structure and motion from line segments in multiple images this paper presents a new method for recovering the three dimensional structure of a scene composed of straight line segments using the image data obtained from a moving camera the recovery algorithm is formulated in terms of an objective function which measures the total squared distance in the image plane between the observed edge segments and the projections perspective of the reconstructed lines this objective function is minimized with respect to the line parameters and the camera positions to obtain an estimate for the structure of the scene the effectiveness of this approach is demonstrated quantitatively through extensive simulations and qualitatively with actual image sequences the implementation is being made publicly available

regularized bundle adjustment to model heads from image sequences without calibration data we address the structure from motion problem in the context of head modeling from video sequences for which calibration data is not available this task is made challenging by the fact that correspondences are difficult to establish due to lack of texture and that a quasi euclidean representation is required for realism we have developed an approach based on regularized bundle adjustment it takes advantage of our rough knowledge of the head s shape in the form of a generic face model it allows us to recover relative head motion and epipolar geometry accurately and consistently enough to exploit a previously developed stereo based approach to head modeling in this way complete and realistic head models can be acquired with a cheap and entirely passive sensor such as an ordinary video camera with minimal manual intervention we chose to demonstrate and evaluate our technique mainly in the context of head modeling we do so because it is the application for which all the tools required to perform the complete reconstruction are available to us we will however argue that the approach is generic and could be applied to other tasks such as body modeling for which generic facetized models exist

camera self calibration from bivariate polynomials derived from kruppa s equations this paper presents a new set of equations for the self calibration of a moving camera with constant intrinsic parameters unlike most existing methods that require solving equations in three or more unknowns the proposed equations are only bivariate in particular we show that the three scale factors appearing in the kruppa s equations that are due to a triplet of images are not independent but rather closely related this relationship is used to derive sextic bivariate polynomial equations and allow the recovery of the unknown scale factors using a homotopy continuation method once the scale factors are calculated an estimate of kruppa s coefficients can be linearly retrieved and then refined through a nonlinear least squares optimization procedure the results of our experiments conducted on simulated data as well as the three dimensional structure reconstruction using real images are also presented in the paper

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

a tensor based algorithm for high order graph matching this paper addresses the problem of establishing correspondences between two sets of visual features using higher order constraints instead of the unary or pairwise ones used in classical methods concretely the corresponding hypergraph matching problem is formulated as the maximization of a multilinear objective function over all permutations of the features this function is defined by a tensor representing the affinity between feature tuples it is maximized using a generalization of spectral techniques where a relaxed problem is first solved by a multidimensional power method and the solution is then projected onto the closest assignment matrix the proposed approach has been implemented and it is compared to state of the art algorithms on both synthetic and real data

independent motion detection in 3d scenes this paper presents an algorithmic approach to the problem of detecting independently moving objects in 3d scenes that are viewed under camera motion there are two fundamental constraints that can be exploited for the problem 1 two multiview camera motion constraint for instance the epipolar trilinear constraint and 2 shape constancy constraint previous approaches to the problem either use only partial constraints or rely on dense correspondences or flow we employ both the fundamental constraints in an algorithm that does not demand a priori availability of correspondences or flow our approach uses the plane plus parallax decomposition to enforce the two constraints it is also demonstrated that for a class of scenes called sparse 3d scenes in which genuine parallax and independent motions may be confounded how the plane plus parallax decomposition allows progressive introduction and verification of the fundamental constraints results of the algorithm on some difficult sparse 3d scenes are promising

feature vector field and feature matching in this paper we propose a feature vector field for images which is built by the inner products and exterior products of image gradients the feature vector field effectively represents image edges and feature points including corners and edge points with big curvature using the feature vector field some novel descriptors are constructed for point matching and curve matching the descriptors are all invariant to image euclidean transformations and linear intensity changes the experiments show that the descriptors also have a good adaptability to small image affine transformation jpeg compression and nonlinear changes of intensity

geometry of single axis motions using conic fitting previous algorithms for recovering 3d geometry from an uncalibrated image sequence of a single axis motion of unknown rotation angles are mainly based on the computation of two view fundamental matrices and three view trifocal tensors we propose three new methods that are based on fitting a conic locus to corresponding image points over multiple views the main advantage is that determining only five parameters of a conic from one corresponding point over at least five views is simpler and more robust than determining a fundamental matrix from two views or a trifocal tensor from three views it is shown that the geometry of single axis motion can be recovered either by computing one conic locus and one fundamental matrix or by computing at least two conic loci a maximum likelihood solution based on this parametrization of the single axis motion is also described for optimal estimation using three or more loci the experiments on real image sequences demonstrate the simplicity accuracy and robustness of the new methods

on the stability of normalized powell sabin b splines in this paper we show that the normalized powell sabin b splines form a stable basis for the max norm the approximation constants depend only on the smallest angle in the underlying triangulation since the b splines refer to the size of the powell sabin triangles we find that small powell sabin triangles yield better approximation constants than big powell sabin triangles next in addition to the max norm we treat the lp norm here the approximation constants depend also on a fraction proper to the triangulation thus the b splines are not stable for the lp norm finally as a special case we consider the b spline bases obtained from powell sabin triangles with minimal area and pay extra attention to the approximation constants for the max norm

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

real time range acquisition by adaptive structured light the goal of this paper is to provide a self adaptive system for real time range acquisition reconstructions are based on a single frame structured light illumination instead of using generic static coding that is supposed to work under all circumstances system adaptation is proposed this occurs on the fly and renders the system more robust against instant scene variability and creates suitable patterns at startup a continuous trade off between speed and quality is made a weighted combination of different coding cues based upon pattern color geometry and tracking yields a robust way to solve the correspondence problem the individual coding cues are automatically adapted within a considered family of patterns the weights to combine them are based on the average consistency with the result within a small time window the integration itself is done by reformulating the problem as a graph cut also the camera projector configuration is taken into account for generating the projection patterns the correctness of the range maps is not guaranteed but an estimation of the uncertainty is provided for each part of the reconstruction our prototype is implemented using unmodified consumer hardware only and therefore is cheap frame rates vary between 10 and 25 fps dependent on scene complexity

image stitching by line guided local warping with global similarity constraint abstract low textured image stitching remains a challenging problem it is difficult to achieve good alignment of images and it is easy to break images structures are often broken due to insufficient and unreliable point correspondences moreover because of the viewpoint variations between multiple images the stitched images suffer from projective distortions to solve these problems this paper presents a line guided local warping method with a global similarity constraint for image stitching line features which serve well for geometric descriptions and scene constraints are employed to guide image stitching accurately on one hand the line features are integrated into a local warping model through a designed weight function on the other hand line features are adopted to impose strong geometric constraints including line correspondence and line colinearity to improve the stitching performance through mesh optimization to mitigate projective distortions we adopt a global similarity constraint which is integrated with the projective warps via a designed weight strategy this constraint causes the final warp to slowly change from a projective to a similarity transformation across the image finally the images undergo a two stage alignment scheme that provides accurate alignment and reduces projective distortion we evaluate our method on a series of images and compare it with several other methods the experimental results demonstrate that the proposed method provides a convincing stitching performance and that it outperforms other state of the art methods

some properties of the e matrix in two view motion estimation in the eight point linear algorithm for determining 3d motion structure from two perspective views using point correspondences the e matrix plays a central role the e matrix is defined as a skew symmetrical matrix containing the translation components postmultiplied by a rotation matrix the authors show that a necessary and sufficient condition for a 3 3 matrix to be so decomposable is that one of its singular values is zero and the other two are equal several other forms of this property are presented some applications are briefly described

multiple motion segmentation with level sets segmentation of motion in an image sequence is one of the most challenging problems in image processing while at the same time one that finds numerous applications to date a wealth of approaches to motion segmentation have been proposed many of them suffer from the local nature of the models used global models such as those based on markov random fields perform in general better in this paper we propose a new approach to motion segmentation that is based on a global model the novelty of the approach is twofold first inspired by recent work of other researchers we formulate the problem as that of region competition but we solve it using the level set methodology the key features of a level set representation as compared to active contours often used in this context are its ability to handle variations in the topology of the segmentation and its numerical stability the second novelty of the paper is the formulation in which unlike in many other motion segmentation algorithms we do not use intensity boundaries as an accessory the segmentation is purely based on motion this permits accurate estimation of motion boundaries of an object even when its intensity boundaries are hardly visible since occasionally intensity boundaries may prove beneficial we extend the formulation to account for the coincidence of motion and intensity boundaries in addition we generalize the approach to multiple motions we discuss possible discretizations of the evolution pde equations and we give details of an initialization scheme so that the results could be duplicated we show numerous experimental results for various formulations on natural images with either synthetic or natural motion

the cycle consistency matrix approach to absorbing sets in separable circulant based ldpc codes for low density parity check ldpc codes operating over additive white gaussian noise channels and decoded using message passing decoders with limited precision absorbing sets have been shown to be a key factor in error floor behavior focusing on this scenario this paper introduces the cycle consistency matrix ccm as a powerful analytical tool for characterizing and avoiding absorbing sets in separable circulant based scb ldpc codes scb codes include a wide variety of regular ldpc codes such as array based ldpc codes as well as many common quasi cyclic codes as a consequence of its cycle structure each potential absorbing set in an scb ldpc code has a ccm and an absorbing set can be present in an scb ldpc code only if the associated ccm has a nontrivial null space ccm based analysis can determine the multiplicity of an absorbing set in an scb code and ccm based constructions avoid certain small absorbing sets completely while these techniques can be applied to an scb code of any rate lower rate scb codes can usually avoid small absorbing sets because of their higher variable node degree this paper focuses attention on the high rate scenario in which the ccm constructions provide the most benefit simulation results demonstrate that under limited precision decoding the new codes have steeper error floor slopes and can provide one order of magnitude of improvement in the low frame error rate region

on near best discrete quasi interpolation on a four directional mesh spline quasi interpolants are practical and effective approximation operators in this paper we construct qis with optimal approximation orders and small infinity norms called near best discrete quasi interpolants which are based on w splines i e b splines with octagonal supports on the uniform four directional mesh of the plane these quasi interpolants are exact on some space of polynomials and they minimize an upper bound of their infinity norms depending on a finite number of free parameters we show that this problem has always a solution in general nonunique concrete examples of such quasi interpolants are given in the last section

hierarchical stereo and motion correspondence using feature groupings hierarchical feature based stereo matching and motion correspondence algorithms are presented the hierarchy consists of lines vertices edges and surfaces matching starts at the highest level of the hierarchy surfaces and proceeds to the lowest lines higher level features are easier to match because they are fewer in number and more distinct in form these matches then constrain the matches at lower levels perceptual and structural relations are used to group matches into islands of certainty a truth maintenance system tms is used to enforce grouping constraints and eliminate inconsistent match groupings the tms is also used to carry out belief revisions necessitiated by additions deletions and confirmations of feature and match hypotheses

conic reconstruction and correspondence from two views conics are widely accepted as one of the most fundamental image features together with points and line segments the problem of space reconstruction and correspondence of two conics from two views is addressed in this paper it is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views given the relative orientation of the two views these two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics a unified closed form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images

fiducial facial point extraction using a novel projective invariant automatic extraction of fiducial facial points is one of the key steps to face tracking recognition and animation great facial variations especially pose or viewpoint changes typically degrade the performance of classical methods recent learning or regression based approaches highly rely on the availability of a training set that covers facial variations as wide as possible in this paper we introduce and extend a novel projective invariant named the characteristic number cn which unifies the collinearity cross ratio and geometrical characteristics given by more 6 points we derive strong shape priors from cn statistics on a moderate size 515 of frontal upright faces in order to characterize the intrinsic geometries shared by human faces we combine these shape priors with simple appearance based constraints e g texture edge and corner into a quadratic optimization thereafter the solution to facial point extraction can be found by the standard gradient descent the inclusion of these shape priors renders the robustness to pose changes owing to their invariance to projective transformations extensive experiments on the labeled faces in the wild labeled face parts in the wild and helen database and cross set faces with various changes demonstrate the effectiveness of the cn based shape priors compared with the state of the art

superconvergent local quasi interpolants based on special multivariate quadratic spline space over a refined quadrangulation abstract in this paper we first recall some results concerning the construction and the properties of quadratic b splines over a refinement of a quadrangulation of a planar domain introduced recently by lamnii et al then we introduce the b spline representation of hermite interpolant in the special space s 2 1 0 of any polynomial or any piecewise polynomial over refined quadrangulation of after that we use this b representation for constructing several superconvergent discrete quasi interpolants the new results that we present in this paper are an improvement and a generalization of those developed in the above cited paper

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

analytical lower bounds on the size of elementary trapping sets of variable regular ldpc codes with any girth and irregular ones with girth 8 in this paper we give lower bounds on the size of a b elementary trapping sets etss of variable regular ldpc codes with any girth g and irregular ones with girth 8 where a is the size and b is the number of degree one check nodes our proposed lower bounds are analytical applicable to all values of g and b based on graph theories and tighter than the existing ones in the literature our results mostly depend on the girth we also propose results which are independent of the girth and rely on the variables a b gamma and the column weight value we obtain the tightest lower bounds on the size of etss of variable regular ldpc codes with girth eight these results provide us with a chance to present a method to achieve the minimum size of etss of irregular ldpc codes with girth especially those whose column weight values are a subset of 2 3 4 5 6 and fulfill the inequality b a moreover we present a range of numerical results about a b etss with girths 8 and 10 to compare the tightness between our proposed lower bounds and the existing bounds in the literature

flexible syntactic matching of curves and its application to automatic hierarchical classification of silhouettes curve matching is one instance of the fundamental correspondence problem our flexible algorithm is designed to match curves under substantial deformations and arbitrary large scaling and rigid transformations a syntactic representation is constructed for both curves and an edit transformation which maps one curve to the other is found using dynamic programming we present extensive experiments where we apply the algorithm to silhouette matching in these experiments we examine partial occlusion viewpoint variation articulation and class matching where silhouettes of similar objects are matched based on the qualitative syntactic matching we define a dissimilarity measure and we compute it for every pair of images in a database of 121 images we use this experiment to objectively evaluate our algorithm first we compare our results to those reported by others second we use the dissimilarity values in order to organize the image database into shape categories the veridical hierarchical organization stands as evidence to the quality of our matching and similarity estimation

stereo calibration from rigid motions we describe a method for calibrating a stereo pair of cameras using general or planar motions the method consists of upgrading a 3d projective representation to affine and to euclidean without any knowledge neither about the motion parameters nor about the 3d layout we investigate the algebraic properties relating projective representation to the plane at infinity and to the intrinsic camera parameters when the camera pair is considered as a moving rigid body we show that all the computations can be carried out using standard linear resolutions techniques an error analysis reveals the relative importance of the various steps of the calibration process projective to affine and affine to metric upgrades extensive experiments performed with calibrated and natural data confirm the error analysis as well as the sensitivity study performed with simulated data

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

analysis and enumeration of absorbing sets for non binary graph based codes in this work we first provide the definition of absorbing sets for linear channel codes over non binary alphabets in a graphical representation of a non binary channel code an absorbing set can be described by a collection of topological and edge labeling conditions in the non binary case the equations relating neighboring variable and check nodes are over a non binary field and the edge weights are given by the non zero elements of that non binary field as a consequence it becomes more difficult for a given structure to satisfy the absorbing set constraints compared to the binary case this observation in part explains the superior performance of non binary codes over their binary counterparts we show that the conditions in the non binary absorbing set definition can be simplified in the case of non binary elementary absorbing sets based on these simplified conditions we provide design guidelines for finite length non binary codes free of small non binary elementary absorbing sets these guidelines demonstrate that even under the preserved topology the performance of a non binary graph based code in the error floor region can be substantially improved by manipulating edge weights so as to avoid small absorbing sets our various simulation results suggest that the proposed non binary absorbing set definition is useful for a range of code constructions and decoders finally by using both insights from graph theory and combinatorial techniques we establish the asymptotic distribution of non binary elementary absorbing sets for regular code ensembles

image sequence analysis using relational structures abstract time varying images are usually analyzed to obtain a description of the observed objects and of their actions an abstraction process is necessary which converts the input images into symbolic descriptions the attributes of image symbols and the relationship between symbols are computed from the sampled intensity or colour measurements relational structures are a formal tool to describe not only the symbolic image representation but furthermore stored models as prototypes of objects and objects as instantiations of such prototypes following this paradigm an essential task of image sequence analysis is the generation of mappings between images to establish the correspondence relationship and between images and prototypes to identify objects different types of morphisms between relational structures rs morphisms are proposed together with an approach for computing them by searching for cliques in a compatibility graph of hypothetical assignments of elements from both structures the common formalism presented here aims at a unification of methods for those steps necessary to instantiate objects and follow them through the sequence one practical reason for this attempt is to make relational database systems available to store and retrieve the large amount of data whidch might be generated during the exploration of a real world image sequence

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

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

minimizing the quasi interpolation error for bivariate discrete quasi interpolants we define a class of discrete quasi interpolants based on bivariate box splines by imposing the exactness on a space of polynomials of total degree depending on the box spline and minimizing a constant appearing in the leading term of an appropriate quasi interpolation error estimate we give some c 1 quadratic and c 2 quartic examples and compare them with other well known quasi interpolants

lines and points in three views and the trifocal tensor this paper discusses the basic role of the trifocal tensor in scene reconstruction from three views this 3 times 3 times 3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two view case in particular the trifocal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views it is further shown in this paper that the trifocal tensor is essentially identical to a set of coefficients introduced by shashua to effect point transfer in the three view case this observation means that the 13 line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences from the trifocal tensor the camera matrices of the images may be computed and the scene may be reconstructed for unrelated uncalibrated cameras this reconstruction will be unique up to projectivity thus projective reconstruction of a set of lines and points may be carried out linearly from three views

projective reconstruction from line correspondences in multiple uncalibrated images a new approach is proposed for reconstructing 3d lines and cameras from 2d corresponding lines across multiple uncalibrated views there is no requirement that the 2d corresponding lines on different images represent the same segment of a 3d line which may not appear on all images a 3d line is reconstructed by minimizing a geometric cost function that measures the distance of the reprojected end points of the 3d segment from the measured 2d lines on different images an algorithmic procedure is provided with guaranteed convergence to a solution where the geometric cost function achieves a local minimum

a highly robust estimator through partially likelihood function modeling and its application in computer vision the authors present a highly robust estimator known as the model fitting mf estimator for general regression they explain that high robustness becomes possible through partially but completely modeling the unknown log likelihood function the partial modeling takes place by taking the bayesian statistical decision rule and a number of important heuristics into consideration while maximizing the log likelihood function applications include the automatic selection of multiple thresholds single rigid motion estimation or multiple rigid motion segmentation and estimation from two perspective views it is believed that the proposed mf estimator will aid in solving many robust estimation problems that demand an estimator that is either highly robust or capable of handling contaminated gaussian mixture models

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

schwarps locally projective image warps based on 2d schwarzian derivatives image warps or just warps capture the geometric deformation existing between two images of a deforming surface the current approach to enforce a warp s smoothness is to penalize its second order partial derivatives bookstein in ieee trans pattern anal mach intell 11 567 585 1989 rueckert et al in ieee trans med imaging 18 712 721 1999 because this favors locally affine warps this fails to capture the local projective component of the image deformation this may have a negative impact on applications such as image registration and deformable 3d reconstruction we propose a novel penalty designed to smooth the warp while capturing the deformation s local projective structure our penalty is based on equivalents to the schwarzian derivatives which are projective differential invariants exactly preserved by homographies we propose a methodology to derive a set of partial differential equations with only homographies as solutions we call this system the schwarzian equations and we explicitly derive them for 2d functions using differential properties of homographies we name as schwarp a warp which is estimated by penalizing the residual of schwarzian equations experimental evaluation shows that schwarps outperform existing warps in modeling and extrapolation power and lead to better results in three deformable reconstruction methods namely shape reconstruction in shape from template camera calibration in shape from template and non rigid structure from motion

a probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix the perspective projections of n physical points on two views stereovision are constrained as soon as n 8 however to prove in practice the existence of a rigid motion between two images more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches in this paper we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points n and the accuracy of the matches this criterion yields an objective way to compare say precise matches of a few points and approximate matches of a lot of points it gives a yes no answer to the question could this rigid points correspondence have occurred by chance since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired it also yields absolute accuracy requirements for rigidity detection in the case of non matched points and optimal values of n depending on the expected accuracy of the matches and on the proportion of outliers we use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90 of outliers which outperforms the best currently known methods like m estimators lmeds classical ransac and tensor voting

moment preserving pattern matching abstract an accurate template matching algorithm of low computational complexity that facilitates low cost hardware design and vlsi implementation is highly desired by many image processing applications this paper describes a template matching method called moment preserving pattern matching mppm which reduces the computational complexity of template matching significantly and provides several advantages in hardware implementation the methodology is based on the concepts of pairing function and moment preserving quantization the experimental results show that it is computationally fast and accurate in locating the template if noise corruption is not too severe for obtaining a template matching algorithm of high accuracy and robustness against noise and low computational cost mppm is applied to a two stage matching scheme a statistical model for estimating the correlation threshold is also given

nonmetric calibration of camera lens distortion differential methods and robust estimation this paper addresses the problem of calibrating camera lens distortion which can be significant in medium to wide angle lenses our approach is based on the analysis of distorted images of straight lines we derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines unlike the other existing approaches we also provide fast closed form solutions to the distortion coefficients we prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm our approach provides a way to get around this and at the same time it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise robust results in addition while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another we present a robust approach to distortion calibration based on the least median of squares estimator our approach is thus able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three dimensional linear segments experiments to evaluate the performance of this approach on synthetic and real data are reported

robust line matching through line point invariants this paper is about line matching by line point invariants which encode local geometric information between a line and its neighboring points specifically two kinds of line point invariants are introduced in this paper one is an affine invariant constructed from one line and two points while the other is a projective invariant constructed from one line and four points the basic idea of our proposed line matching methods is to use cheaply obtainable matched points to boost line matching via line point invariants even if the matched points are susceptible to severe outlier contamination to deal with the inevitable mismatches in the matched points two line similarity measures are proposed one is based on the maximum and the other is based on the maximal median therefore four different line matching methods are obtained by combining different line point invariants with different similarity measures their performances are evaluated by extensive experiments the results show that our proposed methods outperform the state of the art methods and are robust to mismatches in the matched points used for line matching

new measurements and corner guidance for curve matching with probabilistic relaxation reliable curve matching is a difficult yet important problem in many vision based applications including image based modeling we describe in this paper two aspects of our research in this area a new algorithm for curve matching including lines within a probabilistic relaxation framework and an approach of incorporating previously matched points corners to guide curve matching we propose similarity invariant unary and binary measurements suitable for curves and introduce an additional measurement to model the uncertainty of the binary measurements the uncertainty measure is proven to be very important in computing the matching support from neighboring matches we also show how to use a set of previously matched points corners to guide the curve matching the role of the corner guidance is explicitly modeled by a set of unary measurements and a similarity function under the same relaxation framework preprocessing techniques contributing to the success of our curve matching techniques are also developed and discussed experiments with complex real scenes show that the rate of correct matching is higher than 98

new approach to study splines by blossoming method and application to the construction of a bivariate c 1 quartic quasi interpolant this work is a contribution in the approximation theory for studying and analyzing piecewise polynomial functions splines which uses the blossoming approach some existing results in the literature are reformulated such as the smoothness conditions between polynomials of a spline by using the affinity property of the blossom some definitions of sub splines are proposed which can be very useful in the study and the construction of splines such as macro elements or quasi interpolants as an application of the proposed results a c 1 quartic spline quasi interpolant with optimal approximation order is defined without using any mask for smoothness or b spline basis numerical results are presented and compared with other methods given in the literature

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

flexible spatial configuration of local image features local image features have been designed to be informative and repeatable under rigid transformations and illumination deformations even though current state of the art local image features present a high degree of repeatability their local appearance alone usually does not bring enough discriminative power to support a reliable matching resulting in a relatively high number of mismatches in the correspondence set formed during the data association procedure as a result geometric filters commonly based on global spatial configuration have been used to reduce this number of mismatches however this approach presents a trade off between the effectiveness to reject mismatches and the robustness to nonrigid deformations in this paper we propose two geometric filters based on a semilocal spatial configuration of local features that are designed to be robust to nonrigid deformations and to rigid transformations without compromising its efficacy to reject mismatches we compare our methods to the hough transform which is an efficient and effective mismatch rejection step based on the global spatial configuration of features in these comparisons our methods are shown to be more effective in the task of rejecting mismatches for rigid transformations and nonrigid deformations at comparable time complexity figures finally we demonstrate how we can integrate these methods in a probabilistic recognition system such that the final verification step uses not only the similarity between features but also their semilocal configuration

a general method for constructing quasi interpolants from b splines a general method for constructing quasi interpolation operators based on b splines is developed given a b spline f in r s s 1 normalized by i z email protected i 1 the classical structure q f email protected i z email protected i f i for a quasi interpolation operator q is considered a minimization problem is derived from an estimate of the quasi interpolation error associated with q when lf is a linear combination of values of f at points in some neighbourhood of the support of f or a linear combination of values of f and some of its derivatives at some points in this set or a linear combination of weighted mean values of the function to be approximated that linear functional is defined to produce a quasi interpolant exact on the space of polynomials of maximal total degree included in the space spanned by the integer translates of f the solution of that minimization problem is characterized in terms of specific splines which do not depend on l but only on f

feature based sequence to sequence matching this paper studies the problem of matching two unsynchronized video sequences of the same dynamic scene recorded by different stationary uncalibrated video cameras the matching is done both in time and in space where the spatial matching can be modeled by a homography for 2d scenarios or by a fundamental matrix for 3d scenarios our approach is based on matching space time trajectories of moving objects in contrast to matching interest points e g corners as done in regular feature based image to image matching techniques the sequences are matched in space and time by enforcing consistent matching of all points along corresponding space time trajectories by exploiting the dynamic properties of these space time trajectories we obtain sub frame temporal correspondence synchronization between the two video sequences furthermore using trajectories rather than feature points significantly reduces the combinatorial complexity of the spatial point matching problem when the search space is large this benefit allows for matching information across sensors in situations which are extremely difficult when only image to image matching is used including a matching under large scale zoom differences b very wide base line matching and c matching across different sensing modalities e g ir and visible light cameras we show examples of recovering homographies and fundamental matrices under such conditions

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

impsac synthesis of importance sampling and random sample consensus this paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation either due to large rotation or wide baseline of the cameras the method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation the method operates on a pyramid from coarse to fine resolution thus raising the problem of how to propagate information from one level to another in a statistically consistent way the distribution of the parameters at each resolution is encoded nonparametrically as a set of particles at the coarsest level a random sample consensus monte carlo markov chain ransac mcmc estimator is used to initialize this set of particles the posterior can then be approximated as a mixture of gaussians fitted to these particles the distribution at a coarser level influences the distribution at a finer level using the technique of sampling importance resampling sir and mcmc which allows for asymptotically correct approximations of the posterior distribution the estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles which can be further improved by mcmc it is shown that the method is superior to previous single resolution ransac style feature matchers

the geometry and matching of lines and curves over multiple views this paper describes the geometry of imaged curves in two and three views multi view relationships are developed for lines conics and non algebraic curves the new relationships focus on determining the plane of the curve in a projective reconstruction and in particular using the homography induced by this plane for transfer from one image to another it is shown that given the fundamental matrix between two views and images of the curve in each view then the plane of a conic may be determined up to a two fold ambiguity but local curvature of a curve uniquely determines the plane it is then shown that given the trifocal tensor between three views this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third simple expressions are developed for the plane and homography in each case a set of algorithms are then described for automatically matching individual line segments and curves between images the algorithms use both photometric information and the multiple view geometric relationships for image pairs the homography facilitates the computation of a neighbourhood cross correlation based matching score for putative line curve correspondences for image triplets cross correlation matching scores are used in conjunction with line curve transfer based on the trifocal geometry to disambiguate matches algorithms are developed for both short and wide baselines the algorithms are robust to deficiencies in the segment extraction and partial occlusion experimental results are given for image pairs and triplets for varying motions between views and for different scene types the methods are applicable to line curve matching in stereo and trinocular rigs and as a starting point for line curve matching through monocular image sequences

optimal bivariate c1 cubic quasi interpolation on a type 2 triangulation in a guessab o nouisser g schmeisser multivariate approximation by a combination of modified taylor polynomials j comput appl math 196 2006 162 179 a general method is proposed to increase the approximation order of approximation operators in this work by using these enhancement techniques we introduce and study new schemes based on a c 1 spline quasi interpolant on a type 2 triangulation they are designed for approximating real valued functions defined on r 2 the proposed method is based on the following idea from a discrete quasi interpolant defined by the quadratic box spline exact on p 2 and by judiciously choosing the first order taylor coefficients we derive a cubic differential quasi interpolant yielding optimal approximation order in addition when the derivatives are not available or are extremely expensive to compute we approximate them by finite difference approximations having the desired accuracy to derive a new class of discrete quasi interpolants as an essential difference to some of the existing methods we only use the given data values and then we do not modify the original triangulation finally we present some numerical tests which confirm the efficiency of the newly quasi interpolant and demonstrate good visual quality in particular we compare it with a differential quasi interpolant done by lai m j lai approximation order from bivariate c 1 cubics on a four directional mesh is full comput aided geom design 11 2 1994 215 223 which is also exact on p 3 but uses third order partial derivatives

using multiple hypothesis disparity maps and image velocity for 3 d motion estimation in this paper we explore a multiple hypothesis approach to estimating rigid motion from a moving stereo rig more precisely we introduce the use of gaussian mixtures to model correspondence uncertainties for disparity and velocity optical flow estimation we show some properties of the disparity space and show how rigid transformations can be represented an algorithm derived from standard random sampling based robust estimators that efficiently estimates rigid transformations from multi hypothesis disparity maps and velocity fields is given

minimal projective reconstruction including missing data the minimal data necessary for projective reconstruction from image points is well known when each object point is visible in all images we formulate and propose solutions to a family of reconstruction problems for multiple images from minimal data where there are missing points in some of the images the ability to handle the minimal cases with missing data is of great theoretical and practical importance it is unavoidable to use them to bootstrap robust estimation such as ransac and lms algorithms and optimal estimation such as bundle adjustment first we develop a framework to parameterize the multiple view geometry needed to handle the missing data cases then we present a solution to the minimal case of eight points in three images where one different point is missing in each of the three images we prove that there are in general as many as 11 solutions for this minimal case furthermore all minimal cases with missing data for three and four images are catalogued finally we demonstrate the method on both simulated and real images and show that the algorithms presented in the paper can be used for practical problems

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

contour matching using epipolar geometry matching features computed in images is an important process in multiview image analysis when the motion between two images is large the matching problem becomes very difficult in this paper we propose a contour matching algorithm based on geometric constraints with the assumption that the contours are obtained from images taken from a moving camera with static scenes we apply the epipolar constraint between two sets of contours and compute the corresponding points on the contours from the initial epipolar constraints obtained from corner point matching candidate contours are selected according to the epipolar geometry contour end point constraints and contour distance measures in order to reduce the possibility of false matches the number of match points on a contour is also used as a selection measure the initial epipolar constraint is refined from the matched sets of contours the algorithm can be applied to a pair or two pairs of images all of the processes are fully automatic and successfully implemented and tested with various real images

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

ror rejection of outliers by rotations we address the problem of rejecting false matches of points between two perspective views the two views are taken from two arbitrary unknown positions and orientations we present an algorithm for identification of the false matches between the views the algorithm exploits the possibility of rotating one of the images to achieve some common behavior of the correct matches those matches that deviate from this common behavior turn out to be false matches our algorithm does not in any way use the image characteristics of the matched features in particular it avoids problems that cause the false matches in the first place the algorithm works even in cases where the percentage of false matches is as high as 85 percent the algorithm may be run as a post processing step on output from any point matching algorithm use of the algorithm may significantly improve the ratio of correct matches to incorrect matches we present the algorithm identify the conditions under which it works and present results of the test

construction techniques for multivariate modified quasi interpolants with high approximation order in this paper we propose several approximations of a multivariate function by quasi interpolants on non uniform data and we study their properties in particular we characterize those that preserve constants via the partition of unity approach as one of the main results we show how by a very simple modification of a given quasi interpolant it is possible to construct new quasi interpolants with remarkable properties we also provide some results regarding bivariate c 2 quintic spline quasi interpolation finally numerical tests are presented to show the approximation power of these quasi interpolants

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

a theory of the motion fields of curves this article reports a study of the motion field generated by moving 3 d curves that are observed by a camera we first discuss the relationship between optical flow and motion field and show that the assumptions made in the computation of the optical flow are a bit difficult to defend

anisotropic scale junction detection and matching for indoor images junctions play an important role in characterizing local geometrical structures of images and the detection of which is a longstanding but challenging task existing junction detectors usually focus on identifying the location and orientations of junction branches while ignoring their scales which however contain rich geometries of images this paper presents a novel approach for junction detection and characterization which especially exploits the locally anisotropic geometries of a junction and estimates its scales by relying on an a contrario model the output junctions are with anisotropic scales saying that a scale parameter is associated with each branch of a junction and are thus named as anisotropic scale junctions asjs we then apply the new detected asjs for matching indoor images where there are dramatic changes of viewpoints and the detected local visual features e g key points are usually insufficient and lack distinctive ability we propose to use the anisotropic geometries of our junctions to improve the matching precision of indoor images the matching results on sets of indoor images demonstrate that our approach achieves the state of the art performance on indoor image matching

on characterization of elementary trapping sets of variable regular ldpc codes in this paper we study the graphical structure of elementary trapping sets etss of variable regular low density parity check ldpc codes etss are known to be the main cause of error floor in ldpc coding schemes for the set of ldpc codes with a given variable node degree dl and girth g we identify all the nonisomorphic structures of an arbitrary class of a b etss where a is the number of variable nodes and b is the number of odd degree check nodes in the induced subgraph of the ets this paper leads to a simple characterization of dominant classes of etss those with relatively small values of a and b based on short cycles in the tanner graph of the code for such classes of etss we prove that any set s in the class is a layered superset lss of a short cycle where the term layered is used to indicate that there is a nested sequence of etss that starts from the cycle and grows one variable node at a time to generate s this characterization corresponds to a simple search algorithm that starts from the short cycles of the graph and finds all the etss with lss property in a guaranteed fashion specific results on the structure of etss are presented for d l 3 4 5 6 g 6 8 and a b 10 in this paper the results of this paper can be used for the error floor analysis and for the design of ldpc codes with low error floors

structure from motion using line correspondences a theory is presented for the computation of three dimensional motion and structure from dynamic imagery using only line correspondences the traditional approach of corresponding microfeatures interesting points highlights corners high curvature points etc is reviewed and its shortcomings are discussed then a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views the theory is compared with previous ones that are based on nonlinear equations and iterative methods

contextual inference in contour based stereo correspondence standard approaches to stereo correspondence have difficulty when scene structure does not lie in or near the frontal parallel plane in part because an orientation disparity as well as a positional disparity is introduced we propose a correspondence algorithm based on differential geometry that takes explicit advantage of both disparities the algorithm relates the 2d differential structure position tangent and curvature of curves in the left and right images to the frenet approximation of the 3d space curve a compatibility function is defined via transport of the frenet frames and they are matched by relaxing this compatibility function on overlapping neighborhoods along the curve the remaining false matches are concurrently eliminated by a model of near and far neurons derived from neurobiology examples on scenes with complex 3d structures are provided

binocular matching constraints from motion abstract structure from motion and structure from stereo are two vision cues for achieving 3d reconstruction the two cues have complementary strengths while 3d reconstruction is accurate but correspondence establishment is difficult in the stereo cue the reverse is true in the motion cue this paper addresses how to combine the two cues when a stereo pair of cameras are available to capture image data for 3d reconstruction the work is distinct in that in contrast with the previous ones it is not to exploit the redundancy in the image data for boosting the reconstruction accuracy but to make the two vision cues complementary preserving their strengths and avoiding their weaknesses a mechanism is introduced that allows dense motion correspondences in the two separate image streams be transferred to dense binocular correspondences across the image streams so that 3d can be reconstructed from the latter and accurate reconstruction is possible even with short motions of the stereo rig both the stereo correspondences and the motion of the stereo rig are assumed to be unknown in this work experiments involving real image data are presented to indicate the feasibility and robustness of the approach

meaningful matches in stereovision this paper introduces a statistical method to decide whether two blocks in a pair of images match reliably the method ensures that the selected block matches are unlikely to have occurred just by chance the new approach is based on the definition of a simple but faithful statistical background model for image blocks learned from the image itself a theorem guarantees that under this model not more than a fixed number of wrong matches occurs on average for the whole image this fixed number the number of false alarms is the only method parameter furthermore the number of false alarms associated with each match measures its reliability this a contrario block matching method however cannot rule out false matches due to the presence of periodic objects in the images but it is successfully complemented by a parameterless self similarity threshold experimental evidence shows that the proposed method also detects occlusions and incoherent motions due to vehicles and pedestrians in nonsimultaneous stereo

what can two images tell us about a third one this paper discusses the problem of predicting image features in an image from image features in two other images and the epipolar geometry between the three images we adopt the most general camera model of perspective projection and show that a point can be predicted in the third image as a bilinear function of its images in the first two cameras that the tangents to three corresponding curves are related by a trilinear function and that the curvature of a curve in the third image is a linear function of the curvatures at the corresponding points in the other two images our analysis relies heavily on the use of the fundamental matrix which has been recently introduced faugeras et al 1992 and on the properties of a special plane which we call the trifocal plane though the trinocular geometry of points and lines has been very recently addressed our use of the differential properties of curves for prediction is unique we thus completely solve the following problem given two views of an object predict what a third view would look like the problem and its solution bear upon several areas of computer vision stereo motion analysis and model based object recognition our answer is quite general since it assumes the general perspective projection model for image formation and requires only the knowledge of the epipolar geometry for the triple of views we show that in the special case of orthographic projection our results for points reduce to those of ullman and basri ullman and basri 1991 we demonstrate on synthetic as well as on real data the applicability of our theory

two view line matching algorithm based on context and appearance in low textured images a novel approach for line detection and matching is proposed aimed at achieving good performance with low textured scenes under uncontrolled illumination conditions line detection is performed by means of phase based edge detector over gaussian scale space followed by a multi scale fusion stage which has been proven to be profitable in minimizing the number of fragmented and overlapped segments line matching is performed by an iterative process that uses structural information collected through the use of different line neighborhoods making the set of matched lines grow robustly at each iteration results show that this approach is suitable to deal with low textured scenes and also robust under a wide variety of image transformations highlightsa novel approach for line detection and matching is proposed lines are detected through a fusion process over the gaussian scale space lines are matched based on their appearance geometric properties and neighborhoods our proposal minimizes the number of fragmented and overlapped segments our proposal is suitable for low textured scenes under uncontrolled illumination

a computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

stereo correspondence through feature grouping and maximal cliques the authors propose a method for solving the stereo correspondence problem the method consists of extracting local image structures and matching similar such structures between two images linear edge segments are extracted from both the left and right images each segment is characterized by its position and orientation in the image as well as its relationships with the nearby segments a relational graph is thus built from each image for each segment in one image as set of potential assignments is represented as a set of nodes in a correspondence graph arcs in the graph represent compatible assignments established on the basis of segment relationships stereo matching becomes equivalent to searching for sets of mutually compatible nodes in this graph sets are found by looking for maximal cliques the maximal clique best suited to represent a stereo correspondence is selected using a benefit function numerous results obtained with this method are shown

near best quasi interpolants associated with h splines on a three direction mesh spline quasi interpolants with optimal approximation orders and small norms are useful in several applications in this paper we construct the so called near best discrete and integral quasi interpolants based on h splines i e b splines with regular hexagonal supports on the uniform three directional mesh of the plane these quasi interpolants are obtained so as to be exact on some space of polynomials and to minimize an upper bound of their infinite norms which depend on a finite number of free parameters we show that this problem has always a solution which is not unique in general concrete examples of these types of quasi interpolants are given in the two last sections

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

semi local projective invariants for the recognition of smooth plane curves recently several methods have been proposed for describing plane non algebraic curves in a projectively invariant fashion these curve representations are invariant under changes in viewpoint and therefore ideally suited for recognition we report the results of a study where the strengths and weaknesses of a number of semi local methods are compared on the basis of the same images and edge data all the methods define a distinguished or canonical projective frame for the curve segment which is used for projective normalisation in this canonical frame the curve has a viewpoint invariant signature measurements on the signature are invariants all the methods presented are designed to work on real images where extracted data will not be ideal and parts of curves will be missing because of poor contrast or occlusion we compare the stability and discrimination of the signatures and invariants over a number of example curves and viewpoints the paper concludes with a discussion of how the various methods can be integrated within a recognition system

three dimensional tracking of coronary arteries from biplane angiographic sequences using parametrically deformable models a new method for coronary artery tracking in biplane digital subtraction is presented the dynamic tracking of nonrigid objects from two views is achieved using a generalization of parametrically deformable models three dimensional 3 d fourier descriptors used for shape representation are obtained from the two dimensional 2 d descriptors of the projections a new constraint inferred from epipolar geometry is applied to the contour model direct 3 d tracking is compared with the classical approach in two steps independent 2 d tracking in each of the two projection planes 3 d reconstruction using the epipolar constraint convergence quality and accuracy of the 3 d reconstruction are analyzed for several sequences showing different displacement amplitudes deformation rates and image contrasts

new characterization and efficient exhaustive search algorithm for leafless elementary trapping sets of variable regular ldpc codes in this paper we propose a new characterization for leafless elementary trapping sets letss of variable regular low density parity check codes recently karimi and banihashemi proposed a characterization of letss which was based on viewing an lets as a layered superset lss of a short cycle in the code s tanner graph a notable advantage of lss characterization is that it corresponds to a simple lss based search algorithm expansion technique that starts from short cycles of the graph and finds the letss with lss structure efficiently compared with the lss based characterization of karimi and banihashemi which is based on a single lss expansion technique the new characterization involves two additional expansion techniques the introduction of the new techniques mitigates two problems that lss based characterization search suffers from 1 exhaustiveness not every lets structure is an lss of a cycle and 2 search efficiency lss based search algorithm often requires the enumeration of cycles with length much larger than the girth of the graph where the multiplicity of such cycles increases rapidly with their length we prove that using the three expansion techniques any lets structure can be obtained starting from a simple cycle no matter how large the size of the structure a or the number of its unsatisfied check nodes b are i e the characterization is exhaustive we also demonstrate that for the proposed characterization search to exhaustively cover all the lets structures within the a b classes with a leq a max and b leq b max for any value of a max and b max the length of the short cycles required to be enumerated is less than that of the lss based characterization search we in fact show that such a length for the proposed search algorithm is minimal we also prove that the three expansion techniques proposed here are the only expansions needed for characterization of lets structures starting from simple cycles in the graph if one requires each and every intermediate sub structure to be a lets as well extensive simulation results are provided to show that compared with lss based search significant improvement in search speed and memory requirements can be achieved

detecting moving objects using the rigidity constraint a method for visually detecting moving objects from a moving camera using point correspondences in two orthographic views is described the method applies a simple structure from motion analysis and then identifies those points inconsistent with the interpretation of the scene as a single rigid object it is effective even when the actual motion parameters cannot be recovered demonstrations are presented using point correspondences automatically determined from real image sequences

local quasi interpolants based on special multivariate quadratic spline space over a refined quadrangulation in this paper we describe the construction of a suitable normalized b spline representation for special multivariate quadratic spline space s 2 1 0 d over a refined quadrangulation we then develop as an application a general theory of quasi interpolants based on this representation

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

efficient registration of stereo images by matching graph descriptions of edge segments we present a new approach to the stereo matching problem images are individually described by aneighborhood graph of line segments coming from a polygonal approximation of the contours the matching process is defined as the exploration of the largest components of adisparity graph built from the descriptions of the two images and is performed by an efficient prediction and propagation technique this approach was tested on a variety of man made environments and it appears to be fast and robust enough for mobile robot navigation and three dimensional part positioning applications