Pixel Relations

Neighboring, Adjacency N4(p): 4-neighbors ND(p): 4-diagonal neighbors N8(p) = N4(p) ND(p) : 8-neighbors Adjacency: V: a set of gray levels s.t. if a pixel’s gray level in V, it will be used to establish adjacency. 4-adjacency 8-adjacency m-adjacency p p q s p r q s p r

Path, Connectivity, Region a path from p = (s,t) to q = (x,y) is a set adjacent points P(p,q) = {(s,t), …, (xi, yi), …, (x, y)} If (s, t) = (x, y), P is a closed path. p and q are connected in S if P(p,q)  S. The set {q; P(p,q)  S} is a Connected Component of p  S. S is a connected set if it has only one connected component. S is also called a Region. The boundary of a region R = {p; p  R, exists q  R, q  N(p)} If R is entire image, its boundary is the first and last rows and columns of pixels.

Distance Metrics Normed distance Euclidean distance Given pixels p, q, r, a function D(p,q) is a distance function if Euclidean distance L2 norm City-block distance L1 norm Chessboard distance L norm