In the book: 4-neighbourhood, D-neighbourhood, 8-neighbourhood. Ignore these.
Usual: 1-neighbourhood, 2-neighbourhood, etc.
A "metric" measures distances between pixels
- Conditions on a metric $D(p,q)$ between pixel locations $p$ and $q$
- $D(p,q) \geq 0$
- $D(p,q) = 0 \quad \textrm{iff} \quad p=q$
- $D(p,q) = D(q,p)$
- $D(p,q) \leq D(p,r) + D(r,q)$
- Example metrics:
- Euclidean
- Manhattan (i.e. sum of absolute coordinates)
- Chessboard (i.e. max of absolute coordinates)
- On metric to rule them all: the "p-norm" = $( \sum_i |x_i|^p )^{1 \over p}$
- Euclidean is 2-norm
- Manhattan is 1-norm
- Chessboard is infinity-norm