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Derivative Measurement in 3-D

Our three-dimensional filters are just the usual seperable product of three 1-D filters, so the 3-D partial derivative filters are some combination of reconstruction and derivative filters along X, Y, and Z.

This is sort of filter you'll need for the gradient, these are thes sorts of things you'll need for the Hessian.

Remember that we're using different filters, convolved with the same data, to get different derivatives, so there is no pre-computing or storage overhead. Everything is computed on the fly.

So the last issue is, how do you pick these filters?