A powerful and popular approach for estimating radial lens distortion parameters is to use the fact that lines which are straight in the scene should be imaged as straight lines under the pinhole camera model. This paper revisits this problem using the division model to parameterise the lens distortion. This turns out to have significant advantages over the more conventional parameterisation, especially for a single parameter model. In particular, we demonstrate that the locus of distorted points from a straight line is a circular arc. This allows distortion estimation to be reformulated as circle-fitting for which many algorithms are available. We compare a number of suboptimal methods offering closed-form solutions with an optimal, iterative technique which minimises a cost function on the actual image plane as opposed to existing techniques which suffer from a bias due to the fact that they optimise a geometric cost function on the undistorted image plane.

Although a considerable amount of work has been published on material classification, relatively little of it studies situations with considerable variation within each class. Many experiments use the exact same sample, or different patches from the same image, for training and test sets. Thus, such studies are vulnerable to effectively recognising one particular sample of a material as opposed to the material category. In contrast, this paper places firm emphasis on the capability to generalise to previously unseen instances of materials. We adopt an appearance-based strategy, and conduct experiments on a new database which contains several samples of each of eleven material categories, imaged under a variety of pose, illumination and scale conditions. Together, these sources of intra-class variation provide a stern challenge indeed for recognition. Somewhat surprisingly, the difference in performance between various state-of-the-art texture descriptors proves rather small in this task. On the other hand, we clearly demonstrate that very significant gains can be achieved via different SVM-based classification techniques. Selecting appropriate kernel parameters proves crucial. This motivates a novel recognition scheme based on a decision tree. Each node contains an SVM to split one class from all others with a kernel parameter optimal for that particular node. Hence, each decision is made using a different, optimal, class-specific metric. Experiments show the superiority of this approach over several state-of-the-art classifiers

Statistical background modelling and subtraction has proved to be a popular and effective class of algorithms for segmenting independently moving foreground objects out from a static background, without requiring any a priori information of the properties of foreground objects. We present two contributions on this topic, aimed towards robotics where an active head is mounted on a mobile vehicle. In periods when the vehicle's wheels are not driven, camera translation is virtually zero, and background subtraction techniques are applicable. This is also highly relevant to surveillance and video conferencing. The first part presents an efficient probabilistic framework for when the camera pans and tilts. A unified approach is developed for handling various sources of error, including motion blur, subpixel camera motion, mixed pixels at object boundaries, and also uncertainty in background stabilisation caused by noise, unmodelled radial distortion and small translations of the camera. The second contribution regards a Bayesian approach to specifically incorporate uncertainty concerning whether the background has yet been uncovered by moving foreground objects. This is an important requirement during initialisation of a system. We cannot assume that a background model is available in advance since that would involve storing models for each possible position, in every room, of the robot's operating environment.. Instead the background mode must be generated online, very possibly in the presence of moving objects.

Algorithms for self-calibrating cameras whose changes in calibration parameters are confined to rotation and zooming are useful since many real-world imaging situations do not permit translations-consider, for instance, cameras mounted on tripods and desk or wall-mounted active heads. In practice, however, the assumption of pure rotation is often violated because the optic center of the camera and the rotation center do not completely coincide. This work determines how such misalignments affect the estimation of the camera focal length. Expressions for the errors in focal length and recovered rotations are derived and results are confirmed with experiments on synthetic data. We show that the approximation of pure rotation is indeed sufficient in many cases, especially since other sources of error, such as noise and particularly radial distortion, tend to be more detrimental.

In this paper we will show how rotation matrices obtained from image measurements, for instance via self-calibration of rotating cameras, may be used to self-align an active stereo head such that the optic axes of the cameras are parallel, horizontal and perpendicular to the elevation axis. Whereas general rotation matrices have three degrees of freedom, with robot heads we may generate motions with fewer degrees of freedom, and use prior knowledge of the kinematic chain to constrain the rotation matrices to have a particular form. We demonstrate how these constraints provide sufficient alignment information, and we provide fast, accurate and stable algorithms to achieve this task. Both a linear method, which minimizes an algebraic error, and two nonlinear methods which minimize meaningful errors, are presented, and we show in theory and experiments that they give virtually identical results. Results from both simulated data and from real images obtained from an active stereo head are presented.

A linear self-calibration method is given for computing the calibration of a stationary but rotating camera. The internal parameters of the camera are allowed to vary from image to image, allowing for zooming (change of focal length) and possible variation of the principal point of the camera. In order for calibration to be possible some constraints must be placed on the calibration of each image. The method works under the minimal assumption of zero-skew (rectangular pixels), or the more restrictive but reasonable conditions of square pixels, known pixel aspect ratio, and known principal point. Being linear the algorithm is extremely rapid, and avoids the convergence problems characteristic of iterative algorithms.

This paper considers the problem of self-calibration of a camera from an image sequence in the case where the camera's internal parameters (most notably focal length) may change. The problem of camera self-calibration from a sequence of images has proven to be a difficult one in practice, due to the need ultimately to resort to non-linear methods, which have often proven to be unreliable. In a stratified approach to self-calibration, a projective reconstruction is obtained first and this is successively refined first to an affine and then to a Euclidean (or metric) reconstruction. It has been observed that the difficult step is to obtain the affine reconstruction, or equivalently to locate the plane at infinity in the projective coordinate frame. The problem is inherently non-linear and requires iterative methods that risk not finding the optimal solution. The present paper overcomes this difficulty by imposing chirality constraints to limit the search for the plane at infinity to a 3-dimensional cubic region of parameter space. It is then possible to carry out a dense search over this cube in reasonable time. For each hypothesised placement of the plane at infinity, the calibration problem is reduced to one of calibration of a nontranslating camera, for which fast non-iterative algorithms exist. A cost function based on the result of the trial calibration is used to determine the best placement of the plane at infinity. Because of the simplicity of each trial, speeds of over 10,000 trials per second are achieved on a 256 MHz processor. It is shown that this dense search allows one to avoid areas of local minima effectively and find global minima of the cost function.

This paper describes methods for tracking using point and line features in affine views to provide fundamental invariance to changes of focal length. It first demonstrates how an earlier method of transfer-based tracking using spatio-temporal matching of point features in a stereo active head is indeed zoom-invariant. In order to also make use of lines the paper then illustrates how the affine tri- and quadrifocal tensors may be applied to tracking with zoom in monocular and stereo systems respectively. The usefulness of the tensors is evident from their ability to transfer a fixation point in two uncalibrated images into novel views. Whereas the trifocal tensor is already familiar and in common use for matching and reconstruction we believe this to be the first practical application of a quadrifocal tensor. We develop expressions for affine tri- and quadrifocal tensors, and using novel affine specializations of existing projective algorithms we show how computation of the tensors is faster simpler and more stable. Experiments on real images are presented.

We present a method for self-calibration of a camera which is free to rotate and change its intrinsic parameters, but which cannot translate. The method is based on the so-called infinite homography constraint which leads to a non-linear minimisation routine to find the unknown camera intrinsics over an extended sequence of images. We give experimental results using real image sequences for which ground truth data was available. 1

Zoom interacts strongly with both vision and control processes in an active visual system, causing problems for many commonly used tracking methods. This paper demonstrates the use of afne transfer to track while zooming, using clusters of corner features. Afne transfer not only is fundamentally invariant to zoom but also provides a natural mechanism to allow features to appear and disappear while tracking, events which will occur as detail sharpens and dissolves during zooming. The paper demonstrates ofine 3D afne transfer during zoom for objects undergoing substantial rotation, and describes real-time experiments using 2D afne transfer while zooming and tracking using an active camera platform.