CONTENTS
Foreword
Acknowledgements
Notation
Preface
xv
xvii
xix
xxiii
CHAPTER 1 Digital topology
1.1
1.2
1.3
1.4
1.5
Continuous to discrete images
Neighbourhoods
Discrete sets
Discrete distances
Compatibility with continuous distances
CHAPTER 2 Discrete geometry
2.1
2.2
2.3
2.4
2.5
Introduction
Discrete straightness
Discrete convexity
Discrete curvature
Parallelism and orthogonality
CHAPTER 3 Algorithmic graph theory
3.1
3.2
3.3
Definitions
Optimisation
Analogies with digital image processing
CHAPTER 4
Acquisition and storage
4.1
4.2
Digitisation
Storage of binary digital images
CHAPTER 5 Distance transformations
5.1
5.2
5.3
5.4
Definitions and properties
Discrete distance transformations
Euclidean distance transformations
Related results
CHAPTER 6 Binary
digital image characteristics
6.1
6.2
6.3
Connected component labelling
Noise reduction
Shape factors
1
3
6
12
26
35
35
36
56
68
74
77
77
84
96
105
105
126
139
139
142
153
166
173
173
180
188
vi BINARY DIGITAL IMAGE PROCESSING
CHAPTER 7 Image thinning
7.1 Skeleton models
7.2 Thinning algorithms
7.3 Binary line images
CHAPTER 8 Some applications
8.1 Circuit image
8.2 Road map image
8.3 Fingerprint image
8.4 Text image
8.5 Drawing image
References
199
199
205
211
223
223
226
227
228
230
233
Index 247
LIST OF FIGURES
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Different sampling schemes
Resulting pixels from sampling
N6(p): 6-neighbourhood of the point p on the triangular lattice
Neighbourhoods on the hexagonal grid
Neighbourhoods on the square grid
A 6-digital closed curve
A 3-digital closed curve
A 12-digital closed curve
A 4-digital closed curve
A 8-digital closed curve
Borders of a binary digital image
A 6-discrete disc of radius 4, centred at p
Distribution of discrete points on regular lattices
4-Disc of radius 3: A4(3)
8-Disc centred at p and of radius 3: As(p, 3)
Knight-discs
Mapping from the triangular to the square lattice
Hexagonal discs on the square lattice
Oct-disc
of radius 4, Aoct(4)
Chamfer discs
Neighbourhoods corresponding to Farey sequences
Calculation of
d~,b
in the first octant
The graph of
E,,b
in the first octant
Calculation of
da,b,c
in the first octant
The graph of
Ea,b,c
in the first octant
Geometrical inconsistencies in the discrete distance calculations
Non-invariance of
da,b
against rotation
Geometrical explanation of the non-invariance of
da,b
Grid-intersect quantisation
Freeman's codes in the 8-neighbourhood
An example of the use of Freeman's codes
A general sketch for the chord properties
Example of the validity of the chord property
Example for the violation of the chord property
Example for the validity of the compact chord property
Example for the violation of the compact chord property
vii
2
2
4
5
5
8
8
9
9
9
11
14
15
16
17
19
20
20
21
23
25
28
28
29
30
32
33
33
37
38
39
41
42
42
43
44

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