Each of them are at a unit distance from P brPage 3br The four diagonal neighbors of p xy are given by x1 y1 x1 y1 x1 y1 x1 y1 This set is denoted by N P Each of them are at Euclidean distance of 1414 from P Neighbors of a Pixel Contd brPage 4br ID: 29131
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The four diagonal neighbors of pThis set is denoted by NEach of them are at Euclidean distance of Neighbors of a pixel a.4-neighborsb.8-neighbors 4 8 Adjacency Two pixels are connected if they are neighbors and their gray levels satisfy some specified criterion of similarity.For example, in a binary image two pixels are connected if they are 4-neighbors and Connectivity a.4-connected,b.8-connected,c.m-connected,i.q is in Nii.q is in N 011020 V = {1, 2})()(44qNpN 020 Pixel p is adjacentto pixel q if they are connected. image subsetsS1and S2 are adjacent if some pixel in S1is adjacent to some pixel in S2 1S2 Connected Components are pixels of an image subset S in S if there is a path from pconsisting entirely of pixels in S.For every pixel pin S, the set of pixels in S that are connected to pis called a connected componentof S.If S has only one connected component then S is called Connected Set. Distance measures a.D(p, q) 0 [D(p, q) = 0, iffp = q]b.D(p, q) = D(q, p)c.D(p, z) D(p, q) + D(q, z) (p, q) = [(x-s)b.City Block Distance: ÃD4(p, q) = |x-s| + |y-t|c.Chess Board Distance: (p, q) = max(|x-s|, |y-t|) 2 Neighborhood based arithmetic/Logic Value assigned to a pixel at position e is a function of its neighbors and a set of window functions. 9 8 7 6 5 4 3 2 1 ifwwwwwwwwwp i)hgfedcba(w 987654321 s(NExtrapolation of image