A SYSTEM FOR IMAGE/VIDEO OBJECT QUERY BY SHAPE - Video Object Extraction and Representation: Theory and Applications - page 137

Figure 6.6. The Quantization of Hierarchy: Consider a continuum of continuous
contours on the top half of the figure. From left to right, protrusions grow out of
center of the line segment. At some point in the continuum, the protrusions are
over the threshold, causing a large change in hierarchy of the mapped ordered tree.
Although the contours are continuous, their ordered tree representations are highly
sensitive to noise near the threshold. This sensitivity will be problematic in our shape
comparisons.
representation described in Chapter 5 and extends the ordered tree to
represent a complex partitioning of the VOS. In this section, we discuss
the pitfalls of the ordered tree representation, introduce a new data
structure, DAG-Ordered trees (DOTs), and motivate the DOT data
structure for VOS representation. To handle a complex partitioning,
we generalize the data structure of an ordered tree to a DAG-ordered
tree where we order both the ancestor-descendent and sibling-sibling
relationships with a DAG.
QUANTIZATION OF HIERARCHY
Whenever a continuous structure such as the VOS of a contour is
mapped onto a discrete hierarchy such as a graph, a quantization of hier-
archy affects the robustness of our ordered tree representation. Consider
this simple case: let us consider a continuum of contour substructures in
Fig. 6.6. At some point in the continuum, the thresholding associated
with the VOS will not remove the branches, resulting in a drastic change
in the ordered tree associated with the skeleton. While the contour is
continuous, its corresponding ordered tree is discrete. This sensitivity
within the correspondence between contours and ordered trees can cause