Digital Signal Processing Reference
In-Depth Information
Figure 6.4.
The Extraction of a Voronoi Order Skeleton (VOS): From Chapter 3, we
merely calculate the Voronoi Order on the interior of the shape contour in a), and
apply the Eq. 3.1 for an approximation of the VOS. Note the lightness of the image
is proportional to the Voronoi Order and VOS values.
for the assumptions of support structure existence and classification.
The location and values of the Voronoi Order Skeleton quantifies the
concepts of support structure placement and strength, respectively.
As shown in Figure 6.4, the VOS reduces the shape to a skeleton-like
structure and, for certain classes of objects, the VOS corresponds well
to the projection of physical skeleton. The assumptions of the support
structure existence and classification are dependent on the object class.
Currently, we blindly apply VOS shape extraction to our shape contours.
In the future, we would have preprocessing to recognize whether our
shape descriptor is applicable to the object. It is important to note that
while the physical support structure is a 3-D concept, the VOS extracts
only a projection of this support structure and is also highly dependent
on viewing angle of the object.
An equidistance property of the VOS formalizes our placement as-
sumption. For the support structure placement assumption, the loca-
tions of non-zero points on the VOS are equivalent to the Medial Axis
Transform (MAT). The MAT is the set of points that axe equidistant
from two or more points on the shape contour. Thus, the non-trivial
VOS values are merely a thinned version of the original contour.
The relationship between the VOS value and the internal structure
of the Voronoi Areas describes our assumption of support strength (see
Section 6.). If we relate the support structure strength to the perime-
ter contained by the largest Voronoi Area of a point, the values of the
Voronoi Order Skeleton match this support structure strength assump-
tion.
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