Slide 22 of 42
Then the second question about histogram volume measurement- just how
do you measure those directional derivatives. Well, the first
derivative is easy- its just the gradient magnitude, and we're using
central differences to get the partial derivatives needed for the
gradient vector. The second directional derivative is a little more
complicated, and there are actually a few expressions that you can use
for this. We've chosen this one, a matrix product of g, the unit
length gradient direction, and H, the hessian, which is a 3x3 matrix
of partial derivatives. For this too, there are simple discrete masks
which can be used to measure the partial derivatives needed. So
now we know how to make a histogram volume.
