: 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 perpective 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 [7] and on the properties of a special plane which we call the trifocal plane. We thus answer completely the following question: given two views of an object, what would a third view look like? the question and its answer bear upon several areas of computer vision, stereo, motion analysis, and model-based object re...

We address in this paper the problem of self-calibration and metric reconstruction (up to a scale) from one unknown motion of an uncalibrated stereo rig, assuming the coordinates of the principal point of each camera are known (This assumption is not necessary if one more motion is available). The epipolar constraint is first formulated for two uncalibrated images. The problem then becomes one of estimating unknowns such that the discrepancy from the epipolar constraint, in terms of distances between points and their corresponding epipolar lines, is minimized. The initialization of the unknowns is based on the work of Maybank, Luong and Faugeras on self-calibration of a single moving camera, which requires to solve a set of so-called Kruppa equations. Redundancy of the information contained in a sequence of stereo images makes this method more robust than using a sequence of monocular images. Real data have been used to test the proposed method, and the results obtained are quite goo...

Recently, different approaches for uncalibrated stereo have been suggested which permit projective reconstructions from multiple views. These use weak calibration which is represented by the epipolar geometry, and so we require no knowledge of the intrinsic or extrinsic camera parameters. In this paper we consider projective reconstructions from pairs of views, and compare a number of the available methods. Projective stereo algorithms can be categorized by the way in which the 3D coordinates are computed. The first class is similar to traditional stereo algorithms in that the 3D world geometry is made explicit; the initial phase of the processing always involves the estimation of the camera matrices from which the 3D coordinates are computed. We show how the camera matrices can be computed either from point correspondences, or how they are constrained by the fundamental matrices. The second class of algorithms are based on implicit image measurements which are used to compute project...

In the present paper we address the problem of computing structure and motion, given a set point and/or line correspondences, in a monocular image sequence, when the camera is not calibrated. Considering point correspondences rst, we analyse how to parameterize the retinal correspondences, in function of the chosen geometry: Euclidean, a ne or projective geometry. The simplest of these parameterizations is called the FQs-representation and is a composite projective representation. The main result is that considering N + 1 views in such a monocular image sequence, the retinal correspondences are parameterized by 11N,4parameters in the general projective case. Moreover, 3 other parameters are required to work in the a ne case and 5 additional parameters in the Euclidean case. These 8 parameters are \calibration " parameters and must be calculated considering at least 8 external informations or constraints. The method being constructive, all these representations are made explicit. Then, considering line correspondences, we show howthe the same parameterizations can be used when we analyse the motion of lines, in the uncalibrated case. The case of three views is extensively studied and a geometrical interpretation is proposed, introducing the notion of trifocal geometry which generalizes the well known epipolar geometry. It is also discussed how tointroduce line correspondences, in a framework based on point correspondences, using the same equations. Finally, considering the FQs-representation, one implementation is proposed as a \motion module", taking retinal correspondences as input, and providing and estimation of the 11 N, 4 retinal motion parameters. As discussed in this paper, this module can also estimate the 3D depth of the points up to an a ne and projective transformation, de ned by the 8 parameters identi ed in the rst section. Experimental results are provided. Keywords: Motion, Auto-calibration, Points and Lines 1

From two calibrated perspective views of a scene we make a direct metric reconstruction. From assumptions of translational, rotational, and scale invariance of 3D space and camera models we deduce the priors needed for a Bayesian estimation. This means that the reconstruction is optimal in the sense of Bayesian estimation with assumptions of Gaussian uncorrelated image noise and no preferred position, direction, and scale in the scene. It is shown that depth discontinuities can be reconstructed and results are presented. The constraint induced by the assumption of isotropy is shown to be invariant under change of the extrinsic camera parameters. It is argued that relaxation algorithms created to solve the stereo correspondance problem by optimization of non-convex functionals in general will rely on initial estimates or bias towards a predefined solution. We use a multi-scale GNC-like algorithm to find a solution from the initial estimates. Keywords: Binocular stereo, Bayesian...

In this paper, we investigate the issue of accurate estimation of the three-dimensional (3D) coordinates of a static scene from real images, combining xation and stereo cues. We may need to compute 3D data in many applications: vehicle positioning and maneuver, object observation and recognition, moving or xed obstacle avoidance, 3D mapping for surveillance, etc. More speci cally, we discuss the idea of using xation to recover the 3D coordinates of some points in the robotic frame to help an uncalibrated camera to reconstruct a static scene.