BMVC 2004, Kingston, 7th-9th Sept, 2004

On the Probabilistic Epipolar Geometry
S. S. Brandt (Helsinki University of Technology, Finland)

In this paper, we are going to answer the following question: assuming that
we have estimates for the epipolar geometry and its uncertainty between two
views, how probable it is that a new, independent point pair will satisfy the
true epipolar geometry and be, in this sense, a feasible candidate correspondence
pair? If we knew the true fundamental matrix, the answer would be
trivial but in reality it is not because of estimation errors. So, as a point in the
first view is given, we will show that we may compute a probability density
for the feasible correspondence locations in the second view that describes
the current level of knowledge of the epipolar geometry between the views.
We will thus have a point-probability-density relation which can be understood
as a probabilistic form of the epipolar constraint; it also approaches the
true point-line relation as the number of training correspondences tends to in-
finity. We will also show that the eigenvectors of the epipolar line covariance
matrix have certain interpretations on the image plane, of which one is the
previously observed, narrowest point of the epipolar envelope. The results
of this paper are novel and important since the uncertainty of the epipolar
constraint can be now taken into account in a sound way in applications.
(pdf article)