
subvoxelprecise estimation of the extremum of a tabulated function
Posted:
Mar 6, 2012 3:40 AM


I have a regular 3D voxel grid (spacing 1) and a arbitrary (real) function evaluated at a 3x3x3 window in ('voxel grid') around a 'center' position (xc, yc, zc). So I have 27 function values at the postions (xc +{101}, yc +(101}, zc + (101})).
Now i want to interpolate a quadratical 'taylor' polynom into the function and find the position (xc_0, yc_0, zc_0) where the quadratical polynom has an extremum. How to do ? For the 1D case, i know how to do  see fn. 'P3Interpolate_Extremum_1' from http://www.ebyte.it/library/codesnippets/P3Interpolation.html. But how to 'generalize' this function to 3 dimensions ?? Furthermore, I'd like to know whether these 27 grid points and function values define my an unique quadratical polynom, or whether I have to fit a 'bestfitting' quadratical polynom into these points.
By the way the problem comes from implementing section 2 in paper http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A9B821E909E3269BFFDCB11CC4C07DA9?doi=10.1.1.1.8475&rep=rep1&type=pdf
Many thx for any suggestions.

