CIPA 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
58 
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With the Abuner matrix one can determine the degree of 
similarity between leaves. This matrix is used to find the 
sequence. 
2.5 Spatial Boundary Intersection 
Apart from the Fourier descriptors another shape similarity 
measure was also used. In this approach, boundaries of every 
leaf pair were intersected (Figure 8), and two features of the 
intersected area were calculated: intersected area and standard 
deviation of the intersection distances (in pixel unit). 
The standard deviation of the intersection distances were 
calculated according to Equation (9). Start and end points of the 
inner lines were determined according to junction points of two 
boundaries (Figure 8). Equally spaced points were determined 
along both boundaries between the two junction points, and 
these points were linked as inner lines. 
IT Ad 2 
int dist = -I -= n: number of lines (9) 
V n 
2.6 Evaluation of the Shape Data using Tree Search 
In the evaluation step. Df ouner and Antersection matrices were 
used to generate the proposed sequence. These matrices can 
easily solve the partial problems: which leaves might be 
ancestor and successor for a pointed leaf in the sequence? But 
the global problem still remains: how can this information be 
evaluated efficiently in order to generate the full sequence? In 
the first attempt, a simple evaluation scheme (Figure 9) was 
designed. 
Figure 9: Implemented simple evaluation scheme. 
Since the first 18 leaves were already fixed by the Museum, the 
algorithm started from the 18 th leaf. Although it provides good 
results for the first 1 st - 3 rd quarter of the full sequence, some of 
the last leaves are slightly different with respect to their 
neighbor leaves on the sequence. The reason of the outcoming 
result was the one-way search strategy of the implementation. 
In order to develop a better evaluation scheme, a tree search 
method was adopted. One of the well-known application topics 
of tree search methods is relational matching. The more general 
matching scheme has been developed by computer vision 
researchers (Shapiro and Haralick 1987, Boyer and Kak 1988). 
Successful applications of relational matching in 
photogrammetry were given by Haala and Vosselman (1992), 
Zilberstein (1992), Cho (1996), and Wang (1996). Several 
examples of potential applications of tree search methods in 
digital photogrammetry were also given by Vosselman (1995). 
Since cropping of individual leaf images followed by the 
rectification process was carried out in a common coordinate 
system that is defined by the holes in center of every leaf, all 
leaves have the same alignment. These two different shape 
descriptors were merged to one value using proper weights 
(Equation 10). 
dl t) = int disty • W mK _ dist + int area ■ fV int _ area i * j (10) 
Jfj ntdlst and lTj nt ar ea weight values were determined 
empirically (ITint dist = 10 > lTj nt _ area = 0.002). All dl\j values 
among the leaves were calculated, and an overall matrix was 
generated. 
A, 
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Similar to 
information about the similarity of a leaf pair. In the processing 
steps it was observed that both matrices (Afourier and 
Antersection) give very similar results. 
Search trees consist of hierarchical nodes connected by arcs. 
Tree starts from a root node and descends into successor nodes 
in a branched structure. An ancestor node can only branch into 
possible successor nodes in order to keep the volume of tree in 
acceptable limits. In the case of relational matching, the 
problem is to match two primitive sets, namely relational 
descriptions. The primitives p, = {p, , p 2 , ..., p n } P\ e P of 
one relational description are called units, and the primitives of 
the description to be matched q, = (qi , q 2 ,..., q m } q, £ Q are 
termed labels. The number of units defines the depth of the tree. 
The best mapping of P->Q is the path with the lowest cost. In 
our example a tree search scheme that starts from the 18 
(fixed) leaf and ends at the 66 th (relaxed) leaf was established. 
The rings of the sequence chain are defined as units. Therefore, 
the number of units, namely depth of the tree, and the number 
of labels are the same (49). Every node in the tree was defined 
as a leaf and branched to the most probable neighbor leaves. 
The root node is the 18 th leaf, which is the last leaf of the page 
numbered leaves. The similarity measures, calculated using 
shape descriptors, were expressed as the costs of the arcs, which 
connect two nodes in the tree. The implemented tree search 
method proposes the total path with minimum cost as the most 
probable sequence. Figure (10) shows a part of the designed 
tree search.