A heuristic method has been developed for registering two sets of 3-D curves obtained by using an edge-based stereo system, or two dense 3-D maps obtained by using a correlation-based stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3-D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subset-subset matching. A least-squares technique is used to estimate 3-D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.

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

: Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. In this tutorial, we present what is probably the most commonly used techniques for parameter estimation. These include linear least-squares (pseudo-inverse and eigen analysis); orthogonal least-squares; gradient-weighted least-squares; bias-corrected renormalization; Kalman øltering; and robust techniques (clustering, regression diagnostics, M-estimators, least median of squares). Particular attention has been devoted to discussions about the choice of appropriate minimization criteria and the robustness of the dioeerent techniques. Their application to conic øtting is described. Key-words: Parameter estimation, Least-squares, Bias correction, Kalman øltering, Robust regression (R#sum# : tsvp) Unite de recherche INRIA Sophia-Antipolis 2004 route des Lucioles, BP 93, 06902 SOPHIA-ANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77 -- Telecopie : (33) 9...

In this paper, we propose and analyze several methods to estimate a rigid transformation from a set of 3-D matched points or matched frames, which are important features in geometric algorithms. We also develop tools to predict and verify the accuracy of these estimations. The theoretical contributions are: an intrinsic model of noise for transformations based on composition rather than addition; a unified formalism for the estimation of both the rigid transformation and its covariance matrix for points or frames correspondences, and a statistical validation method to verify the error estimation, which applies even when no "ground truth" is available. We analyze and demonstrate on synthetic data that our scheme is well behaved. The practical contribution of the paper is the validation of our transformation estimation method in the case of 3-D medical images, which shows that an accuracy of the registration far below the size of a voxel can be achieved, and in the case of protein substructure matching, where frame features drastically improve both selectivity and complexity. 1.

This paper deals with the analysis of the uncertainty of the fundamental matrix. The basic idea is to compute the fundamental matrix and its uncertainty in the same time. We shall show two different methods. The first one is a statistical approach. As in all statistical methods the precision of the results depends on the number of analyzed samples. This means that we can always improve our results if we increase the number of samples but this process is very time consuming. We propose a much simpler method which gives results which are close to the results of the statistical methods. At the end of paper we shall show some experimental results obtained with synthetic and real data.

We present in this paper an algorithm for determining 3D motion and structure from correspondences of line segments between two perspective images. To our knowledge, this paper is the first investigation on use of line segments in motion and structure from motion. Classical methods use their geometric abstraction, namely straight lines, but then three images are necessary. We show in this paper that two views are in general sufficient when using line segments. The assumption we use is that two matched line segments contain the projection of a common part of the corresponding line segment in space. Indeed, this is what we use to match line segments between different views. Both synthetic and real data have been used to test the proposed algorithm, and excellent results have been obtained with real data containing about one hundred line segments. The results are comparable with those obtained with calibrated stereo.

Camera calibration has been studied extensively in computer vision and photogrammetry and the proposed techniques in the literature include those using 3D apparatus (two or three planes orthogonal to each other or a plane undergoing a pure translation, etc.), 2D objects (planar patterns undergoing unknown motions), and 0D features (self-calibration using unknown scene points). Yet, this paper proposes a new calibration technique using 1D objects (points aligned on a line), thus filling the missing dimension in calibration. In particular, we show that camera calibration is not possible with free-moving 1D objects, but can be solved if one point is fixed. A closed-form solution is developed if six or more observations of such a 1D object are made. For higher accuracy, a nonlinear technique based on the maximum likelihood criterion is then used to refine the estimate. Singularities have also been studied. Besides the theoretical aspect, the proposed technique is also important in practice especially when calibrating multiple cameras mounted apart from each other, where the calibration objects are required to be visible simultaneously.

Complex geometric features such as oriented points, lines or 3D frames are increasingly used in image processing and computer vision. However, processing these geometric features is far more difficult than processing points, and a number of paradoxes can arise. We establish in this article the basic mathematical framework required to avoid them and analyze more specifically three basic problems: (1) what is a random distribution of features, (2) how to define a distance between features, (3) and what is the "mean feature" of a number of feature measurements ? We insist on the importance of an invariance hypothesis for these definitions relative to a group of transformations that models the different possible data acquisitions. We develop general methods to solve these three problems and illustrate them with 3D frame features under rigid transformations. The first problem has a direct application in the computation of the prior probability of a false match in classical model-based object recognition algorithms. We also present experimental results of the two other problems for the statistical analysis of anatomical features automatically extracted from 24 three dimensional images of a single patient's head. These experiments successfully confirm the importance of the rigorous requirements presented in this article.

The classical approach to motion and structure estimation problem from two perspective projections consists of two stages: (i) using the 8-point algorithm to estimate the 9 essential parameters defined up to a scale factor, which is a linear estimation problem; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a five-dimensional space. Unfortunately, the results obtained using this approach are often not satisfactory, especially when the motion is small or when the observed points are close to a degenerate surface (e.g. plane). The problem is that the second stage is very sensitive to the initial guess, and that it is very difficult to obtain a precise initial estimate from the first stage. This is because we perform a projection of a set of quantities which are estimated in a space of 8 dimensions, much higher than that of the real space which is five-dimensional. We propose in this paper a novel approach by introducing...

. There are emerging interests from both computer vision and computer graphics communities in obtaining photorealistic modeling of a scene or an object from real images. This paper presents a tentative review of the computer vision techniques used in such modeling which guarantee the generated views to be geometrically correct. The topics covered include mosaicking for building environment maps, CAD-like modeling for building 3D geometric models together with texture maps extracted from real images, image-based rendering for synthesizing new views from uncalibrated images, and techniques for modeling the appearance variation of a scene or an object under different illumination conditions. Major issues and difficulties are addressed. Keywords: photorealistic modeling, image-based rendering, multiple-view geometry, photometric models, CAD, camera calibration, 3D reconstruction, uncalibrated images, domain knowledge, illumination variation. 1 Introduction Considerable effort in computer...