Image Processing Reference
In-Depth Information
TABLE 6.1: Percentage average error between the rotated image using pixel
representation and the rotated reconstructed image using approximated Eu-
clidean circles for medial disks in MATs.
B
Avg. E
rot
(θ)
B
Avg. E
rot
(θ)
{1}
9.98
{12}
7.01
{1112}
4.94
{122}
10.23
{112}
4.58
{1222}
11.84
TABLE 6.2: Percentage average error between the rotated image using voxel
representation and the rotated reconstructed image using approximated Eu-
clidean spheres for medial disks in MATs.
B
Avg. E
rot
(θ)
B
Avg. E
rot
(θ)
{1}
12.8
{13}
12.6
{112}
7.7
{133}
17.5
{113}
8.6
{2}
23.2
{12}
9.7
{223}
23.5
{122}
13.3
{23}
24.7
{123}
14.6
{233}
26.3
The experimental results confirm that distance metrics with octagonal
neighborhood sequences {112} and {1112} are good approximations for the
representation of 2-D data. Similarly in 3-D, good octagonal distances are
found to be {112} and {113}.
6.5 Computation of Normals at Boundary Points of 2-D
Objects
In this section, we discuss how MAT is useful in computing normals at
boundary points of a 2-D binary object. In Fig. 6.12, the principle behind this
computation is illustrated. Let p be a point on the contour of a 2-D object
and let a medial disk touch the contour at p. Let its center be o. Then po
forms the inward normal at point p. This concept is extended for computing
normals using digital disks. It can easily be seen that the technique requires
correspondences between boundary points and their touching medial disks.
Additional computation is required to derive this necessary information from
the MAT representation. However, the technique as opposed to analytical
