Slide 12 of 42
So, what does it mean to do edge detection in the data value domain?
Well, like any edge detector we're going to have to measure some kind
of derivatives. Specifically, we're interested in how the data value
chanages as we move from one material to another, through a boundary.
Now, vector calculus tells us that the gradient direction points in
the direction of fastest increase, so that means we want to know how
the data value changes as we move along a path in the gradient
direction. That kind of derivitive is called a "directional
derivative", and that means we're interested in the first and second
directional derivatives along the gradient direcion. There's a
precise notation for that, but I'm going to just be using this short
hand of f' and f''. That short hand also emphasizes the fact that
these derivatives are scalar quantities, and not vectors or tensors.
