Abstracts of recent papers:



Motion estimation using the differential epipolar equation

L. Baumela, L. de Agapito, P. Bustos and I. Reid
Email
lbaumelalourdes,pbustos,ian

In the Proceedings of the International Conference on Pattern Recognition, 3rd - 8th September 2000

Postscript

We consider the motion estimation problem in the case of very closely spaced views. We revisit the differential epipolar equation providing an interpretation of it. On the basis of this interpretation we introduce a cost function to estimate the parameters of the differential epipolar equation, which enables us to compute the camera extrinsics and some intrinsics. In the synthetic tests performed we compare this continuous method with traditional discrete motion estimation and contrary to previous findings cannot perceive any computational advantage for the continuous method.



Self-calibration of rotating and zooming cameras

L. de Agapito, E. Hayman and I. Reid
Email
lourdes,hayman,ian

Technical Report OUEL 0225/00, Department of Engineering Science, University of Oxford

Postscript

In this paper we describe the theory and practice of self-calibration of cameras which are fixed in location and may freely rotate while changing their internal parameters by zooming. The basis of our approach is to make use of the so-called {\it infinite homography constraint} which relates the unknown calibration matrices to the computed inter-image homographies. In order for the calibration to be possible some constraints must be placed on the internal parameters of the camera. We present various self-calibration methods. First an iterative non-linear method is described which is very versatile in terms of the constraints that may be imposed on the camera calibration: each of the camera parameters may be assumed to be known, constant throughout the sequence but unknown, or free to vary. Secondly, we describe a fast linear method which works under the minimal assumption of zero camera skew or the more restrictive conditions of square pixels (zero skew and known aspect ratio) or known principal point. We show experimental results on both synthetic and real image sequences (where ground truth data was available) to assess the accuracy and the stability of the algorithms and to compare the result of applying different constraints on the camera parameters. We explore the degenerate configurations and identify that pure pan-tilt motion exhibits degeneracies when minimal constraints are imposed on the intrinsic parameters. We also identify some near-ambiguities that arise under rotational motions showing that coupled changes of certain parameters are barely observable making them indistinguishable. We then derive an optimal Maximum Likelihood estimator for the calibration and the motion parameters. Prior knowledge about the distribution of the estimated parameters (such as the location of the principal point) may also be incorporated via Maximum a Posteriori estimation. Finally we study the negative effect of radial distortion in the self-calibration process and point out some possible solutions to it.



Camera calibration and the search for infinity

R. Hartley, E. Hayman, L. de Agapito and I. Reid
Email
hartley , hayman , lourdes , ian

In the Proceedings of the International Conference on Computer Vision, Sept 1999.

PDF

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 limiting 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 non-translating 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 256Mhz 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.



Linear calibration of a rotating and zooming camera

L. de Agapito, R. Hartley and E. Hayman
Email
lourdes,hartley,hayman

In the Proceedings of the Computer Vision and Pattern Recognition Conference, June 1999.

Postscript

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.



Self-calibration of a rotating camera with varying intrinsic parameters

L. de Agapito, E. Hayman and I. Reid
Email
lourdes,hayman,ian

In Proceedings of the ninth British Machine Vision Conference, Sept 1998.

Postscript

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.



Self-calibrating a stereo head: an error analysis in the neighbourhood of degenerate configurations

L. de Agapito, D.Q. Huynh and M.J. Brooks
Email
lourdes,du,mjb

in Proceedings of the sixth International Conference on Computer Vision, 1998. Bombay (India).

Postscript

We show that the self-calibration of a stereo head from corresponding points in an image pair is in certain circumstances prone to considerable error. A novel error analysis reveals that the automated determination of relative orientation and focal length is adversely affected when the cameras verge inwards a similar amount, and when the principal point locations have a horizontal error. This analysis is facilitated by the adoption of closed-form solutions for self-calibration from previous work of Brooks et al. It is also shown that estimation of the fundamental matrix associated with a stereo head image pair is improved when a domain-specific parameterization and associated computational techniques are adopted. Experiments conducted with such image pairs suggest that, given cognisance of sensitive configurations and adoption of the revised method of fundamental matrix estimation, robust reconstructions are attainable. This is demonstrated on the problem of metrically reconstructing a scene from two pairs of images obtained by an uncalibrated stereo head undergoing unknown ground-plane motion.



Towards robust metric reconstruction via a dynamic stereo head.

M.J. Brooks, L. de Agapito, D.Q. Huynh and L. Baumela
Email
mjb,lourdes,du,lbaumela

submitted.

Postscript

We consider the problem of metrically reconstructing a scene viewed by a moving stereo head. The head features two cameras with coplanar optical axes arranged on a lateral rig, each camera being free to vary its angle of vergence. Under various constraints, we derive novel explicit forms for the epipolar equation, and show that a static stereo head constitutes a degenerate camera configuration for carrying out self-calibration in the sense of Hartley. The situation is retrieved by consideration of a stereo head undergoing ground plane motion. New closed-form solutions for self-calibration are thereby obtained. It is also shown that the quality of scene reconstruction is much enhanced by the adoption of domain-specific techniques for computation of the fundamental matrix. An error analysis reveals that reconstruction is adversely affected by inward-facing camera vergence angles that are similar in value, and by a principal point location whose horizontal component is in error. Experiments conducted with dynamic stereo head images suggest that, given cognisance of these sensitivities, robust reconstructions are attainable.



Direct methods for self-calibration of a moving stereo head

M.J. Brooks, L. de Agapito, D.Q. Huynh and L. Baumela
Email
mjb,lourdes,du,lbaumela

in Proc. Fourth European Conference on Computer Vision, Cambridge, UK. April 1996.Lecture Notes in Computer Science, 1065, Vol. II, pages 415-426. Springer-Verlag, B. Buxton and R. Cipolla (eds.).

Postscript

In this paper we consider the self-calibration problem in the special context of a stereo head, perhaps the most commonly adopted binocular camera configuration in robotics. Here two cameras are arranged on a lateral rig with coplanar optical axes, each being free to vary its angle of vergence. Under various constraints, we derive explicit forms for the epipolar equation, and show that a static stereo head constitutes a degenerate camera configuration for carrying out self-calibration in the sense of Hartley. The situation is retrieved by consideration of a special kind of motion of the stereo head in which the baseline remains confined to a plane. A new direct method for self-calibration is thereby obtained, inspired by an earlier discrete analysis approach by Zhang et al. Key factors in this approach are the development of explicit, analytical forms of the fundamental matrix, and the use of the vergence angles in the parameterisation of the problem.


Lourdes de Agapito Vicente
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