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## Multiresolution

Deals with the problem of scale, in two ways:

• It allows for large, global displacements with smaller, localised variations. This is exactly the sort of model we have in mind.
• It is computationally fast because it allows for `coarse-fine' processing: the solution at a large scale can be computed quickly and serves as a good constraint for that at the next scale.... and so on, until the full image resolution is reached. One way to look at it is as an analogue of the familiar Taylor series. Suppose we have the solution at scale m, then the solution at scale m-1 can be written, at least formally, as  (5)
where (dfm,dgm) is the vector of differences between the scale m+1 and scale m images. It is the case that the amount of energy at the smallest scales in these images is tiny - more than of the image energy is contained in the largest scales used in the geometry correction.
• In other words, the prior model is that we can express the warp via a conditionally normal model:  (6)

Next: Experiments Up: So What's the Problem? Previous: Geometry Correction

Roland Wilson
5/31/2000