Digital Geometry in Image Processing

List of Tables

2.1 Common neighborhood definitions in n-D [60, 58]. Neighbor-

hood conditions and co sts are shown for neighbors u, v ∈ Z

n

. 33

2.2 Illustrations for metric behaviour of transformed Euclidean

distance in 2-D. . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.3 MPT examples. . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.4 m-Neighbor Norms in 2-D and 3-D. . . . . . . . . . . . . . . 45

2.5 t-Cost norms in 2-D and 3-D. . . . . . . . . . . . . . . . . . 49

2.6 Functional forms of d(x; B)’s in 2-D [71], p = 1, 2, 3, 4. For

compactness we use α

1

= max(|x

1

|, |x

2

|), α

2

= |x

1

| + |x

2

|. . 56

2.7 Functional forms of d(x; B)’s in 3-D [71], ...