# Digital geometry in image processing by Jayanta Mukhopadhyay, (College teacher); et al

By Jayanta Mukhopadhyay, (College teacher); et al

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Extra info for Digital geometry in image processing

Sample text

These planes are called digital neighborhood planes (DNP) of p. They are illustrated in Fig. 11. The neighboring condition of p determines the plane in which p lies. 11. In a digital picture, P = (G3 , 18, 6, O), the neighborhood plane set (NPS) of a point p belonging to an object O, is defined as: [p]k = {i||N18 (p) ∩ O ∩ Pi | > k)}, k ≥ 3. Here, |S| defines the cardinality of set S. The value of k usually lies between 3 and 5. It may be noted that in the above, N (p) denotes the set of neighboring points of p.

4. 1) paths in low dimensions [60]. Neighborhood set N (·) is represented simply by m. 2-D: Consider u = (2, 3) and v = (5, 8). Distance Functions in Digital Geometry Π1 (u, v; 1) = Π2 (u, v; 1) = = = = Π3 (u, v; 1) 35 {(2, 3), (3, 3), (4, 3), (5, 4), (6, 5), (6, 6), (7, 7), (8, 8), (7, 8), (6, 8), (5, 8)} {(2, 3), (3, 3), (4, 3), (5, 4), (6, 5), (6, 6), (7, 7), (6, 8), (5, 8)} {(2, 3), (3, 3), (3, 4), (3, 5), (4, 5), (5, 5), (5, 6), (5, 7), (5, 8)} Note: |Π1 | = 10 & |Π2 | = |Π3 | = 8 Π4 (u, v; 2) Π5 (u, v; 2) Π6 (u, v; 2) = = = = {(2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 5), (6, 6), (5, 7), (5, 8)} {(2, 3), (3, 4), (3, 5), (4, 6), (5, 7), (5, 8)} {(2, 3), (2, 4), (2, 5), (3, 6), (4, 7), (5, 8)} Note: |Π4 | = 8 and |Π5 | = |Π6 | = 5 3-D: Consider u = (3, 5, 6) and v = (2, 7, 4).

2 Chain Code . . . . . . . . . . . . . . . . 3 Neighborhood Plane Set (NPS) . . . . . . Topology Preserving Operations . . . . . . . . . . . . . . . . . 1 Skeletonization . . . . . . . . . . . . . . . . . . . . . . 2 Adjacency Tree . . . . . . . . . . . . . . . . . . . . . The Euler Characteristics . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . .