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Pixel Relations

Pixel Relations. N 4 ( p ): 4-neighbors N D ( p ): 4-diagonal neighbors N 8 ( p ) = N 4 ( p )  N D ( 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.

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Pixel Relations

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  1. Pixel Relations

  2. 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 Neighboring, Adjacency

  3. Path: 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. Path, Connectivity, Region

  4. Normed 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 Distance Metrics

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