A Semi-Automatic Method for Resolving Occlusions in Augmented Reality
Computing the viewpoints
Our approach to motion computation takes advantage of 3D knowledge on the
scene as well as 2D/2D correspondences over time. The viewpoints are recovered
by minimizing :
A complete explanation is given here.
What you have to know to understand
the estimation of the uncertainty on the viewpoints is that the viewpoints
p
are recovered by minimizing a function (p).
Estimating the uncertainty on the viewpoints
It is reasonable to assume that values of
almost as low as (p*)
would satisfy us as much as (p*).
Indeed, we generally observe that slightly different viewpoints give similar
reprojection errors. This gives rise to an -indifference
region in p space described by :
In a sufficiently small neighborhood of p*, we may approximate
by means of the first few terms of its Taylor equation :
where H(p*) is the hessian of
computed at p = p*.
As p* is the minimum of
, the gradient is null at the optimum
so :
The indifference region is
then defined by :
which is the equation of a 6-dimensional ellipsoid. The next figure
shows the indifference regions for the translation parameters over a sequence
: