4 New Developments and Open Questions 
This paper has mainly concentrated on single view (object recognition) or two views 
(motion based grouping, structure recovery) for a perspective (central) projection 
camera. Similar uncalibrated models have been developed for a pushbroom camera 
by Hartley and applied to SPOT images [11], and X-ray analysis. 
The fundamental matrix is a bilinear relationship between two images that does 
not depend on structure. In a similar manner there exist trilinear relationships [7] 
between a triplet of images which are structure independent (i.e. only depending on 
the camera internal parameters and relative dispositions). These relationships are 
encapsulated in the “tri-focal tensor” which was originally developed by Shashua [25] 
for point correspondences between three images, and shown by Hartley [12] to apply 
also to line correspondences between image triplets. Recently, Carlsson [5] has 
established a duality relation so that uncalibrated methods developed for m points 
in n views can be applied directly to n + 4 points in m — 4 views. This has opened 
up a host of possibilities for initialising structure and cameras from 4+ views. 
There are a number of questions which the uncalibrated approach repeatably 
generates, for example: 
1. Is accuracy (e.g. of computed epipolar geometry) lost by taking an uncalibrated 
route, as compared to the calibrated? 
2. Where internal calibration is available or partially available, how can it be 
used to advantage? 
The answer to the first question appears to be no, the second is harder to answer so 
succinctly, though calibration can be used to reduce search regions in uncalibrated 
matching through image sequences. Other questions, such as how to carry out an 
error analysis in projective 3-space, are less easy to handle. 
Acknowledgements 
This paper is based on the work of the Oxford Robotics Group, particularly Paul 
Beardsley and Phil Torr. Financial support was provided by EU Esprit Project 6448 
‘VIVA’. 
References 
[1] Armstrong, M., Zisserman, A. and Beardsley, P.A., Euclidean reconstruction from 
uncalibrated images. Proc. British Machine Vision Conference, 1994. 2 3 
[2] Ayache, N. and Faugeras, O.D. “HYPER: A New Approach for the Recognition and 
Positioning of Two-Dimensional Objects,” IEEE Trans. PAMI, Vol. 8, No. 1, p.44-54, 
January 1986. 
[3] Beardsley, P.A., Zisserman, A. and Murray, D.W., Navigation using affine structure 
and motion. Proc. ECCV, LNCS 800-801, Springer-Verlag, 1994. 
Zisserman - 13