Linear and Non-linear regression in the Flies Project

There are several ``opportunities'' for regression in the fly project:

• When we do the correction for the shift in images, we do it by doing a ``variance check'' in the neighborhood of a pixel. If the variance is lowest for a shift of two pixels right, one pixel up between two images, we assume that the images has moved by that amount. There's rounding, of course - the image hasn't really shifted by that amount, but by some fractional part thereof - but we need to compare pixels on a pixel by pixel basis (or do we?). At any rate, we do this right up the stack, pairing up images; we should really do a global fit, to see how the trajectory is working out. We might be able to fit a better trajectory by working over the whole stack, rather than simply pair-wise.
• Once we have the pixels all aligned, we try to figure out where a given pixel is in focus (if anywhere). We do a variance calculation as we proceed through the stack, hoping that we'll find a point where the variance is highest (and assume that this is the point where the pixel is in focus). We fit the variance, and so can assign a non-integral value to the ``height'' of the pixel's information (generating what we call the height map).