estimation via dynamic vision estimating the three dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics such as autonomous navigation manipulation servo tracking docking planning and surveillance although visual motion estimation is an old problem the first formulations date back to the beginning of the century only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions in this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold such a formulation has structural advantages over previous recursive schemes since the estimation of motion is decoupled from the estimation of the structure of the object being viewed and therefore it is possible to handle occlusions in a principled way

implicit meshes for effective silhouette handling using silhouettes in uncontrolled environments typically requires handling occlusions as well as changing or cluttered backgrounds which limits the applicability of most silhouette based methods for the purpose of 3 d shape modeling we show that representing generic 3 d surfaces as implicit surfaces lets us effectively address these issues this desirable behavior is completely independent from the way the surface deformations are parame trized to show this we demonstrate our technique in three very different cases modeling the deformations of a piece of paper represented by an ordinary triangulated mesh reconstruction and tracking a person s shoulders whose deformations are expressed in terms of dirichlet free form deformations reconstructing the shape of a human face parametrized in terms of a principal component analysis model

new entropic inequalities for qubit and unimodal gaussian states abstract the tsallis relative entropy s q measures the distance between two arbitrary density matrices and in this work the approximation to this quantity when q 1 1 is obtained it is shown that the resulting series is equal to the von neumann relative entropy when 0 analyzing the von neumann relative entropy for an arbitrary and a thermal equilibrium state e h tr e h is possible to define a new inequality relating the energy the entropy and the partition function of the system from this inequality a parameter that measures the distance between the two states is defined this distance is calculated for a general qubit system and for an arbitrary unimodal gaussian state in the qubit case the dependence on the purity of the system is studied for t 0 and also for t 0 in the gaussian case the general partition function given a unimodal quadratic hamiltonian is calculated and the comparison of the thermal light state as a thermal equilibrium state of the parametric amplifier is presented

curve and surface duals and the recognition of curved 3d objects from their silhouettes this article addresses the problem of recognizing a solid bounded by a smooth surface in a single image the proposed approach is based on a new representation for two and three dimensional shapes called their signature that exploits the close relationship between the dual of a surface and the dual of its silhouette in weak perspective images objects are modeled by rotating them in front of a camera without any knowledge of or constraints on their motion the signatures of their silhouettes are concatenated into a single object signature to recognize an object from novel viewpoint other than those used during modeling the signature of the contours extracted from a test photograph is matched to the signatures of all modeled objects signatures this approach has been implemented and recognition examples are presented

1d camera geometry and its application to the self calibration of circular motion sequences this paper proposes a novel method for robustly recovering the camera geometry of an uncalibrated image sequence taken under circular motion under circular motion all the camera centers lie on a circle and the mapping from the plane containing this circle to the horizon line observed in the image can be modelled as a 1d projection a 2times2 homography is introduced in this paper to relate the projections of the camera centers in two 1d views it is shown that the two imaged circular points of the motion plane and the rotation angle between the two views can be derived directly from such a homography this way of recovering the imaged circular points and rotation angles is intrinsically a multiple view approach as all the sequence geometry embedded in the epipoles is exploited in the estimation of the homography for each view pair this results in a more robust method compared to those computing the rotation angles using adjacent views only the proposed method has been applied to self calibrate turntable sequences using either point features or silhouettes and highly accurate results have been achieved

regularization of inverse visual problems involving discontinuities inverse problems such as the reconstruction problems that arise in early vision tend to be mathematically ill posed through regularization they may be reformulated as well posed variational principles whose solutions are computable standard regularization theory employs quadratic stabilizing functionals that impose global smoothness constraints on possible solutions discontinuities present serious difficulties to standard regularization however since their reconstruction requires a precise spatial control over the smoothing properties of stabilizers this paper proposes a general class of controlled continuity stabilizers which provide the necessary control over smoothness these nonquadratic stabilizing functionals comprise multiple generalized spline kernels combined with noncontinuous continuity control functions in the context of computational vision they may be thought of as controlled continuity constraints these generic constraints are applicable to visual reconstruction problems that involve both continuous regions and discontinuities for which global smoothness constraints fail

self calibration of turntable sequences from silhouettes this paper addresses the problem of recovering both the intrinsic and extrinsic parameters of a camera from the silhouettes of an object in a turntable sequence previous silhouette based approaches have exploited correspondences induced by epipolar tangents to estimate the image invariants under turntable motion and achieved a weak calibration of the cameras it is known that the fundamental matrix relating any two views in a turntable sequence can be expressed explicitly in terms of the image invariants the rotation angle and a fixed scalar it will be shown that the imaged circular points for the turntable plane can also be formulated in terms of the same image invariants and fixed scalar this allows the imaged circular points to be recovered directly from the estimated image invariants and provide constraints for the estimation of the imaged absolute conic the camera calibration matrix can thus be recovered a robust method for estimating the fixed scalar from image triplets is introduced and a method for recovering the rotation angles using the estimated imaged circular points and epipoles is presented using the estimated camera intrinsics and extrinsics a euclidean reconstruction can be obtained experimental results on real data sequences are presented which demonstrate the high precision achieved by the proposed method

minimal entropy of states emerging from noisy quantum channels we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel which is modeled by the action of a completely positive trace preserving or stochastic map we provide strong support for the conjecture that this minimal entropy is additive namely that the minimum entropy can be achieved when product states are transmitted explicitly we prove that for a tensor product of two unital stochastic maps on qubit states using an entanglement that involves only states which emerge with minimal entropy cannot decrease the entropy below the minimum achievable using product states we give a separate argument based on the geometry of the image of the set of density matrices under stochastic maps which suggests that the minimal entropy conjecture holds for nonunital as well as for unital maps we also show that the maximal norm of the output states is multiplicative for most product maps on n qubit states including all those for which at least one map is unital for the class of unital channels on c sup 2 we show that additivity of minimal entropy implies that the holevo see ieee trans inform theory vol 44 p 269 73 1998 and russian math surv p 1295 1331 1999 capacity of the channel is additive over two inputs achievable with orthogonal states and equal to the shannon capacity this implies that superadditivity of the capacity is possible only for nonunital channels

affine reconstruction of curved surfaces from uncalibrated views of apparent contours in this paper we consider uncalibrated reconstruction of curved surfaces from apparent contours since apparent contours are not fixed features viewpoint independent we cannot directly apply the recent results of the uncalibrated reconstruction from fixed features we show that nonetheless curved surfaces can be reconstructed up to an affine ambiguity from their apparent contours viewed from uncalibrated cameras with unknown linear translations furthermore we show that even if the reconstruction is nonmetric non euclidean we can still extract useful information for many computer vision applications just from the apparent contours we first show that if the camera motion is linear translation but arbitrary direction and magnitude the epipolar geometry can be recovered from the apparent contours without using any optimization process the extracted epipolar geometry is next used for reconstructing curved surfaces from the deformations of the apparent contours viewed from uncalibrated cameras the result is applied to distinguishing curved surfaces from fixed features in images it is also shown that the time to contact to the curved surfaces can be computed from simple measurements of the apparent contours

a theory of shape by space carving in this paper we consider the problem of computing the 3d shape of an unknown arbitrarily shaped scene from multiple photographs taken at known but arbitrarily distributed viewpoints by studying the equivalence class of all 3d shapes that reproduce the input photographs we prove the existence of a special member of this class the photo hull that 1 can be computed directly from photographs of the scene and 2 subsumes all other members of this class we then give a provably correct algorithm called space carving for computing this shape and present experimental results on complex real world scenes the approach is designed to 1 capture photorealistic shapes that accurately model scene appearance from a wide range of viewpoints and 2 account for the complex interactions between occlusion parallax shading and their view dependent effects on scene appearance

reconstruction of general curves using factorization and bundle adjustment in this paper we extend the notion of affine shape introduced by sparr from finite point sets to curves the extension makes it possible to reconstruct 3d curves up to projective transformations from a number of their 2d projections we also extend the bundle adjustment technique from point features to curves the first step of the curve reconstruction algorithm is based on affine shape it is independent of choice of coordinates is robust does not rely on any preselected parameters and works for an arbitrary number of images in particular this means that except for a small set of curves e g a moving line a solution is given to the aperture problem of finding point correspondences between curves the second step takes advantage of any knowledge of measurement errors in the images this is possible by extending the bundle adjustment technique to curves finally experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

efficient polyhedral modeling from silhouettes modeling from silhouettes is a popular and useful topic in computer vision many methods exist to compute the surface of the visual hull from silhouettes but few address the problem of ensuring good topological properties of the surface such as manifoldness this article provides an efficient algorithm to compute such a surface in the form of a polyhedral mesh it relies on a small number of geometric operations to compute a visual hull polyhedron in a single pass such simplicity enables the algorithm to combine the advantages of being fast producing pixel exact surfaces and repeatably yield manifold and watertight polyhedra in general experimental conditions with real data as verified with all datasets tested the algorithm is fully described its complexity analyzed and modeling results given

using extremal boundaries for 3 d object modeling the extremal boundaries of 3 d curved objects are the images of special curves drawn on the object and are called rims they are viewpoint dependent and characterized by the fact that the optical rays of their points are tangential to the surface of the object the mathematics of the relationship between the extremal boundaries and the surface of the object is studied this study makes it possible to design an algorithm for detecting those boundaries in the images that are likely to be extremal once this has been done one can reconstruct the rims and compute the differential properties of the surface of the object along them up to the second order if a qualitative description is sufficient the sign of the gaussian curvature of the surface along the rim can be computed in a much simpler way experimental results are presented on synthetic and real images the work provides a better understanding of the relationship between the apparent and real shape of a 3 d object as well as algorithms for reconstructing the local shape of such an object along the rims

on recognizing and positioning curved 3 d objects from image contours an approach for explicitly relating the shape of image contours to models of curved three dimensional objects is presented this relationship is used for object recognition and positioning object models consist of collections of parametric surface patches and their intersection curves this includes nearly all representations used in computer aided geometric design and computer vision the image contours considered are the projections of surface discontinuities and occluding contours elimination theory provides a method for constructing the implicit equation of these contours for an object observed under orthographic or perspective projection this equation is parameterized by the object s position and orientation with respect to the observer determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points the proposed approach readily extends to parameterized models it has been implemented for a simple world composed of various surfaces of revolution and tested on several real images

semidefinite programming strong converse bounds for classical capacity we investigate the classical communication over quantum channels when assisted by no signaling and positive partial transpose preserving ppt codes for which both the optimal success probability of a given transmission rate and the one shot epsilon error capacity are formalized as semidefinite programs sdps based on this we obtain improved sdp finite blocklength converse bounds of general quantum channels for entanglement assisted codes and unassisted codes furthermore we derive two sdp strong converse bounds for the classical capacity of general quantum channels for any code with a rate exceeding either of the two bounds of the channel the success probability vanishes exponentially fast as the number of channel uses increases in particular applying our efficiently computable bounds we derive an improved upper bound on the classical capacity of the amplitude damping channel we also establish the strong converse property for the classical and private capacities of a new class of quantum channels we finally study the zero error setting and provide efficiently computable upper bounds on the one shot zero error capacity of a general quantum channel

entropy energy inequalities for qudit states we establish a procedure to find the extremal density matrices for any finite hamiltonian of a qudit system these extremal density matrices provide an approximate description of the energy spectrum of the hamiltonian in the case of restricting the extremal density matrices by pure states we show that the energy spectrum of the hamiltonian is recovered for d 2 and 3 we conjecture that by means of this approach the energy spectrum can be recovered for the hamiltonian of an arbitrary finite qudit system for a given qudit system hamiltonian we find new inequalities connecting the mean value of the hamiltonian and the entropy of an arbitrary state we demonstrate that these inequalities take place for both the considered extremal density matrices and generic ones

the local projective shape of smooth surfaces and their outlines this article examines projectively invariant local geometric properties of smooth curves and surfaces oriented projective differential geometry is proposed as a general framework for establishing such invariants and characterizing the local projective shape of surfaces and their outlines it is applied to two problems 1 the projective generalization of koenderink s famous characterization of convexities concavities and inflections of the apparent contours of solids bounded by smooth surfaces and 2 the image based construction of rim meshes which provide a combinatorial description of the arrangement induced on the surface of an object by the contour generators associated with multiple cameras observing it

acquiring 3d models of non rigid moving objects from time and viewpoint varying image sequences a step toward left ventricle recovery this paper describes a method for the accurate recovery of time varying 3d shapes with known cycle from images with different viewpoints as well as times aiming at the recovery of the left ventricular shapes our recovery method is based on the integration of apparent contours from different viewpoints we perform direct fitting to a 4d closed surface model based on b splines so as to deal with fragmented contours such as extracted from x ray cineangiocardiograms the method is quantitatively evaluated using synthesized and real image sequences

parametric reconstruction of generalized cylinders from limb edges the three dimensional 3 d reconstruction of generalized cylinders gcs is an important research field in computer vision one of the main difficulties is that some contour features in images cannot be reconstructed by traditional stereovision because they do not correspond to reflectance discontinuities of surface in space in this paper we present a novel parametric approach for the 3 d reconstruction of circular generalized cylinders cgcs only from the limb edges of cgcs in two images instead of exploiting the invariant and quasiinvariant properties of some specific subclasses of gcs in projections our reconstruction is achieved by some general assumptions on gcs and can therefore be applied to a broader subclass of gcs in order to improve robustness we perform the extraction and labeling of the limb edge interactively and estimate the epipolar geometry between two images by an optimal algorithm then for different types of gcs three kinds of symmetries parallel symmetry skew symmetry and local smooth symmetry are employed to compute the symmetry of limb edges the surface points corresponding to limb edges in images are reconstructed by integrating the recovered epipolar geometry and the properties induced from the assumptions that we make on the gcs finally a homography based method is exploited to further refine the 3 d description of the gc with a coplanar curved axis

projective visual hulls this article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras the visual hull is the intersection of the visual cones formed by back projecting the silhouettes found in the corresponding images we characterize its surface as a generalized polyhedron whose faces are visual cone patches edges are intersection curves between two viewing cones and vertices are frontier points where the intersection of two cones is singular or intersection points where triples of cones meet we use the mathematical framework of oriented projective differential geometry to develop an image based algorithm for computing the visual hull this algorithm works in a weakly calibrated setting that is it only requires projective camera matrices or equivalently fundamental matrices for each pair of cameras the promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state of the art method

following cusps it is known that the deformation of the apparent contours of a surface under perspective projection and viewer motion enable the recovery of the geometry of the surface for example by utilising the epipolar parametrization these methods break down with apparent contours that are singular i e with cusps in this paper we study this situation and show how nevertheless the surface geometry including the gauss curvature and mean curvature of the surface can be recovered by following the cusps indeed the formulae are much simpler in this case and require lower spatio temporal derivatives than in the general case of nonsingular apparent contours we also show that following cusps does not by itself provide us with information on viewer motion

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

generalized euler angle parametrization for su n in a previous paper 1 an euler angle parametrization for su 4 was given here we present the derivation of a generalized euler angle parametrization for su n the formula for the calculation of the haar measure for su n as well as its relation to marinov s volume formula for su n 2 3 will also be derived as an example of this parametrization s usefulness the density matrix parametrization and invariant volume element for a qubit qutrit three qubit and two three state systems also known as two qutrit systems 4 will also be given

global surface reconstruction by purposive control of observer motion abstract what viewpoint control strategies are important for performing global visual exploration tasks such as searching for specific surface markings building a global model of an arbitrary object or recognizing an object in this paper we consider the task of purposefully controlling the motion of an active monocular observer in order to recover a global description of a smooth arbitrarily shaped object we formulate global surface reconstruction as the task of controlling the motion of the observer so that the visible rim slides over the maximal connected reconstructible surface regions intersecting the visible rim at the initial viewpoint we show that these regions are bounded by a subset of the visual event curves defined on the surface by studying the epipolar parameterization we develop two basic strategies that allow reconstruction of a surface region around any point in a reconstructible surface region these strategies control viewpoint to achieve and maintain a well defined geometric relationship with the object s surface rely only on information extracted directly from images e g tangents to the occluding contour and are simple enough to be performed in real time we then show how global surface reconstruction can be provably achieved by 1 appropriately integrating these strategies to iteratively grow the reconstructed regions and 2 obeying four simple rules

robust shape recovery from occluding contours using a linear smoother recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent for three or more views shape recovery is possible and several algorithms have recently been developed for this purpose we present a new approach to the multiframe stereo problem that does not depend on differential measurements in the image which may be noise sensitive instead we use a linear smoother to optimally combine all of the measurements available at the contours and other edges in all of the images this allows us to extract a robust and reasonably dense estimate of surface shape and to integrate shape information from both surface markings and occluding contours results are presented which empirically show that in the presence of noise smoothing over more than three views reduces the error even when the epipolar curve is nonplanar

counterexamples to additivity of minimum output p renyi entropy for p close to 0 complementing recent progress on the additivity conjecture of quantum information theory showing that the minimum output p renyi entropies of channels are not generally additive for p 1 we demonstrate here by a careful random selection argument that also at p 0 and consequently for sufficiently small p there exist counterexamples

squeeze tomography of quantum states a new type of tomogram squeeze tomograms of quantum states of light is introduced which is based on measuring photon statistics after the action of a squeeze operator on the states density matrix the introduced tomograms are photon number probability functions depending on two real parameters which are a scaling factor and a rotation angle the rotation angle and scaling factor label the reference frame in the phase space of field quadratures in which the photon statistics is measured the expressions of the squeeze tomogram in terms of the wigner function and density matrix in quadrature representation are obtained the examples of squeezed states even and odd coherent states and thermal states are considered in detail the multimode generalization is discussed

acquiring 3 d models from sequences of contours this paper explores shape from contour for acquiring 3 d graphics models in this method a continuous sequence of images is taken as an object rotates a smooth convex shape can be estimated instantaneously from its contour and by the first derivative of contour movement trace of contour or contour distribution with time we also analyze shapes that do not satisfy the conditions of smoothness and visibility which are indispensable for modeling an object a region that does not expose as contour yields a nonsmoothness in the tracked contour movement we can thus detect such a region by contour distribution filtering and extract its accurate location by computing the left and right derivatives of the distribution this has not been studied previously these unknown regions are obtained for further investigation using other visual cues a general approach for building a geometrical object model using contours is then described the entire process from silhouettes to a 3 d model is based local computation this is promising for producing shapes in real time our direct goal is to establish 3 d graphics models of human faces for the growing needs of visual communications we have obtained some good results

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

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

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

recursive parametrization and invariant phases of unitary matrices we present further properties of a previously proposed recursive scheme for parametrization of n by n unitary matrices we show that the factors in the recursive formula may be introduced in any desired order the method is used to study the invariant phases of unitary matrices the case of four by four unitary matrices is investigated in detail we also address the question of how to construct symmetric unitary matrices i e unitary matrices u that satisfy the condition uij uji using the recursive approach

pictorial recognition of objects employing affine invariance in the frequency domain describes an efficient approach to pose invariant pictorial object recognition employing spectral signatures of image patches that correspond to object surfaces which are roughly planar based on singular value decomposition svd the affine transform is decomposed into slant tilt swing scale and 2d translation unlike previous log polar representations which were not invariant to slant our log log sampling configuration in the frequency domain yields complete affine invariance the images are preprocessed by a novel model based segmentation scheme that detects and segments objects that are affine similar to members of a model set of basic geometric shapes the segmented objects are then recognized by their signatures using multidimensional indexing in a pictorial dataset represented in the frequency domain experimental results with a dataset of 26 models show 100 percent recognition rates in a wide range of 3d pose parameters and imaging degradations 0 360 spl deg swing and tilt 0 82 spl deg of slant more than three octaves in scale change window limited translation high noise levels 0 db and significantly reduced resolution 1 5

perception of 3 d surfaces from 2 d contours inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision the authors survey classes of techniques proposed in the past and provide a critical analysis they show that two kinds of symmetries in figures which are known as parallel and skew symmetries give significant information about surface shape for a variety of objects they derive the constraints imposed by these symmetries and show how to use them to infer 3 d shape they also discuss the zero gaussian curvature zgc surfaces in depth and show results on the recovery of surface orientation for various zgc surfaces

no signalling assisted zero error capacity of quantum channels and an information theoretic interpretation of the lovasz number we study the one shot zero error classical capacity of a quantum channel assisted by quantum no signalling correlations and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one quantum no signalling correlations are viewed as two input and two output completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal both problems lead to simple semidefinite programmes sdps that depend only on the choi kraus operator space of the channel in particular we show that the zero error classical simulation cost is precisely the conditional min entropy of the choi jamiolkowski matrix of the given channel the zero error classical capacity is given by a similar looking but different sdp the asymptotic zero error classical capacity is the regularization of this sdp and in general we do not know of any simple form interestingly however for the class of classical quantum channels we show that the asymptotic capacity is given by a much simpler sdp which coincides with a semidefinite generalization of the fractional packing number suggested earlier by aram harrow this finally results in an operational interpretation of the celebrated lovasz vartheta function of a graph as the zero error classical capacity of the graph assisted by quantum no signalling correlations the first information theoretic interpretation of the lovasz number

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

multiple view geometry of general algebraic curves we introduce a number of new results in the context of multi view geometry from general algebraic curves we start with the recovery of camera geometry from matching curves we first show how one can compute without any knowledge on the camera the homography induced by a single planar curve then we continue with the derivation of the extended kruppa s equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve as part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus we then establish new results on the reconstruction of general algebraic curves from multiple views we address three different representations of curves i the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions one of degree d and the other of degree d d 1 moreover using this representation we address the problem of homography recovery for planar curves ii dual space representation tangents for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus and iii a new representation to computer vision based on the set of lines meeting the curve which does not require any curve fitting in image space for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone