We describe how 3D affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image. This minimal information is typically the vanishing line of a reference plane, and a vanishing point for a direction not parallel to the plane. It is shown that affine scene structure may then be determined from the image, without knowledge of the camera's internal calibration (e.g. focal length), nor of the explicit relation between camera and world (pose). In particular, we show how to (i) compute the distance between planes parallel to the reference plane (up to a common scale factor); (ii) compute area and length ratios on any plane parallel to the reference plane; (iii) determine the camera's (viewer's) location. Simple geometric derivations are given for these results. We also develop an algebraic representation which unifies the three types of measurement and, amongst other advantages, permits a first order error pr...

We describe a method to determine affine and metric calibration for a stereo rig. The method does not involve the use of calibration objects or special motions, but simply a single general motion of the rig with fixed parameters (i.e. camera parameters and relative orientation of the camera pair). The novel aspects of this work are: first, relating the distinguished objects of Euclidean geometry to fixed entities of a Euclidean transformation matrix; second, showing that these fixed entities are accessible from the conjugate Euclidean transformation arising from the projective transformation of the structure under a motion of the fixed stereo rig; third, a robust and automatic implementation of the method. Results are included of affine and metric calibration and structure recovery using images of real scenes. 1 Introduction It is known that from two uncalibrated views, 3D structure can be recovered modulo a projectivity of 3space [5, 8]. Furthermore, given three or more views acquir...

We present a canonical frame construction for determining projectively invariant indexing functions for non-algebraic smooth plane curves. These invariants are semi-local rather than global, which promotes tolerance to occlusion. Two applications are demonstrated. Firstly, we report preliminary work on building a model based recognition system for planar objects. We demonstrate that the invariant measures, derived from the canonical frame, provide sufficient discrimination between objects to be useful for recognition. Recognition is of partially occluded objects in cluttered scenes. Secondly, jigsaw puzzles are assembled and rendered from a single strongly perspective view of the separate pieces. Both applications require no camera calibration or pose information, and models are generated and verified directly from images.

This paper demonstrates a method of using nonmetric visual information derived from an uncalibrated active vision system to navigate an autonomous vehicle through free-space regions detected in a cluttered environment. The structure of 3-space is recovered modulo an affine transformation using an uncalibrated active stereo head carried by the vehicle. The plane at infinity, necessary for recovering affine structure from projective structure, is found in a novel manner by making controlled rotations of the head. The structure is composed of 3D points obtained by detecting and matching image corners through the stereo image sequence. Considerable care has been taken to ensure that the processing is reliable, robust and automatic. Driveable regions are determined from the projection of the affine structure onto a plane parallel to the ground determined using projective constructs. Two methods of negotiating the regions are explored. The first introduces metric information to allow contro...

this paper we describe a method for achieving affine calibration for a fixed stereo rig on an AGV using constraints that arise naturally during motion - namely, that translation is in a plane perpendicular to the rotation axis. We describe and compare two approaches which employ these constraints: first, by recovering structure modulo a projectivity, and thence the plane at infinity; second, by using only image measurements based on the fundamental matrix (i.e. no structure recovery). The methods require no knowledge of the translation or angle of rotation. All processing - point correspondence based on corners, computation of the fundamental matrix, 3D structure recovery, affine calibration - is robust and automatic.

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...

The systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years. Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpoint. This problem is entirely avoided if the geometric description is unaffected by the imaging transformation. Such invariant descriptions can be measured from images without any prior knowledge of the position, orientation and calibration of the camera. These invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification. Object models can be acquired directly from images, allowing efficient construction of model libraries without manual intervention. A significant part of the paper is a summary of recent results on the construction of ...

It is demonstrated that grouping together features which satisfy a geometric relationship can be used both for (automatic) detection and estimation of vanishing points and lines. We describe the geometry of three commonly occurring types of geometric grouping and present efficient grouping algorithms which exploit these geometries. The three types of grouping are : (1) a family of equally spaced coplanar parallel lines, (2) a planar pattern obtained by repeating some element by translation in the plane, and (3) a set of elements arranged in a regular planar grid. Examples of automatically computing groupings, together with their vanishing points and lines, are given for a number of real images. Key words: Grouping, Vanishing Point and Line Detection, Repetition. 1 Introduction Suppose a plane in the world is imaged by a perspective camera. Then the line at infinity of the plane is projected to a line in the image, the vanishing line. The objective of this paper is to automatically e...

The image motion of a planar surface between two camera views is captured by a homography (a 2D projective transformation). The homography depends on the intrinsic and extrinsic camera parameters, as well as on the 3D plane parameters.

. The objective of this work is to automatically estimate the trifocal tensor and feature correspondences over images triplets, under unrestricted camera motions and changes in internal parameters between views. To this end we extend a previous wide baseline 2-view algorithm to 3-views. The algorithm is based on establishing feature correspondences between views together with a homography which enables a viewpoint invariant affinity score. The input is the three images, and the output the trifocal tensor and image correspondences, which in turn facilitate a projective reconstruction of the cameras and scene. We also investigate the direct computation of the fundamental matrix for view pairs, and the trifocal tensor for view triplets, from the homographies alone. This method is successful, but not as yet as accurate as computation from point correspondences. Finally, it is shown that the 3-view algorithm allows reconstruction of 3D points, lines and cameras from a disparate set of 11 vi...