In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of the principal points, pixels aspect ratio and focal lengths). This is important for two reasons. First, it is more realistic in applications where these parameters may vary according to the task (active vision). Second, the general case considered here, captures all the relevant information that is necessary for establishing correspondences between two pairs of images. This information is fundamentally projective and is hidden in a confusing manner in the commonly used formalism of the Essential matrix introduced by Longuet-Higgins [40]. This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 \Theta 3 ma...

This paper describes the extraction of 3D geometrical data from image sequences, for the purpose of creating 3D models of objects in the world. The approach is uncalibrated - camera internal parameters and camera motion are not known or required. Processing an image sequence is underpinned by token correspondences between images. We utilise matching techniques which are both robust (detecting and discarding mismatches) and fully automatic. The matched tokens are used to compute 3D structure, which is initialised as it appears and then recursively updated over time. We describe a novel robust estimator of the trifocal tensor, based on a minimum number of token correspondences across an image triplet; and a novel tracking algorithm in which corners and line segments are matched over image triplets in an integrated framework. Experimental results are provided for a variety of scenes, including outdoor scenes taken with a hand-held camcorder. Quantitative statistics are included to asses...

. We describe progress in completely automatically recovering 3D scene structure together with 3D camera positions from a sequence of images acquired by an unknown camera undergoing unknown movement. The main departure from previous structure from motion strategies is that processing is not sequential. Instead a hierarchical approach is employed building from image triplets and associated trifocal tensors. This is advantageous both in obtaining correspondences and also in optimally distributing error over the sequence. The major step forward is that closed sequences can now be dealt with easily. That is, sequences where part of a scene is revisited at a later stage in the sequence. Such sequences contain additional constraints, compared to open sequences, from which the reconstruction can now benefit. The computed cameras and structure are the backbone of a system to build texture mapped graphical models directly from image sequences. 1 Introduction The goal of this work is to obtain ...

This work is in the context of motion and stereo analysis. It presents a new uni ed representation which will be useful when dealing with multiple views in the case of uncalibrated cameras. Several levels of information might be considered, depending on the availability of information. Among other things, an algebraic description of the epipolar geometry of N views is introduced, as well as a framework for camera self-calibration, calibration updating, and structure from motion in an image sequence taken by a camera which is zooming and moving at the same time. We show how a special decomposition of a set of two or three general projection matrices, called canonical enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations. These representations are minimal and capture completely the properties of each level of description considered: Euclidean (in the context of calibration, and in the context of structure from motion, which we distinguish clearly), a ne, and projective, that we also relate to each other. In the last case, a new decomposition of the well-known fundamental matrix is obtained. Dependencies, which appear when three or more views are available, are studied in the context of the canonic decomposition, and new composition formulas are established. The theory is illustrated by tutorial examples with real images.

A new method is presented for robustly estimating multiple view relations from point correspondences. The method comprises two parts. The first is a new robust estimator MLESAC which is a generalization of the RANSAC estimator. It adopts the same sampling strategy as RANSAC to generate putative solutions, but chooses the solution that maximizes the likelihood rather than just the number of inliers. The second part of the algorithm is a general purpose method for automatically parameterizing these relations, using the output of MLESAC. A difficulty with multiview image relations is that there are often nonlinear constraints between the parameters, making optimization a difficult task. The parameterization method overcomes the difficulty of nonlinear constraints and conducts a constrained optimization. The method is general and its use is illustrated for the estimation of fundamental matrices, image–image homographies, and quadratic transformations. Results are given for both synthetic and real images. It is demonstrated that the method gives results equal or superior to those of previous approaches. c ○ 2000 Academic Press 1.

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.

Scene flow is the three-dimensional motion field of points in the world, just as optical flow is the twodimensional motion field of points in an image. Any optical flow is simply the projection of the scene flow onto the image plane of a camera. In this paper, we present a framework for the computation of dense, non-rigid scene flow from optical flow. Our approach leads to straightforward linear algorithms and a classification of the task into three major scenarios: (1) complete instantaneous knowledge of the scene structure, (2) knowledge only of correspondence information, and (3) no knowledge of the scene structure. We also show that multiple estimates of the normal flow cannot be used to estimate dense scene flow directly without some form of smoothing or regularization. 1

. 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 ...

Abstruct-Zstimating the three-dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics, such as autonomous navigation, manipulation, servo, tracking, docking, planning, and surveillance. Although “visual motion estimation” is an old problem (the first formulations date back to the beginning of the century), only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions. In this paper we formulate the visual motion estimation lproblem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold. Such a formulation has structural advantages over previous recursive schemes, since the estimation of motion is decoupled from the estimation of the structure of

Active cameras provide a navigating vehicle with the ability to fixate and track features over extended periods of time, and wide fields of view. While it is relatively straightforward to apply fixating vision to tactical, short-term navigation tasks, using serial fixation on a succession of features to provide global information for strategic navigation is more involved. However, active vision is seemingly well-suited to this task: the ability to measure features over such a wide range means that the same ones can be used as a robot makes a wide range of movements. This has advantages for map-building and localisation. The core work of this thesis concerns simultaneous localisation and map-building for a robot with a stereo active head, operating in an unknown environment and using point features in the world as visual landmarks. Importance has been attached to producing maps which are useful for extended periods of navigation. Many map-building methods fail on extended runs because ...