Thesis (PDF) - Signal & Image Processing Lab

3.2. TOPOGRAPHIC DISTANCE TREE IMPLEMENTATION 39
to the topographic-distance) of a previously processed flat zone. The new flat zone
then becomes a new node of the TD-Tree, linked as a son to the latter flat zone.
Its topographic-distance-function value is computed as that of the father plus the
topographic-distance between them.
A pseudo code of the modified Moore algorithm is given in Algorithm 1.
Algorithm 1 Modified Moore Algorithm
We modified algorithm of Moore, for topographic distance calculation, using definition
(2.18) of cost. Our modified algorithm is used not only for topographic distance
calculation, but also for TD-Tree building.
The algorithm, involves the following stages:
1: Assign zero to the topographic distance of the root node of the TD-Tree, and, to
the other nodes, assign an infinite topographic distance.
2: Initialize status vector of all flat zones to status ”in-queue”.
3: while not all nodes are ”done” do
4: Find the node with the minimal topographic distance.
5: Based on this minimal topographic distance, calculate the topographic distance
of the neighboring nodes, whose status are ”in-queue”, using the
graph structure. Store the node with the minimal topographic distance as
a father node of these neighboring nodes in the TD-Tree.
6: In the status vector, assign status ”done” to the node with minimal topographic
distance.
7: end while
The proposed representation is more efficient in storing the information about
alternating sequences than storing an alternating sequence for every flat zone. The
storage volume required for the alternating sequence for every flat zone depends on
the number of flat zones multiplied by the mean alternating sequence length. Size =
O(N · Length(AS)) � O(N 2 ), where N is a number of flat zones. Typical values of
N is in order of 10 4 for small images, and in order of 10 5 for larger images. When the
same information is presented as a tree, the required storage volume depends on the
number of flat zones multiplied by the size of the pointer to the father node, which is
much smaller than the average size of an alternate sequence. In this case the required
storage volume is linear to N: Size � O(N).