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Generally the relative exposure values are not known a-priori.
Thus simultaneously solving for and is an optimization
problem:
- Initially, pairwise comparagrams are constructed and unrolled, each
assuming an arbitrary value of (e.g. ).
The resulting function estimates for each pair of images
will have the same overall shape, but each be scaled differently,
apart from noise.
- Next these estimates of are used to estimate
the relative values. Without loss of generality,
may be assumed, and
may be found.
- Next the estimates of are consolidated (averaged together)
by using the above estimates of
to register
them. This registered and averaged is now used to
re-estimate the values, by comparing ratios:
K_i = F^-1 - Q
where is the logarithm of the reference quantity of light.
(At this point, this first guess is often good enough to stop, but
may undergo successive refinements by continuing as follows...)
- Finally, if desired, images are sorted in increasing order
of exposure (least to greatest), and a final estimate
of is made across all pairs of images,
using the estimates of .
- If desired, this process may again be repeated, e.g. using that estimate
to again estimate and so on.
Subsections
Next: The general case: multiple
Up: . Introduction: Variable gain image
Previous: Estimation with more than
Steve Mann
2002-05-25