• If x and x' are corresponding image points in two views, then 
x' T Fx = 0. (2) 
• 1' = Fx is the epipolar line corresponding to x (since x' T l' = 0). 1 = F T x' is 
the epipolar line corresponding to x'. 
• The epipoles satisfy the equations Fe = 0, F T e' = 0. 
• F has 7 DOF — there are 9 matrix elements but only their ratio is significant, 
which leaves 8 DOF. In addition the elements satisfy the constraint detF = 0 
which leaves 7 DOF. 
• Given the image correspondences of 7 points in general position, there are one 
or three real solutions for F. Given the image correspondences of 8 or more 
points in general position F is determined uniquely up to scale from the eight 
linear equations provided by (2). 
2.1.2 Computation of F for an uncalibrated image sequence 
We assume here that the scene viewed by the moving camera is static. In an image 
sequence (acquired at 25Hz) the constraints available are that features will generally 
not have moved “too far” between frames, and will not have changed “too much” 
in appearance. Algorithms have been developed which use these constraints and 
no others in order to compute the epipolar geometry and match features between 
two views — i.e. there is no a priori knowledge of motion or internal calibration. 
Generally, the algorithm proceeds by extracting point features from each image 
using interest operators (often termed “corner detectors”). These point features 
are then matched automatically between views. The two constraints are utilised 
in the matching by restricting correspondence search to a window centred on the 
current position of the feature, and assessing matching strength by measuring the 
cross correlation of intensity around the putative corner match. 
Generally far more correspondences are obtained than the minimum of eight 
required for a unique solution (typically there may be 100+ correspondences in a 
512 x 512 image), and a least-squares type scheme is employed to improve the estima 
tion of F. Mismatches severely disrupt such least squares schemes (and mismatches 
will inevitably occur). Consequently there has been increasing use of robust tech 
niques, particularly the RANSAC algorithm, to reject outliers (mismatches) during 
the estimation. 
The random sample consensus paradigm (RANSAC) is the opposite to conven 
tional least squares techniques where as much data as possible is used to obtain a 
solution. Instead, as small a subset as is feasible is used to estimate the parameters, 
and the support for this solution measured. For example, in the computation of the 
fundamental matrix, putative fundamental matrices are estimated using random 
samples of seven correspondences. The distance of all points from their correspond 
ing epipolar line (defined by the fundamental matrix) is then calculated, and if it is 
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