1. compute edges
2. derivatives using kernels and neighborhood operations
3. three methods for computing edges using kernels
4. image noise can complicate the computation of gradient
5. the canny edge detector
Derivatives as a local product
δF(x,y)/δx = F(x+1,y) – F(x,y)
=[-1 1]*[F(x,y), F(x+1,y)]^T
Desired: An “operator” that effectively compute discrete derivative values with cross-correlation(i.e. using finite differences*)
Hx, Hy
Average of “left” and “right” derivatives
Impact of Noise on Gradients
It gets harder to detect an edge when there is significant noise in the signal.
original signal no noise
original signal + 0.1 x noise
original signal + 0.25 x noise
BWB, increse noise
Convolution and Gradients
recall, convolution is G = h * F
derivative of a convolution δG/δx = δ/δx(h*F)
If D is a kernel to compute derivatives and H is the Kernel for smoothing…
