Image Processing Reference
In-Depth Information
Chapter 3
Digitization of Straight Lines and
Planes
3.1
2-D Discrete Straight Line Segments ............................ 90
3.1.1
Computation of Support Line of DSLS ................. 93
3.1.2
Number Theoretic Characterization and Domain of
DSLS ..................................................... 95
3.2
Iterative Refinement: An Algebraic Characterization ...........
98
3.2.1
Gradient and Intercept Estimation ...................... 98
3.2.2
Reconstruction of a DSLS ............................... 100
3.2.3
Computation of Precise Domain of a DSLS ............. 102
3.2.4
Speed and Convergence of Iterative Refinement ........ 106
3.2.5
Length Estimators ....................................... 107
3.2.5.1
(n)-characterization [76, 79] ............... 109
3.2.5.2
(n
e
,n
o
)-characterization [76, 79] ........... 109
3.2.5.3
(n,q,p,s)-characterization [76, 79] ......... 109
3.3
Three-Dimensional Digital Straight Line Segments ............. 109
3.3.1
Geometric Preliminaries, Digitization, and
Characterization ......................................... 110
3.3.1.1
Digitization of a 3-D Line Segment ........ 112
3.3.1.2
Characterization of a 3-D DSLS ........... 113
3.3.2
Characterization of Chain Codes of 3-D DSLS ......... 113
3.3.2.1
n-characterization .......................... 114
3.3.2.2
(n,n
o1
,n
o2
)-characterization ............... 114
3.3.2.3
(n,n
o1
,n
c1
,n
o2
,n
c2
)-characterization ...... 114
3.3.2.4
(n,q
1
,p
1
,s
1
,q
2
,p
2
,s
2
)-characterization .... 114
3.3.3
Length Estimators for Different Characterizations ..... 114
3.3.3.1
(n)-characterization [39] ................... 115
3.3.3.2
(n,n
o1
,n
o2
)-characterization [39] .......... 116
3.3.3.3
(n,n
o1
,n
c1
,n
o2
,n
c2
)-characterization [39] . 116
3.3.3.4
(n,q
1
,p
1
,s
1
,q
2
,p
2
,s
2
)-characterization .... 116
3.4
Digital Plane Segments .......................................... 117
3.4.1
Digitization and Netcode Representation .............. 117
3.4.2
Geometric Characterization ............................. 119
3.4.3
Characterization by Convex Hull Separability .......... 120
3.4.4
Area Estimators ......................................... 122
3.4.4.1
n
2
-characterization ......................... 123
3.4.4.2
(n
1
,n
2
,n
3
) -characterization ............... 123
89
