Digital Signal Processing Reference
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Figure 6.5.
Mapping a Voronoi Order Skeleton (VOS) to a Ordered Tree: in a) we
threshold the VOS values, removing noise and small shape protrusions, next, in b),
we compose the image as a series of line segments joined at points, and, in c), we map
the skeleton structure to ordered tree where the children are ordered by angle in the
image plane.
of ancestors and descendants. An ordered tree is a tree that adds another
order to the sibling relationships, i.e., between the children of the same
parent. In a VOS, the sibling order and the ancestor-descendent order
represent the VOS multiresolution property and the clockwise orienta-
tion of the children w.r.t. their parent, respectively. Thus, an ordered
tree captures all the key features of the VOS. However, the ordered tree
is sensitive to noise and partitioning errors.
4. VOS REPRESENTATION VIA
DAG-ORDERED TREES (DOTS)
Although the VOS suggests an ordered tree structure, the concept of
ordered trees must be generalized to DAG-Ordered Trees (DOTs, to be
defined in this section) to give the necessary robustness for our shape
comparison. The representation of the Voronoi Order Skeleton as an
ordered tree composition of line segments may be ambiguous and/or
sensitive to noise. Our solution will be based upon the DAG-based
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