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the predicted grouping (aj), instead of on the whole image. Second, the relational descriptions for straight lines of
homologous grouping (ai and a’) are accomplished. Finally, the matching strategy is applied to identify the correct
correspondences between straight lines of grouping a; and a',. This strategy is then repeated for other homologous
groupings.
2.1 Feature Extraction
The feature extraction is applied only in the small window enclosing the predicted position of the selected ground
control grouping. The following steps are then sequentially applied to the automatically extracted sub-image: 1-
gradient magnitude and direction are computed for each pixel; 2- an automatic thresholding process eliminates those
pixels with low gradient response; 3- edges are thinned with non-maxima suppression; 4- isolated pixel are eliminated:
5- edge pixels are labeled and connected; and 6- a line fitting is finally applied to compute the straight line parameters
and the endpoints of each segmented line. Details of this method can be found in Tommaselli and Dal Poz (1999).
The results of this step are the predicted grouping (a;) and the extracted grouping (a';). The prediction process is initially
carried out by using the approximate exterior orientation parameters (k , £ , w , X,, Y,, Z,) and those filtered by IEKF
after each correspondence is obtained. The related covariance matrixes are used to define the window where the
grouping a'; is to be extracted.
2.2 Relational Descriptions for Homologous Groupings
The relational descriptions are established for each straight line of homologous groupings (a; and a’;). A relational
description is a list of relations. Let O4 be an object and A be the set of its parts. An N-ary relation over A is a subset of
the Cartesian product AF- Ax...xA (N times) (Shapiro and Haralick, 1987).
A special type of relation, called 2 3
2 3 f f
star structure, is used in the f; f T S2 r
matching strategy. As defined by t he En
Cheng and Huang (1984), a star S3 f
structure rooted at node i is node i ' e 7
itself plus all its links and * :
neighboring nodes. Let consider S^ sr S1 Sm :
the straight lines fic a’; and f, c a;.
Thus, the following relational " fn fl fm
descriptions based on star structure, ' f f
whose roots are f, and f, (figure 1), (a) (b)
can be written:
Figure 1. Relational descriptions for f; (a) and f, (b)
Si. = IS’ }= ts}; 1.405 {8 1 .... Sn] (1)
gi = {S)= {shhie nn {ts os Su) Q)
In the figure 1(a), n is the number of neighboring nodes in the star gf: and f; is its root node. The neighboring nodes are
the straight lines f i5 f? . Therefore, the n+1 nodes in the star gf, are the straight lines of grouping a^i. Similarly, the
figure 1(b) shows the star ç* , whose components are the m straight lines f. Shor fm (1. e., the neighboring nodes) and
the straight line f,, i. e., the root node.
Each component (or links) of the star structure gf; (or gf) is a 5-tuple, expressed generically as follows:
s=(f,, f>, a, a, a3) 3
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 207
