Relations
Pixel 2002 by Yu Hen Hu
ECE533 Digital Image Processing
Neighboring, Adjacency
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N4(p): 4-neighbors N (p): 4-diagonal
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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
2002 by Yu Hen Hu
q s p r
q s p r
ECE533 Digital Image Processing
Path, Connectivity, Region
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Path:
a path from p = (s,t) to q = (x,y) is a set adjacent points
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P(p,q) = {(s,t), ..., (xi, yi), ..., (x, y)}
If (s, t) = (x, y), P is a closed path.
q
q
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.
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S is a connected set if it has only one connected S component. 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.
2002 by Yu Hen Hu
ECE533 Digital Image Processing
Distance Metrics
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Normed distance
Given pixels p, q, r, a function D(p,q) is a distance function if
a) D( p, q ) p 0 and D( p, q ) = 0 iff p = q b) D( p, q ) = D(q, p ) c) D( p, r ) D(...