pattern matching with affine moment descriptors this paper proposes a method for matching images based on their higher order moments without knowing the point correspondences it is assumed that the disparity between the images can be explained by an affine transformation the second order statistics is used to transform the image points into canonical form which reduces the affine matching problem for determining an orthonormal transformation matrix between the two point sets next higher order complex moments are used to solve the remaining transformation these affine moment descriptors are expressed in terms of the central moments of the original data it is also shown that the resulting descriptors can be converted into affine moment invariants a general framework for deriving affine moment descriptors as well as moment invariants is described the experiments carried out with simulated data and real images indicate that the proposed method utilizing the second and third order statistics can provide good alignment results from noisy and spurious observations

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

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

affine invariant pattern recognition using multiscale autoconvolution this paper presents a new affine invariant image transform called multiscale autoconvolution msa the proposed transform is based on a probabilistic interpretation of the image function the method is directly applicable to isolated objects and does not require extraction of boundaries or interest points and the computational load is significantly reduced using the fast fourier transform the transform values can be used as descriptors for affine invariant pattern classification and in this article we illustrate their performance in various object classification tasks as shown by a comparison with other affine invariant techniques the new method appears to be suitable for problems where image distortions can be approximated with affine transformations

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

complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

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

vessiot structure for manifolds of hyperbolic type darboux integrability and symmetry it is well known that if a scalar second order hyperbolic partial differential equation in two independent variables is darboux integrable then its local cauchy problem may be solved by ordinary differential equations in addition such an equation has infinitely many non trivial conservation laws moreover darboux integrable equations have properties in common with infinite dimensional completely integrable systems in this paper we employ a geometric object intrinsically associated with any hyperbolic partial differential equation its hyperbolic structure to study the darboux integrability of the class e of semilinear second order hyperbolic partial differential equations in one dependent and two independent variables it is shown that the problem of classifying the darboux integrable equations in e contains as a subproblem that of classifying the manifolds of p q hyperbolic type of rank 4 and dimension 2k 3 k 2 p 2 q 2 in turn it is shown that the problem of classifying these manifolds in the two lowest cases p q 2 2 2 3 contains as a subproblem the classification problem for lie groups this generalizes classical results of e vessiot the main result is that if an equation in e is 2 2 or 2 3 darboux integrable on the k jets k 2 then its intrinsic hyperbolic structure admits a lie group of symmetries of dimension 2k 1 or 2k 2 respectively it follows that part of the moduli space for the darboux integrable equations in e is determined by isomorphism classes of lie groups the lie group in question is the group of automorphisms of the characteristic systems of the given equation which leaves invariant the foliation induced by the characteristic or riemann invariants of the equation the tangential characteristic symmetries the isomorphism class of the tangential characteristic symmetries is a contact invariant of the corresponding darboux integrable partial differential equation

laplace maps and constraints for a class of third order partial differential operators we explore the existence of a class of generalised laplace maps for third order partial differential operators of the form 1 2 3 a1 2 3 a2 1 3 a3 1 2 a12 3 a23 1 a13 2 a123 and related first order 3 systems and show that they require the satisfaction of constraints on the invariants for such operators

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

affine parameter estimation from the trace transform in this paper we assume that we are given the images of two segmented objects one of which may be an affinely distorted version of the other and wish to recover the values of the parameters of the affine transformation between the two images the images may also differ by the overall level of illumination the multiplicative constant of such difference may also be recovered we present a generic theoretical framework to solve this problem in terms of this framework other proposed methods may be interpreted we show how in this framework one can recover the affine parameters in a way that is robust to various effects such as occlusion and illumination variation the proposed method is generic enough to be applicable also to matching two images that do not depict the same scene or object

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

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

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

belyi functions for hyperbolic hypergeometric to heun transformations abstract a complete classification of belyi functions for transforming certain hypergeometric equations to heun equations is given the considered hypergeometric equations have the local exponent differences 1 k 1 l 1 m that satisfy k l m n and the hyperbolic condition 1 k 1 l 1 m 1 there are 366 galois orbits of belyi functions giving the considered non parametric hypergeometric to heun pull back transformations their maximal degree is 60 which is well beyond reach of standard computational methods to obtain these belyi functions we developed two efficient algorithms that exploit the implied pull back transformations

second noether theorem for quasi noether systems quasi noether differential systems are more general than variational systems and are quite common in mathematical physics they include practically all differential systems of interest at least those that have conservation laws in this paper we discuss quasi noether systems that possess infinite dimensional infinite symmetries involving arbitrary functions of independent variables for quasi noether systems admitting infinite symmetries with arbitrary functions of all independent variables we state and prove an extension of the second noether theorem in addition we prove that infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial and that the associated differential system is under determined we discuss infinite symmetries and infinite conservation laws of two important examples of non variational quasi noether systems the incompressible euler equations and the navier stokes equations in vorticity formulation and we show that the infinite sets of conservation laws involving arbitrary functions of all independent variables are trivial we also analyze infinite symmetries involving arbitrary functions of not all independent variables prove that the fluxes of conservation laws in these cases are total divergences on solutions and demonstrate examples of this situation

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

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

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

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

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

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

the geometrically invariant form of evolution equations we study the evolution of geometric invariants for equations such as the davey stewartson and novikov veselov equations

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

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

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

determination of blur and affine combined invariants by normalization the determination of invariant characteristics is an important problem in pattern recognition in many situations images to be processed are usually subjected to geometric distortion and or blur degradation in this paper we introduce an approach to derive blur and affine combined invariants bai firstly we normalize the image to a standard form by using blur invariant moments as normalization constraints then we construct the blur and affine combined invariants at the standard form using the method proposed in this paper a set of blur and affine combined invariant features can be obtained easily and effectively several experimental results are presented to illustrate the performance of the invariants for simultaneously affine deformed and blur degraded images

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

the gurevich zybin system we present three different linearizable extensions of the gurevich zybin system their general solutions are found by reciprocal transformations in this paper we rewrite the gurevich zybin system as a monge ampere equation by application of reciprocal transformation this equation is linearized infinitely many local hamiltonian structures local lagrangian representations local conservation laws and local commuting flows are found moreover all commuting flows can be written as monge ampere equations similar to the gurevich zybin system the gurevich zybin system describes the formation of large scale structure in the universe second harmonic wave generation is known in nonlinear optics in this paper we prove that the gurevich zybin system is equivalent to a degenerate case of second harmonic generation thus the gurevich zybin system is recognized as a degenerate first negative flow of two component harry dym hierarchy up to two miura type transformations a reciprocal transformation between the gurevich zybin system and degenerate case of the second harmonic generation system is found a new solution for second harmonic generation is presented in implicit form

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

template matching based object recognition with unknown geometric parameters we examine the problem of locating an object in an image when size and rotation are unknown previous work has shown that with known geometric parameters an image restoration method can be useful by estimating a delta function at the object location when the geometric parameters are unknown this method becomes impractical because the likelihood surface to be minimized across size and rotation has numerous local minima and areas of zero gradient we propose a new approach where a smooth approximation of the template is used to minimize a well behaved likelihood surface a coarse to fine approximation of the original template using a diffusion like equation is used to create a library of templates using this library we can successively perform minimizations which are locally well behaved as detail is added to the template the likelihood surface gains local minima but previous estimates place us within a well behaved bowl around the global minimum leading to an accurate estimate numerical experiments are shown which verify the value of this approach for a wide range of values of the geometric parameters

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

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

invariants of hyperbolic partial differential operators we present a construction of a large class of laplace invariants for linear hyperbolic partial differential operators of fairly general form and arbitrary order

second order type changing evolution equations with first order intermediate equations abstract this paper presents a partial classification for c type changing symplectic monge ampere partial differential equations pdes that possess an infinite set of first order intermediate pdes the normal forms will be quasi linear evolution equations whose types change from hyperbolic to either parabolic or to zero the zero points can be viewed as analogous to singular points in ordinary differential equations in some cases intermediate pdes can be used to establish existence of solutions for ill posed initial value problems

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

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

algebraic feature extraction of image for recognition abstract the extraction of image features is one of the fundamental tasks in image recognition up until now there have been several kinds of features to be used for the purpose of image recognition as follows 1 visual features 2 statistical features of pixel 3 transform coefficient features in addition there is another kind of feature which the author believes is very useful i e 4 algebraic features which represent intrinsic attributions of an image singular values sv of image are this kind of feature in this paper we prove that sv feature vector has some important properties of algebraic and geometric invariance and insensitiveness to noise these properties are very useful for the description and recognition of images as an example sv feature vector is used for the problem of recognizing human facial images in this paper using sv feature vector samples of facial images a normal pattern bayes classification model based on sammon s optimal descriminant plane is constructed the experimental result shows that sv feature vector has good performance of class separation

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

some classification results for hyperbolic equations f x y u ux uy uxx uxy uyy 0 abstract we provide a contact invariant characterization for equations of the form u xy a x y u u x b x y u u y c x y u 0 u xy a x y u x b x y u y c x y u 0 uxy c x y u 0 uxy 0 we classify all equations of the form uxy f x y u ux uy 0 for which the two ovsiannikov s invariants are constants these results include characterization of the klein gordon equation uxy u the liouville equation uxy eu and the class of euler poisson darboux equations it is shown that the wave equation uxy 0 liouville equation and the linear equation uxy 2u x y 2 are the only variational equations darboux integrable at level one we also show that a hyperbolic monge ampere equation darboux integrable at level one is equivalent to an equation of type uxy f x y u ux uy 0 we prove that the hyperbolic fermi ulam pasta fpu equation uyy ux 2 uxx is contact equivalent to a linear equation of type uxy c x y u and we classify all fpu equations darboux integrable at level one we also apply our results to equations of type uxy f u ux that describe pseudo spherical surfaces

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

characteristics and the geometry of hyperbolic equations in the plane abstract this paper focuses on the implementation and application of elie cartan s ideas on characteristics for second order non linear hyperbolic equations in the plane the topics include a discussion of both intrinsic and extrinsic contact equivalence a description of the theory of backlund and laplace transformations based on characteristics a geometric approach to the notion of riemann invariants and a study of the various possibilities for their existence resulting in a new simple proof of lie s description of the contact orbit of the wave equation the initial value problem is analyzed from the viewpoint of exterior differential systems and applied to establish a smooth existence theorem with an application to a shock wave problem

affine invariant classification and retrieval of texture images in this paper we propose a new method of extracting affine invariant texture signatures for content based affine invariant image retrieval cbair the algorithm discussed in this paper exploits the spectral signatures of texture images based on spectral representation of affine transform anisotropic scale invariant signatures of orientation spectrum distributions are extracted peaks distribution vector pdv obtained from signature distributions captures texture properties invariant to affine transform the pdv is used to measure the similarity between textures extensive experimental results are included to demonstrate the performance of the method in texture classification and cbair c 2002 pattern recognition society published by elsevier science ltd all rights reserved

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

period computations for covers of elliptic curves in this article we construct algebraic equations for a curve c and a map f to an elliptic curve e with pre specified branching data we do this by determining certain relations that the periods of c and e must satisfy and use these relations to approximate the coefficients to high precision we then conjecture which algebraic numbers the coefficients are and then we prove this conjecture to be correct

characteristic invariants and darboux s method we develop a method that allows us to derive reductions and solutions to hyperbolic systems of partial differential equations the method is based on using functions that are constant in the direction of characteristics of the system these functions generalize well known riemann invariants as applications we consider the gas dynamics system and ideal magnetohydrodynamics equations in special cases we find solutions of these equations depending on some arbitrary functions

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

relationships between symmetries depending on arbitrary functions and integrals of discrete equations the paper is devoted to the conjecture that an equation is darboux integrable if and only if it possesses symmetries that depend on arbitrary functions we note that the results of previous works together prove this conjecture for scalar partial differential equations of the form for autonomous semi discrete and discrete analogues of these equations we prove that the sequence of laplace invariants is terminated by zero for an equation if this equation admits an operator mapping any function of one independent variable into a symmetry of the equation the vanishing of a laplace invariant allows us to construct a formal integral i e an operator that maps symmetries into integrals including generally speaking trivial integrals this paper and the results of previous works together prove a formal version of the aforementioned conjecture for semi discrete and pure discrete cases

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

superposition formulas for exterior differential systems abstract in this article we solve an inverse problem in the theory of quotients for differential equations we characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original the fact that a system can be written as a quotient can be used to find the general solution to these equations some examples are given to demonstrate the theory

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

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

brief review of invariant texture analysis methods this paper considers invariant texture analysis texture analysis approaches whose performances are not affected by translation rotation affine and perspective transform are addressed existing invariant texture analysis algorithms are carefully studied and classified into three categories statistical methods model based methods and structural methods the importance of invariant texture analysis is presented first each approach is reviewed according to its classification and its merits and drawbacks are outlined the focus of possible future work is also suggested

wavelet based affine invariant representation a tool for recognizing planar objects in 3d space a technique is developed to construct a representation of planar objects undergoing a general affine transformation the representation can be used to describe planar or nearly planar objects in a three dimensional space observed by a camera under arbitrary orientations the technique is based upon object contours parameterized by an affine invariant parameter and the dyadic wavelet transform the role of the wavelet transform is the extraction of multiresolution affine invariant features from the affine invariant contour representation a dissimilarity function is also developed and used to distinguish among different object representations this function makes use of the extrema on the representations thus making its computation very efficient a study of the effect of using different wavelet functions and their order or vanishing moments is also carried out experimental results show that the performance of the proposed representation is better than that of other existing methods particularly when objects are heavily corrupted with noise

affine invariant features from the trace transform the trace transform is a generalization of the radon transform that allows one to construct image features that are invariant to a chosen group of image transformations in this paper we propose a methodology and appropriate functionals that can be computed from the image function and which can be used to calculate features invariant to the group of affine transforms we demonstrate the usefulness of the constructed image descriptors in retrieving images from an image database and compare it with relevant state of the art object retrieval methods

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

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

an obstruction to the integrability of a class of non linear wave equations by 1 stable cartan characteristics we examine in detail the cauchy problem for a class of non linear hyperbolic equations in two independent variables this class is motivated by the analysis of the dynamics of a line of non linearly coupled particles by fermi pasta and ulam and extends the recent investigation of this problem by gardner and kamran we find conditions for the existence of a 1 stable cartan characteristic of a pfaffian exterior differential system whose integral curves provide a solution to the cauchy problem the same obstruction to involution is exposed in darboux s method of integration and the two approaches are compared a class of particular solutions to the obstruction is constructed

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

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

application of affine invariant fourier descriptors to recognition of 3 d objects the method of fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation translation rotation scaling and shearing the method is based on a parameterized boundary description which is transformed to the fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions as is demonstrated by processing silhouettes of aircraft maneuvering in three space