interpreting perspective images a fundamental problem in computer vision is how to determine the 3 d spatial orientation of curves and surfaces appearing in an image the problem is generally underconstrained and is complicated by the fact that metric properties such as orientation and length are not invariant under projection under perspective projection the correct model for most real images the transform is nonlinear and therefore hard to invert two constructive methods are presented the first finds the orientation of parallel lines and planes by locating vanishing points and vanishing lines the second determines the orientation of planes by backprojection of two intrinsic properties of contours angle magnitude and curvature

a new generalized computational framework for finding object orientation using perspective trihedral angle constraint this paper investigates a fundamental problem of determining the position and orientation of a three dimensional 3 d object using a single perspective image view the technique is focused on the interpretation of trihedral angle constraint information a new closed form solution based on kanatani s formulation is proposed the main distinguishing feature of the authors method over the original kanatani formulation is that their approach gives an effective closed form solution for a general trihedral angle constraint the method also provides a general analytic technique for dealing with a class of problem of shape from inverse perspective projection by using angle to angle correspondence information a detailed implementation of the authors technique is presented different trihedral angle configurations were generated using synthetic data for testing the authors approach of finding object orientation by angle to angle constraint the authors performed simulation experiments by adding some noise to the synthetic data for evaluating the effectiveness of their method in a real situation it has been found that the authors method worked effectively in a noisy environment which confirms that the method is robust in practical application

an adaptive finite element method for viscoplastic fluid flows in pipes the numerical modelling of the fully developed poiseuille flow of a yield stress fluid in a square section is presented the dead regions in outer corners and the plug region in the center are exhibited numerical computations cover the complete range of the dimensionless number describing the yield stress effect from a newtonian flow to a fully stopped flow the resolution of variational inequalities describing the flow is based on the augmented lagrangian method and a specific mixed finite element method the localization of yield surfaces is approximated by an anisotropic auto adaptive mesh procedure the limit load analysis and the associated limit yield surface are obtained by an extrapolation procedure

segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

quasi invariant parameterisations and matching of curves in images in this paper we investigate quasi invariance on a smooth manifold and show that there exist quasi invariant parameterisations which are not exactly invariant but approximately invariant under group transformations and do not require high order derivatives the affine quasi invariant parameterisation is investigated in more detail and exploited for defining general affine semi local invariants from second order derivatives only the new invariants are implemented and used for matching curve segments under general affine motions and extracting symmetry axes of objects with 3d bilateral symmetry

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

perceptual grouping for generic recognition we address the problem of recognition of generic objects from a single intensity image this precludes the use of purely geometric methods which assume that models are geometrically and precisely designed instead we propose to use descriptions in terms of features and their qualitative geometric relationships to succeed it is clear that these features need to be high level rather than points or lines we propose to detect groups using perceptual organization criteria such as proximity symmetry parallelism and closure the detection of these features is performed in an efficient way using proximity indexing since many groups are created we also perform selection of relevant groups by organizing them into sets of similar perceptual content finally we present an implementation of a recognition system using these sets as primitives it is an efficient colored graph matching algorithm using the adjacency matrix representation of a graph using indexing we retrieve matching hypotheses which are verified against each other with respect to topological constraints groups of consistent hypotheses represent detected model instances in a scene the complete system is illustrated on real images we also discuss further extensions

interpreting image curve from multiframes abstract a method of reconstructing the structure of a rigid space curve from multiframes is presented the problem is formulated as does there exist a unique reconstruction of a general smooth space curve from images if the curve is moving constantly in the space what is the minimum information needed to allow such a reconstruction the motion here is taken to be general but rotates about a fixed axis uniformly the only featured points are the two endpoints of the curve we first establish a necessary and sufficient condition on the number of frames for determining the motion with only two feature points observable also whether the underlying motion meets the formulation of the problem can be checked from the observables next we show that the ambiguities of matching a given nonfeatured point on the curve in one frame are limited to the intersections of a straight line and the image curve on the other frame the ambiguities of matching nonfeature points can then be resolved and the reconstruction of the space curve follows readily experiments and examples are provided to illustrate each step of the method furthermore we find that conclusions obtained by yuille and poggio 8 generalized ordering constraint in the case of parallel projection are either special cases of or can be easily derived from this method

line drawing interpretation bilateral symmetry results previously derived by the author are used to investigate the implication of bilateral symmetry in line drawings it is shown that the line drawing of an orthographically protected surface of revolution exhibits bilateral symmetry about the projection of its axis of revolution irrespective of the viewing direction barring one exception a bilaterally symmetric line drawing is necessarily the orthographic projection of a local surface of revolution whenever its symmetry axis continues to be the projection of a fixed line in space under perturbation of viewpoint the axis of revolution is the invariant preimage of the symmetry axis various line drawing causes are detailed which facilitate the deduction of invariant preimages of symmetry axes and consequently of local surfaces of revolution

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

statistical physics of random binning we consider the model of random binning and finite temperature decoding for slepian wolf codes from a statistical mechanical perspective while ordinary random channel coding is intimately related to the random energy model a statistical mechanical model of disordered magnetic materials it turns out that random binning for slepian wolf coding is analogous to another related statistical mechanical model of strong disorder which we call the random dilution model we use the latter analogy to characterize phase transitions pertaining to finite temperature slepian wolf decoding which are somewhat similar but not identical to those of finite temperature channel decoding we then provide the exact random coding exponent of the bit error rate as a function of the coding rate and the decoding temperature and discuss its properties finally a few modifications and extensions of our results are outlined and discussed

estimation of 3d structure and motion from image corners abstract this paper deals with motion estimation from image corner correspondences in two cases the orthogonal corner and the general corner with known space angles the contribution of the paper is in three folds first the three dimensional structure of a corner is recovered easily from its image by introducing a new coordinate system second it is shown that the one corner and two points correspondences over two views are sufficient to uniquely determine the motion i e the rotation and translation third experiments using both simulated data and real images are conducted which present good results

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

contour based corner detection via angle difference of principal directions of anisotropic gaussian directional derivatives this paper presents a contour based corner detector using the angle difference of the principal directions of anisotropic gaussian directional derivatives andds on contours the noise robust andds can characterize fine directional intensity variations around edge pixels and corners the proposed corner detector consists of three steps extraction of edge map by the canny edge detector improvement of contours by the douglas peucker d p polygonal approximation and filling small gaps between contours and finding corners from contours by using the angle difference of the principal directions of the andds as the corner measure different from the existing contour based detectors where corner measures correspond to the geometric properties of a contour the new corner measure utilizes the directional intensity variations at the pixels on a contour and thus has high angular resolution good localization and noise robustness the proposed detector is compared with the three state of the art detectors from two aspects two test images with ground truths are used to assess its detection capability and localization accuracy twenty four test images with various scenes and without ground truths are used to evaluate its repeatability under affine transforms jpeg compression and noise degradation the experimental results show that the proposed detector attains better overall performance anisotropic directional derivatives are applied to corner detection of images a corner detector using the principal direction of the anisotropic directional derivatives is presented the detector is compared with the three state of the art corner detector the detector behaves better in detection localization repeatability and noise robustness

shape from regular patterns niis paper describes an aigoritlitr1 to obtaitl local surface orierltatiorr frofti the apparetlt surface pattertl distortion in an image we propose a spherical projection to model perspctiue imaging a trtappitlg is debtled based of1 the measurement of the local distortions of a repeated known rexture pattern due io the image projection 77tis mapping maps an apparent shape on the image sphere lo a locus of possible surface orienrations on the gaussian sphere an ireratiw constraint propagation algorithm with the orientations at occluding boundaries reduces possible surface orientations to a unique orientation 7lis algorithm can recover local surface orientation as well as interpolate surjace orientations where no information is auailable xis algorithm is applied to a real image ro demonstrate its perfontlance

robust detection of skewed symmetries by combining local and semi local affine invariants abstract affine invariant feature vector ip and shen image vision comput 16 2 1998 135 146 that captures both local and semi local geometric features around each point of the object boundary is applied here for the detection of skewed symmetries based on the affine invariant shape representation the problem of detecting symmetry axes has been formulated as a problem of detecting lines with known orientations in a local similarity matrix of an object since the feature vector extracts sufficient local and semi local shape information for every point along the object boundary the process of checking symmetric point pairs is thus robust against both noises and deformations moreover our technique is able to detect all the local reflectional symmetries contained in the object various experimental results have shown the robustness and effectiveness of our method in detecting skewed symmetries from both self symmetric objects and generalized objects

using dynamic programming for solving variational problems in vision dynamic programming is discussed as an approach to solving variational problems in vision dynamic programming ensures global optimality of the solution is numerically stable and allows for hard constraints to be enforced on the behavior of the solution within a natural and straightforward structure as a specific example of the approach s efficacy applying dynamic programming to the energy minimizing active contours is described the optimization problem is set up as a discrete multistage decision process and is solved by a time delayed discrete dynamic programming algorithm a parallel procedure for decreasing computational costs is discussed

analyzing skewed symmetries symmetry is pervasive in both man made objects and nature since symmetries project to skew symmetries finding axes of skew symmetry is an important vision task this paper presents a linear time algorithm for finding the axes of skew symmetry where the degree of symmetry is known first we present a review and critique of current methods for finding the axes of skew symmetry next we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a shear symmetry and recovering the shear parameter of a reflexive symmetry using this approach the authors derive a direct non heuristic moment based technique for finding the axes of skew symmetry for skew symmetric figures with degree of symmetry less than five we obtain a closed form solution the method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour s degree of symmetry it is the first algorithm to find the axes of skew symmetry ino n time where n is the number of contour points the method is especially suited to industrial applications where the degree of symmetry is often knowna priori examples of the method are presented for both real and synthetic images and an error analysis of the method is given

improving dynamic programming to solve image registration a new method of dynamic programming dp is presented a picture is paired with a reference map in order to arrive at picture registration an ordered sequence of primitive patterns is formed from the map an attempt is made to locate a similar sequence from the picture using classical picture processing methods this yields a distorted and unordered sequence marked by noise dp is then used to search for a common match to the two sequences both the initial and final registration states are however unknown moreover the continuity of the path is frequently interrupted due to shortcomings in detection or perhaps occlusions thus classical dp algorithms appear to give only poor results under practical conditions when well adapted to treat signals issued from a first order markovian process they can be used as this method shows to treat kth order processes the concept of the virtual state kept in memory suspends broken paths until they can be reconnected thus bridging the existing gaps between the different parts of the path the proposed algorithm has been applied to satellite images with their contours sectioned by clouds the result leads to the guarantee of very good registration in spite of image contours badly hampered by noise and or clouds

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

a tree matching algorithm based on node splitting and merging an algorithm that computes the best matching of two trees is described the degree of mismatch i e the distance is measured in terms of the number of node splitting and merging operations required the proposed tree distance is a more appropriate measurement of structural defonnation than the tree distance measure in terms of the number of insertions deletions and substitutions of tree nodes as defined in previous studies an algorithm that uses a divide and conquer strategy is presented the analysis shows that the time complexity is o nm2 where n and al are the number of nodes of the two trees respectively the algorithm has been implemented on a vax 11 780

distributed rate distortion with common components we describe a scheme for rate distortion with distributed encoding in which the sources to be compressed contain a common component we show that this scheme is optimal in some situations and that it strictly improves upon existing schemes which do not make full use of common components this establishes that independent quantization followed by independent binning is not optimal for the two encoder problem with a distortion constraint on one source we also show that independent quantization and binning is suboptimal for the three encoder problem in which the goal is to reproduce one of the sources losslessly this provides a counterexample that is fundamentally different from one provided earlier by korner and marton the proofs rely on the binary analogue of the entropy power inequality and the existence of a rate loss for the binary symmetric wyner ziv problem

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

on the optimality of binning for distributed hypothesis testing we study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data the aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value for related problems in distributed source coding schemes based on random binning perform well and are often optimal for distributed hypothesis testing however the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process we show that despite this complication binning is optimal for a class of problems in which the goal is to test against conditional independence we then use this optimality result to give an outer bound for a more general class of instances of the problem

matching three dimensional objects using a relational paradigm abstract a relational model for describing three dimensional objects has been designed and implemented the model which provides a rough description to be used at the top level of a hierarchy for describing objects was designed for initial matching attempts on an unknown object each description is in terms of the set of simple parts of an object simple parts can be sticks long thin parts plates flat wide parts and blobs parts that have three significant dimensions the relations include an attribute value table for global properties of the object the properties of the simple parts binary connection and support relationships ternary connection relationships parallel relationships perpendicular relationships and binary constraints an important use of the model is to characterize the similarity and differences between three dimensional objects toward this end we have defined a measure of relational similarity between three dimensional object models and a measure of feature similarity based only on euclidean distance between attribute value tables in a series of computer tests we compare the results of using the two different similarity measures and conclude that the relational similarity is much more powerful than the feature similarity and should be used when grouping the objects in the database for fast access

an algebraic method for detection and recognition of polyhedral objects from a single image abstract this paper proposes an algorithm to recognize rotated scaled or overlapping polyhedral objects using only one orthographic projection the procedure is not based on the numerical solution of nonlinear equations and does not require any a priori knowledge it is an algebraic method for testing whether a cluster of edges and vertices in a line drawing correspond to an orthographic view of a given 3d model it has the advantage of being based on simple algebraic equations which are easy to solve and do not require time consuming numerical procedures

3d object localisation from multi view image detections in this work we present a novel approach to recover objects 3d position and occupancy in a generic scene using only 2d object detections from multiple view images the method reformulates the problem as the estimation of a quadric ellipsoid in 3d given a set of 2d ellipses fitted to the object detection bounding boxes in multiple views we show that a closed form solution exists in the dual space using a minimum of three views while a solution with two views is possible through the use of non linear optimisation and object constraints on the size of the object shape in order to make the solution robust toward inaccurate bounding boxes a likely occurrence in object detection methods we introduce a data preconditioning technique and a non linear refinement of the closed form solution based on implicit subspace constraints results on synthetic tests and on different real datasets involving challenging scenarios demonstrate the applicability and potential of our method in several realistic scenarios

shape from texture general principle abstract the 3d shape of a textured surface is recovered from its projected image on the assumption that the texture is homogeneously distributed our method does not require recognition of the structure regularity periodicity parallelism orthogonality etc of the texture distribution first the homogeneity of a discrete texture is precisely defined in terms of the theory of distributions next distortion of the observed texture due to perspective projection is described in terms of the first fundamental form expressed as a function of the image coordinates based on this result the 3d recovery equations for determining the surface shape are derived for both planar and curved surfaces some numerical schemes for solving these equations are proposed ambiguity in the interpretation of curved surfaces is also analyzed finally some numerical examples for synthetic data are presented and our method is compared with other existing methods

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

hierarchical generalized hough transforms and line segment based generalized hough transforms abstract generalized hough transforms are fast point pattern matching algorithms which have applications in image processing two extensions to generalized hough transforms are described the first allows for matching hierarchically organized point patterns an example concerning image registration using hierarchical point patterns is described the second extension concerns matching patterns of simple geometric objects such as line segments rather than patterns of points

an abstraction based approach to 3 d pose determination from range images an abstraction based paradigm that makes explicit the process of imposing assumptions on data is discussed the units of abstraction are models in which levels of abstraction are determined by the degree of assumption necessary for their application a general to specific refinement process provides a mechanism to proceed gracefully through the abstraction hierarchy this strategy was applied to the recognition and pose determination of objects comprising simple and compound cylindrical and planar surfaces in dense range data a method of computing reliable gaussian and mean curvature sign map descriptors from the polynomial approximations of surfaces is demonstrated a means for determining the pose of constructed geometric forms whose algebraic surface descriptions are nonlinear in terms of their orienting parameters is developed it is shown that biquadratic surfaces are suitable companion linear forms for cylinder approximation and parameter estimation the estimates provide the initial parametric approximations necessary for a nonlinear regression stage to fine tune the estimates by fitting the actual nonlinear form to the data

improved source coding exponents via witsenhausen s rate we provide a novel upper bound on witsenhausen s rate the rate required in the zero error analogue of the slepian wolf problem our bound is given in terms of a new information theoretic functional defined on a certain graph and is derived by upper bounding complementary graph entropy we use the functional along with graph entropy to give a single letter lower bound on the error exponent for the slepian wolf problem under the vanishing error probability criterion where the decoder has full i e unencoded side information we demonstrate that our error exponent can beat the expurgated source coding exponent of csiszar and korner for some sources that have zeroes in the channel matrix connecting the source with the side information an extension of our scheme to the lossy case i e wyner ziv is given for the case in which the side information is a deterministic function of the source the exponent of our improved scheme agrees with the sphere packing bound exactly thus determining the reliability function an application of our functional to zero error channel capacity is also given

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

robust and efficient detection of salient convex groups this paper describes an algorithm that robustly locates salient convex collections of line segments in an image the algorithm is guaranteed to find all convex sets of line segments in which the length of the gaps between segments is smaller than some fixed proportion of the total length of the lines this enables the algorithm to find convex groups whose contours are partially occluded or missing due to noise we give an expected case analysis of the algorithm performance this demonstrates that salient convexity is unlikely to occur at random and hence is a strong clue that grouped line segments reflect underlying structure in the scene we also show that our algorithm run time is o n sup 2 log n nm when we wish to find the m most salient groups in an image with n line segments we support this analysis with experiments on real data and demonstrate the grouping system as part of a complete recognition system

universal coding for the slepian wolf data compression system and the strong converse theorem universal coding for the slepian wolf 1973 data compression system is considered we shall demonstrate based on a simple observation that the error exponent given by csiszar and korner 1980 for the universal coding system can strictly be sharpened in general for a region of relatively higher rates this kind of observation can be carried over also to the case of lower rates outside the slepian wolf region which establishes the strong converse along with the optimal exponent

on the geometric interpretation of image contours abstract in this paper we suggest a computational model for the 3d interpretation of a 2d view based on contour classification and contour interpretation we concentrate on those contours arising from discontinuities in surface orientation we combine a generic surface description well suited for visual tasks with a model of the image formation process in order to derive image contour configurations that are likely to be interpreted in terms of surface contours next we describe a computer algorithm which attempts to interpret image contours on the following grounds first an image analysis process produces a description in terms of contours and relationships between them second among these contours we select those which form a desired configuration third the selected contours are combined with constraints available with the image formation process in order to be interpreted in terms of discontinuities in surface orientation as a consequence there is a dramatic reduction in the number of possible orientations of the associated scene surfaces

on line recognition of cursive korean characters using dp matching and fuzzy concept abstract this paper proposes an on line recognition method of cursive korean characters based on dynamic programming dp matching and fuzzy concept the proposed algorithm invariant to rotation and size reduces greatly the computational requirement of dp matching by matching phonemes rather than character patterns where the angle difference and the ratio of lengths between input and reference patterns are adopted as matching features correct matching of poorly written cursive characters becomes possible by introducing the fuzzy concept in representing phoneme features and the positional relationships between adjacent phonemes computer simulation results show the effectiveness of the proposed algorithm

from image quadrilaterals to symmetrical trapezia abstract this paper concerns the 3 d interpretation of image quadrilaterals as the perspective projections of bilateral symmetric trapezia simple algorithms are described for reconstructing a symmetric trapezium from a given image quadrilateral and for determining the 3 d motion of a symmetric trapezium from two matched image quadrilaterals several results are established and or further verified including the necker reversal ambiguity in the interpretation of image quadrilaterals as the perspective projection of bilateral symmetric trapezia experiments with both synthetic and real images are included to demonstrate the validity of the theoretic results

on stable equal order finite element formulations for incompressible flow problems in this work we discuss stable equal order finite element formulations for incompressible flow problems based on petrov galerkin methods constructed by adding to the classical galerkin formulation least squares of the governing equations continuous and discontinuous pressure interpolations are considered numerical results are presented reinforcing the numerical analysis

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

perspective angle transform principle of shape from angles this paper introduces a new relation called the perspective angle transform pat to deal with shape from angle problems together with its application to 3d configuration recovery from an image three main aspects of pat are presented in this paper the first is the derivation of pat which holds between the apparent and real angles under perspective projection a concept is proposed of a virtual image plane and a new coordinate system named the first perspective moving coordinate fpmc system for analysis of the shape from range problems characteristics of fpmc are discussed briefly the second point is the analysis of pat properties for which the general pat form is introduced on another new coordinate system named the second perspective moving coordinate spmc system using this general form the gradient of the plane including the real angle is constrained on a curve pat curve of the fourth degree in the virtual image plane the characteristics of pat curves and relations between the general pat form and skewed symmetry are summarized briefly the last point concerns an application of pat as an example we treat 3d configuration recovery from three arbitrary line segments in the image plane this recovery corresponds to a generalization of the right angled interpretation problem proposed and discussed by s t barnard a solution to the problem is shown using the general pat form in conjunction with the concept of a virtual crossing point the right angled interpretation problem is ascribed to a quadratic equation a simplified solution is also provided for the case where three line segments have a common crossing point in the image plane this solution is based on the primary pat form and is applicable to interpretation of a trihedral vertex with at least two right angles

three dimensional realization of anomalous pictures an application of picture interpretation theory to toy design anomalous pictures are naively regarded as pictures of impossible objects but some of them are realizable as three dimensional polyhedral objects this paper presents an interactive system for generating the unfolded surfaces of those objects thus offering toy material from which children can make impossible objects

image registration by matching relational structures abstract we present a method of image registration where we use relational structures as representations of images and we register two images by finding a match between the two relational structures it is better than traditional cross correlation like techniques in several aspects it is insensitive to scaling rotation gray level modification and small relative motion between the two images the matching process makes use of star structures which have several advantages over conventional node structures

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

graph decomposition a new key to coding theorems a new and simple method is proposed for finding good encoders both for channels and for sources with side information this method relies on the continuous version of a graph decomposition result of lovasz the presently known best exponential error bounds for both problems follow in a unified manner with an improvement on the source coding bound the previous bounds for universal codes of the authors and marton are also improved

maxentropic markov chains corresp the markov chain that has maximum entropy for given first and second moments is determined the solution provides a discrete analog to the continuous gauss markov process

volumetric descriptions from a single intensity image since the early days of computer vision research shape from contour has been one of the most challenging problems many researchers in the field have attempted to understand this problem and proposed different approaches to solve it shape from contour still remains one of the hardest problems in the field the problem has two major difficulties first 2d properties of contours of viewed objects are generally not sufficient by themselves to uniquely determine 3d shape as one dimension is lost in the projection second real images produce imperfect contours that make their interpretation particularly difficult the first problem has received some attention in the research community but in the context of perfect contours the second one however has received very little in this work we propose a promising methodology to address this last problem for a large class of objects generalized cylinders it is based on exploiting mathematical invariant properties of the contours of generalized cylinders in a perceptual grouping approach we show that using these properties greatly helps addressing the figure ground problem in a more rigorous way than previous intuitive perceptual grouping methods our approach exploits the interplay between local and global features by handling different levels of the feature hierarchy we have developed and implemented a method that handles shgcs in complex seenes with markings and occlusion we demonstrate the application of our method of shape description and scene segmentation on complex real images we also demonstrate the usage of the obtained descriptions for recovery of complete 3 d object centered descriptions of viewed objects from a single intensity image

toward object based heuristics recovering the 3 d shape of an object from its 2 d image contour is an important problem in computer vision in this correspondence the author motivates and develops two object based heuristics the structured nature of objects is the motivation for the nonaccidental alignment criterion parallel coordinate axes within the object s bounding contour correspond to object centered coordinate axes the regularity and symmetry inherent in many man made objects is the motivation for the orthogonal basis constraint an oblique set of coordinate axes in the image is presumed to be the projection of an orthogonal set of 3 d coordinate axes in the scene these object based heuristics are used to recover shape in both real and synthetic images

the probabilistic peaking effect of viewed angles and distances with application to 3 d object recognition two novel probabilistic models for viewed angles and distances are derived using an observability sphere method the method which is based on the assumption that the prior probability density is isotropic for all viewing orientations can be used for the computation of observation probabilities for object s aspects features and probability densities of their quantitative attributes using the sphere it is discovered that the probability densities of viewed angles distances and even projected curvature have sharp peaks at their original values from this peaking effect it is concluded that in most cases the values of angles and distances are being altered only slightly by the imaging process and they can still serve as a strong cue for model based recognition the probabilistic models for 3 d object recognition from monocular images are used to form the angular elements that are needed the objects are represented by their linear features and specific points primitives using the joint density model of angles and distances the probabilities of initial matching hypotheses and mutual information coefficients are estimated these results are then used for object recognition by optimal matching search and stochastic labeling schemes various synthetic and real objects are recognized by this approach

recognition of polyhedral objects using triplets of projected spatial edges based on a single perspective image abstract a novel and intuitive mathematical formulation is proposed for the interpretation of the geometric relationships of a triple of spatial edges and their perspective projection forming image lines no restriction is imposed on the configuration of the triple of spatial edges an eighth degree polynomial equation explicitly defined by the space angles between the corresponding three spatial edges in an object frame is derived the crux of this representation is that the angular attributes of pairs of spatial edges are expressed in an object independent coordinate system an effective hypothesis generation scheme is proposed which can take advantage of the representation in the proposed recognition framework triples of connected spatial edges and trihedral vertices are employed as key features for model invocation hypothesis generation and pose estimation extensive experiments are performed to verify the plausibility and robustness of the proposed recognition methods in general the success rate for identifying and localising polyhedral objects using the proposed recognition method is relatively high

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

reliability in source coding with side information we study error exponents for source coding with side information both achievable exponents and converse bounds are obtained for the following two cases lossless source coding with coded information and lossy source coding with full side information wyner ziv these results recover and extend several existing results on source coding error exponents and are tight in some circumstances our bounds have a natural interpretation as a two player game between nature and the code designer with nature seeking to minimize the exponent and the code designer seeking to maximize it in the wyner ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events the gaussian and binary erasure cases are examined in detail

a moment based approach for deskewing rotationally symmetric shapes the covariance matrix of a pattern is composed by its second order central moments for a rotationally symmetric shape its covariance matrix is a scalar identity matrix in this work we apply this property to restore the skewed shape of rotational symmetry the relations between the skew transformation matrix and the covariance matrices of original and skewed shapes are derived by computing the covariance matrix of the skewed shape and letting the covariance matrix of the original shape be a scalar identity matrix the skew transformation matrix can be solved then the rotationally symmetric shape can be recovered by multiplying the inverse transformation matrix with the skewed shape the method does not rely on continuous contours and is robust to noise because only the second order moments of the input shape are required experimental results are also presented

application of elliptic fourier descriptors to symmetry detection under parallel projection in this paper the method of elliptic fourier descriptors using arc length parameterization is applied to tackle the problem of detection and recovery of symmetry under parallel projection a simple and fast iteration algorithm together with the invariants of symmetry provides sufficient information for the detection and recovery of symmetry under parallel projection the proposed method has been extensively tested using symmetric figures under different parallel projections simulation results of the algorithm are presented the extension of this method for planar object recognition under parallel projection is also addressed

optimum tradeoffs between the error exponent and the excess rate exponent of variable rate slepian wolf coding we analyze the optimal tradeoff between the error exponent and the excess rate exponent for variable rate slepian wolf codes in particular we first derive upper converse bounds on the optimal error and excess rate exponents and then lower achievable bounds via a simple class of variable rate codes which assign the same rate to all source blocks of the same type class then using the exponent bounds we derive bounds on the optimal rate functions namely the minimal rate assigned to each type class needed in order to achieve a given target error exponent the resulting excess rate exponent is then evaluated iterative algorithms are provided for the computation of both bounds on the optimal rate functions and their excess rate exponents the resulting slepian wolf codes bridge between the two extremes of fixed rate coding which has minimal error exponent and maximal excess rate exponent and average rate coding which has maximal error exponent and minimal excess rate exponent

the complexity of understanding line drawings of origami scenes this paper deals with the interpretation of line drawings of origami scenes kanade 1980 that is scenes obtained by assembling planar panels of negligible thickness and it addresses the computational complexity of the problem of consistently assigning suitable labels to the segments describing 3d properties as convexity concavity and occlusion labeling problem the main results of the paper are the following a the labeling problem for line drawings of origami scenes is np as for the case of trihedral scenes b the problem remains np even if the location of the vanishing points in the image plane is given whereas for trihedral scenes the problem was polynomially solvable c in case the vanishing points are known the labeling problem can be subdivided into two subproblems the paneling problem and the labeling a paneled line drawing problem which are both polynomially solvable there may be however exponentially many legal panelings to check against labelability

linear codes for sources and source networks error exponents universal coding for slepian wolf source networks the error exponents obtained by korner marton and the author are shown to be universally attainable by linear codes also improved exponents are derived for linear codes with large rates specializing the results to simple discrete memoryless sources reveals their relationship to the random coding and expurgated bounds for channels with additive noise one corollary is that there are universal linear codes for this class of channels which attain the random coding error exponent for each channel in the class the combinatorial approach of csiszar korner marton is used in particular all results are derived from a lemma specifying good encoders in terms of purely combinatorial properties

a shape from shading analysis for a single perspective image of a polyhedron a shape from shading analysis for a single perspective image of a polyhedron is presented given a single perspective image of a polyhedron the depth of any point of the polyhedron from the camera the direction of the light source illuminating the polyhedron and the albedo of the polyhedron a system of algebraic equations are derived which when combined with edge information quantitatively describes the shape of the polyhedron this analysis is best possible in the sense that if any component of what the author has assumed is omitted no similar analysis can provide the same results

learning visual models from shape contours using multiscale convex concave structure matching a novel approach is proposed for learning a visual model from real shape samples of the same class the approach can directly acquire a visual model by generalizing the multiscale convex concave structure of a class of shapes that is the approach is based on the concept that shape generalization is shape simplification wherein perceptually relevant features are retained the simplification does not mean the approximation of shapes but rather the extraction of the optimum scale convex concave structure common to shape samples of the class the common structure is obtained by applying the multiscale convex concave structure matching method to all shape pairs among given shape samples of the class and by integrating the matching results the matching method is applicable to heavily deformed shapes and is effectively implemented with dynamic programming techniques the approach can acquire a visual model from a few samples without any a priori knowledge of the class the obtained model is very useful for shape recognition results of applying the proposed method are presented

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

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

on zero error source coding with decoder side information let x y be a pair of random variables distributed over a finite product set v spl times w according to a probability distribution p x y the following source coding problem is considered the encoder knows x while the decoder knows y and wants to learn x without error the minimum zero error asymptotic rate of transmission is shown to be the complementary graph entropy of an associated graph thus previous results in the literature provide upper and lower bounds for this minimum rate further these bounds are tight for the important class of perfect graphs the algorithmic aspects of instantaneous code design are considered next it is shown that optimal code design is np hard an optimal code design algorithm is derived polynomial time suboptimal algorithms are also presented and their average and worst case performance guarantees are established

recovery of 3 d objects with multiple curved surfaces from 2 d contours abstract inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision often techniques to solve this problem examine each surface in the scene separately whereas our perception of their shapes clearly depends on the interplay between them as well in this paper we describe a technique that attempts to recover the shapes of all the surfaces of an object simultaneously though it is limited to objects made of zero gaussian curvature surfaces our technique is based on an analysis of three kinds of symmetries defined in the paper and the constraints that derive from them and from other boundaries this technique uses some of the constraints developed in an earlier paper that was limited to examining a zero gaussian curvature surface cut by parallel planes this restriction has been removed here and the constraints have been reformulated to allow integration of constraints from all the neighboring surfaces results on some complex examples are shown

identification of riccati dynamics under perspective and orthographic observations the problem of identifying motion and shape parameters of a planar object undergoing a riccati motion from the associated optical flow generated on the image plane of a single ccd camera is studied the optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections an important result we show is that under perspective projection the parameters of a specific riccati dynamics that extend the well known rigid motion can be identified up to choice of a sign the paper also discusses other riccati equations obtained from quadratic extension of a rigid motion and affine motion for each of the various motion models considered and for each of the two projection models we show that the extent to which motion and shape parameters can be recovered from optical flow can in fact be recovered from the linear approximation of the optical flow we also extend our analysis to a pair of cameras

3 d model localization using high resolution reconstruction of monocular image sequences in this paper we present a complete system for the recognition and localization of a three dimensional 3 d model from a sequence of monocular images with known motion the originality of this system is twofold first it uses a purely 3 d approach starting from the 3 d reconstruction of the scene and ending by the 3 d matching of the model second unlike most monocular systems we do not use token tracking to match successive images rather subpixel contour matching is used to recover more precisely complete 3 d contours in contrast with the token tracking approaches which yield a representation of the 3 d scene based on disconnected segments or points this approach provides us with a denser and higher level representation of the scene the reconstructed contours are fused along successive images using a simple result derived from the kalman filter theory the fusion process increases the localization precision and the robustness of the 3 d reconstruction finally corners are extracted from the 3 d contours they are used to generate hypotheses of the model position using a hypothesize and verify algorithm that is described in detail this algorithm yields a robust recognition and precise localization of the model in the scene results are presented on infrared image sequences with different resolutions demonstrating the precision of the localization as well as the robustness and the low computational complexity of the algorithms

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

curved glide reflection symmetry detection we generalize the concept of bilateral reflection symmetry to curved glide reflection symmetry in 2d euclidean space such that classic reflection symmetry becomes one of its six special cases we propose a local feature based approach for curved glide reflection symmetry detection from real unsegmented 2d images furthermore we apply curved glide reflection axis detection for curved reflection surface detection in 3d images our method discovers groups and connects statistically dominant local glide reflection axes in an axis parameter space aps without preassumptions on the types of reflection symmetries quantitative evaluations and comparisons against state of the art algorithms on a diverse 64 test image set and 1 125 swedish leaf data images show a promising average detection rate of the proposed algorithm at 80 and 40 percent respectively and superior performance over existing reflection symmetry detection algorithms potential applications in computer vision particularly biomedical imaging include saliency detection from unsegmented images and quantification of deviations from normality we make our 64 test image set publicly available

interpretation of straight line correspondences using angular relations abstract formal analysis of the structure from motion problem has produced computational schemes that are often unstable and sensitive to image measurement errors this is in part due to the fact that the formal analysis is mainly concerned as it should be with the most general cases treating special cases with marginal interest however special cases abound in man made environments their occurrence if ascertained simplifies drastically the task of 3d interpretation after examining the problem of interpreting general configurations of lines in space this paper proposes a number of simple and efficient computational units that are tuned to the occurrence of special line configurations the process of propagation which allows interpretation to spread over the image is also advocated such computational units and processes can be organized in a rule based framework where the occurrence of special configurations can either be tested directly or hypothesized and used until an inconsistency is demonstrated

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

a generalized method for 3d object location from single 2d images abstract a method is presented to solve for the three dimensional 3d object position and orientation from single two dimensional 2d images based on a systematic hierarchy of features primitive features generalized features and compound structures a virtual viewpoint analysis shows that a feature centered coordinate system allows us to drastically reduce the mathematical complexity of the inverse projection problem for higher order curves at the heart of the matchings are the matching functions for primitive features which are point to point correspondence line to line correspondence and ellipse to ellipse correspondence parametric matching by generalized features is used to solve for viewpoints at any stage of matching the generalized features can be viewed as the generalization of features used by previous researchers the matching method goes top down and then bottom up if necessary models of the objects are analyzed first in the top down process search starts from the most complex features to the least complex features in the bottom up process the least complex generalized features are used to solve for initial viewpoints the viewpoints are further refined by matching the compound structures which are obtained by merging the consistent generalized features the contributions include 1 solving the problem of ellipse to ellipse correspondence thus extending the class of recognizable objects 2 the generalized features can assume various configurations thus enabling the system to detect a multitude of features 3 parametric matching instead of point point matching makes the algorithm robust 4 the top down bottom up strategy combines efficiency with robustness

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

a regularized stabilized mixed finite element formulation for viscoplasticity of bingham type abstract in this article we present a new mixed stabilized regularized finite element formulation in primitive variables with continuous velocity and discontinuous pressure interpolations for the steady flow of an incompressible fluid of bingham type this formulation is based on an augmented lagrangian regularization technique and a least squares stabilization method mathematical analyses are performed for the new formulation in terms of stability existence and uniqueness of the solution optimal orders of convergence are obtained mathematically improving on classical methods which also present limitations as regards the values of the yield stress numerical results are presented confirming the theory developed here and they show the robustness of the new method with stability obtained for the velocity and especially for the pressure when the yield stress is very high

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability