On the Probabilistic Epipolar Geometry

In this paper, we are going to answer the following question: assuming that we have estimates for the epipolar geometry and its uncertainty between two views, how probable it is that a new, independent point pair will satisfy the true epipolar geometry and be, in this sense, a feasible candidate correspon-dence pair? If we knew the true fundamental matrix, the answer would be trivial but in reality it is not because of estimation errors. So, as a point in the first view is given, we will show that we may compute a probability density for the feasible correspondence locations in the second view that describes the current level of knowledge of the epipolar geometry between the views. We will thus have a point–probability-density relation which can be under-stood as a probabilistic form of the epipolar constraint; it also approaches the true point–line relation as the number of training correspondences tends to in-finity. We will also show that the eigenvectors of the epipolar line covariance matrix have certain interpretations on the image plane, of which one is the previously observed, narrowest point of the epipolar envelope. The results of this paper are novel and important since the uncertainty of the epipolar constraint can be now taken into account in a sound way in applications.

Robust Detection of Point Correspondences in Stereo Images

A major challenge in 3D reconstruction is the computation of the fundamental matrix. Automatic computation from uncalibrated image pairs is performed from point correspondences. Due to imprecision and wrong correspondences, only an approximation of the true fundamental matrix can be computed. The quality of the fundamental matrix strongly depends on the location and number of point correspondences.Furthermore, the fundamental matrix is the only geometric constraint between two uncalibrated views, and hence it can be used for the detection of wrong point correspondences. This property is used by current algorithms like RANSAC, which computes the fundamental matrix from a restricted set of point correspondences. In most cases, not only wrong correspondences are disregarded, but also correct ones, which is due to the criterion used to eliminate outliers. In this context, a new criterion preserving a maximum of correct correspondences would be useful.In this paper we introduce a novel criterion for outlier elimination based on a probabilistic approach. The enhanced set of correspondences may be important for further computation towards a 3D reconstruction of the scene.

Integral Geometric Dual Distributions of Multilinear Models

We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view tensors, homographies, or as simple entities as points, lines, and planes. The dual distributions have analytical forms that follow from the asymptotic normality property of the maximum likelihood estimator and an application of integral transforms, fundamentally the generalised Radon transforms, on the probability density of the parameters. The approach allows us, for instance, to look at the uncertainty distributions in feature distributions, which are essentially tied to the distribution of training data, and helps us to derive conditional distributions for interesting variables and characterise confidence intervals of the estimates

Robust matching in an uncertain world

ISSN: 1051-4651 Print ISBN: 978-1-4244-7542-1International audienceFinding point correspondences which are consistent with a geometric constraint is one of the cornerstones of many computer vision problems. This is a difficult task because of spurious measurements leading to ambiguously matched points and because of uncertainty in point location. In this article we address these problems and propose a new robust algorithm that explicitly takes account of location uncertainty. We propose applications to Sift matching and 3D data fusion

Computing the uncertainty of the 8 point algorithm for fundamental matrix estimation

International audienceFundamental matrix estimation is difficult since it is often based on correspondences that are spoilt by noise and outliers. Outliers must be thrown out via robust statistics, and noise gives uncertainty. In this article we provide a closed-form formula for the uncertainty of the so-called 8 point algorithm, which is a basic tool for fundamental matrix estimation via robust methods. As an application, we modify a well established robust algorithm accordingly, leading to a new criterion to recover point correspondences under epipolar constraint, balanced by the uncertainty of the estimation

Robust matching in an uncertain world

Finding a registration between two sets of corresponding 2D or 3D points is one of the keystones of many computer vision tasks. This is difficult since some points may not have correspondences at all, and points are often spoilt by noisy measurements. In this report we propose new robust algorithms, namely an adaptation of Msac algorithm and a new a contrario model. Both of them are based on statistics over the Mahalanobis distance and explicitly take account of location uncertainty. We outline applications to SIFT keypoint matching and 3D data fusion.L'estimation d'un recalage entre deux ensembles de points 2D ou 3D en correspondance est un des principaux problèmes rencontrés dans le domaine de la vision par ordinateur. Il s'agit d'un problème difficile car certains points peuvent n'avoir aucune correspondance dans l'autre ensemble, et la localisation des points est généralement connue à une erreur près. Dans ce report, nous proposons de nouveaux algorithmes: une adaptation de Msac et un nouveau modèle a contrario. Ils sont tous deux basés sur des statistiques sur la distance de Mahalanobis et ils tiennent explicitement compte de l'incertitude dans la localisation des points. Nous suggérons des applications à l'appariement de points Sift et à la fusion de données 3D

Determining point correspondences between two views under geometric constraint and photometric consistency

Matching or tracking points of interest between several views is one of the keystones of many computer vision applications, especially when considering structure and motion estimation. The procedure generally consists in several independent steps, basically 1) point of interest extraction, 2) point of interest matching by keeping only the ``best correspondences'' with respect to similarity between some local descriptors, 3) correspondence pruning to keep those consistent with an estimated camera motion (here, consistent with epipolar constraints or homography transformation). Each step in itself is a touchy task which may endanger the whole process. In particular, repeated patterns give lots of false matches in step 2) which are hardly, if never, recovered by step 3). Starting from a statistical model by Moisan and Stival, we propose a new one-stage approach to steps 2) and 3), which does not need tricky parameters. The advantage of the proposed method is its robustness to repeated patterns

View synthesis for kinetic depth X-ray imaging

This thesis reports the development and analysis of feature based synthesis of transmission X-ray images. The synthetic imagery is formed through matching and morphing or warping line-scan format images produced by a novel multi-view X-ray machine. In this way video type sequences, which periodically alternate between synthetic and detector based views, may be formed. The purpose of these sequences is to provide depth from motion or kinetic depth effect (KDE) in a visual display; while the role of the synthesis is to reduce the total number of detector arrays, associated collimators and X-ray flux per inspection. A specific challenge is to explore the bounds for producing synthetic imagery that can be seamlessly introduced into the resultant sequences. This work is distinct from the image collection and display technique, termed KDEX, previously undertaken by the Imaging Science Group at NTU. The ultimate aim of the research programme in collaboration with The UK Home Office and The US Dept. of Homeland Security is to enhance the detection and identification of threats in X-ray scans of luggage. A multi-view „KDEX scanner‟ was employed to collect greyscale and colour coded image sequences of 30 different bags; each sequence comprised of 7 perspective views separated from one another by 10. This imagery was organised and stored in a database to enable a coherent series of experiments to be conducted. Corresponding features in sequential pairs of images, at various different angular separations, were identified by applying a scale invariant feature transform (SIFT)

Localisation et cartographie simultanées par ajustement de faisceaux local : propagation d'erreurs et réduction de la dérive à l'aide d'un odomètre

The present work is about localisation of vehicle using computer vision methods. In this context, the camera trajectory and the 3D structure of the scene is estimated by a monocular visual odometry method based on local bundle adjustment. This thesis contributions are some improvements of this method. The uncertainty of the estimated position was not provided by the local bundle adjustment method. Indeed, this uncertainty is crucial in a multi-sensorial fusion system to use optimally the estimated position. A study of the uncertainty propagation in this visual odometry method has been done and an uncertainty calculus method has been designed to comply with real time performance. By the way, monocular visual localisation methods are known to have serious drift issues on long trajectories (some kilometers). This error mainly comes from bad propagation of the scale factor. To limit this drift and improve the quality of the given position, we proposed two data fusion methods between an odometer and the visual method. Finally, the two improvements presented here allow us to use visual localisation method in real urban environment on long trajectories under real time constraints.Les travaux présentés ici concernent le domaine de la localisation de véhicule par vision artificielle. Dans ce contexte, la trajectoire d’une caméra et la structure3D de la scène filmée sont estimées par une méthode d’odométrie visuelle monoculaire basée sur l’ajustement de faisceaux local. Les contributions de cette thèse sont plusieurs améliorations de cette méthode. L’incertitude associée à la position estimée n’est pas fournie par la méthode d’ajustement de faisceaux local. C’est pourtant une information indispensable pour pouvoir utiliser cette position, notamment dans un système de fusion multi-sensoriel. Une étude de la propagation d’incertitude pour cette méthode d’odométrie visuelle a donc été effectuée pour obtenir un calcul d’incertitude temps réel et représentant l’erreur de manière absolue (dans le repère du début de la trajectoire). Sur de longues séquences (plusieurs kilomètres), les méthodes monoculaires de localisation sont connues pour présenter des dérives importantes dues principalement à la dérive du facteur d’échelle (non observable). Pour réduire cette dérive et améliorer la qualité de la position fournie, deux méthodes de fusion ont été développées. Ces deux améliorations permettent de rendre cette méthode monoculaire exploitable dans le cadre automobile sur de grandes distances tout en conservant les critères de temps réel nécessaire dans ce type d’application. De plus, notre approche montre l’intérêt de disposer des incertitudes et ainsi de tirer parti de l’information fournie par d’autres capteurs