Thesis (PDF) - Signal & Image Processing Lab

40 CHAPTER 3. IMPLEMENTATION OF BTVT
3.3 Implementation of the BTV Transform
The first phase of the algorithm is to create a Region Adjacency Graph - RAG. The
RAG is a graph (V, E), where V is a set of all flat zones of the image, and E contains
all pairs of flat zones that are adjacent to each other. A theoretical background on
graphs and trees is given in section 2.1. We developed an algorithm for computing the
RAG image representation. A pseudo code of the algorithm is given in Appendix A.
The next step is to use the modified Moore algorithm for creation of a TD-Tree.
The modification of the Moore algorithm was explained in section 3.1.
In order to calculate an alternating sequence of every flat zone, we must fetch
the path variation of a component. The path variation fetch function, is a recursive
function, as can be seen in (3.1).
AS(V ) =
�
{AS(father(V )), GL(V ) − GL(father(V ))} if V �= root
{0} if V = root
(3.1)
Where AS(V ) is an alternating sequence of vertex V in the TD-tree. GL(V ) is the
gray level of V . father(V ) is the vertex preceding V in the TD-tree. For example,
AS(V2) in Fig. 3.1 gives an alternating sequence of {AS(V1), −3} in the first recursion
step, and {5, −3} in the next (and last) recursion step.
The alternating sequence computation can be performed as a preliminary step
before any operators are applied, or during an execution of an operator. The choice
between the two options depends on a specific tradeoff between storage size and
execution time.
In summary, the proposed algorithm for the implementation of the BTV transform
consists of three stages:
1. The input image is represented as a Regional Adjacency Graph (RAG) of the
flat zones partition.
2. Based on this RAG representation, the topographic distance is calculated and
the TD-Tree is obtained, using the modified Moore algorithm.
3. The BTV transform is calculated, using the TD-Tree.
Images of topographic distances, computed for synthetic and natural images, using
the modified Moore algorithm, are shown in Figures 3.2-3.5. The images are built