VORONOI ORDERED SPACE - Video Object Extraction and Representation: Theory and Applications - page 57

Voronoi Ordered Space 57

Figure 3.6. Steps in calculating the Voronoi Ordered Skeleton a) the Original Con-
tour, b) the Voronoi Order of the interior where the image intensities are mapped to
order values, c) the Voronoi Order Skeleton, calculated from the Voronoi Order (see
Eq. 3.6).

a) b)

Figure 3.7. The Tree Structure of Voronoi Ordered Skeleton: given a contour in a),
we can derive a Voronoi Order Skeleton in b). We can map the points on the interior
to a tree where value of χ V

(Eq. 3.6) reflects at what depth the point exists within

the tree.

6. MULTIRESOLUTION PROPERTY OF THE

VOS

In this section, we show that χ V is formally related to a multireso-
lution representation of shape contour. From analysis of the MAT, we