Image Processing Reference
In-Depth Information
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FIGURE 6.12: Schematic diagram for normal computation.
regression-based techniques [206] of fitting boundary curves, is distinguished
by two characteristics. First, it does not require contour tracing, including
the computation for determination of inward or outward direction of normal.
Next, the whole computation can be performed using integer arithmetics only.
We discuss the algorithm below.
6.5.1 Algorithm for Normal Computation
Let the set of contour points of a 2-D object be denoted as C, and let S
be the set of medial disks for the object. The algorithm works in two stages.
First, the correspondence of a contour point and a medial disk is established
by checking its distance from the center. In an ideal case, the distance should
be equal to the radius of the disk. However, to provide tolerance in the com-
putation, a margin of error is allowed. Hence, a boundary point may have
a number of corresponding medial disks. The normal is computed as the re-
sultant of all these vectors. The algorithm [153] is briefly presented below:
6.5.2 Use of Octagonal Distances
As it is observed that digital circles of octagonal distances such as {112},
and {1112} in 2-D, closely resemble Euclidean circles, the NCUM algorithm
should use one of these octagonal metrics. To observe the accuracy of normal
computation, in [153], experiments were carried out with objects of known
geometry, such as circles, squares, and rectangles. A typical example is shown
