Digital Signal Processing Reference
In-Depth Information
→
Figure 3.2.
Voronoi Order of a contour C
E
C:
Given
y on the image space,
→
C
||
φ
(
C,y
) =
(see Definition 3.2) for a contour C b) the Voronoi Order on the
||
-
exterior of C as image intensity can guide the object boundary search through order
consistency in Chapter 4 (see Definition 3.7) c) the Voronoi Order on the interior of
C; its discontinuities lead to a weighted skeleton called Voronoi Order Skeleton, used
for MPEG-7 shape query in Chapter 6.
V
Distance, we create a warped grid where crossings between the two level
sets are orthogonal.
By treating the image plane as a graph where each pixel is a node and
the edges correspond to pixel adjacency, a good approximation of the
Voronoi Ordered Space mapping can be calculated by a modified Dijk-
stra's shortest path algorithm.
This algorithm runs in time
O
(
n
log
n
)
where n is the number of pixels [Cormen et al., 1990].
4. PROPERTIES OF VORONOI ORDERED
SPACE
This section proves some key properties of the Voronoi Ordered Space
and gives some insights of how to apply Voronoi Ordered Space in our
system designs. This section condenses proofs presented by Ogniewicz
and Kubler [Ogniewicz and Kubler, 1995]. We focus upon the Voronoi
Order, and how it orders the image space (see Figure 3.2). If we consider
only contours that are monotonically increasing along its path w.r.t. the
Voronoi Order of a given contour, we can find a subset of contours related
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