Aluir Dal Poz 
  
  
where (figure 2), 
f; and f; are two straight lines of a star; 
a, is the angle between straight lines f, and f; 
a, is the angle between the bisector of f, and f; 
and the axis ox; and 
e à; is the distance between the origin of the 
photographic reference system (oxy) and the 
intersection of straight lines f; and f£, or theirs 
extensions. 
The attribute a; is unstable whenever the straight lines fj 
and f» are close to parallel. In this case, the attribute a; is 
taken as the distance between the two straight lines. 
  
Figure 2. Definition of attributes a;, a», and a; 
  
  
  
2.3 Matching Strategy 
Three different criteria are applied sequentially in the matching process to check the correspondence between a straight 
line (f;) from the grouping a; and another (fj) from the grouping a';. First, the so-called rigidity constraint is used as a 
first filter for the correspondence that is being analyzed (f;, f;). Next, this correspondence is checked by the relational 
distance (nrd). Finally, a statistical decision based on data snooping test is used for verifying whether the 
correspondence (f, f) is accepted or not. 
2.3.1 Rigidity Constraint. As explained previously, the homologous groupings a' and a; are obtained by using, 
respectively, a feature extraction method and the camera model. The differences in position between the two groupings 
are explained by considering the errors in both processes, i.e., the feature extraction and the projection of the object- 
space grouping (A). 
The better the exterior orientation parameters are, the smaller is the deformation of grouping a; Since the exterior 
orientation parameters are refined by IEKF whenever a successful correspondence is obtained, that deformation is then 
reduced accordingly. 
From the above argument, the knowledge of deformation of grouping a; makes possible to know whether the 
correspondence (f;, f;) is possible or not. In practice, the rigidity constraint criterion is carried out by generating a search 
window around the straight line f, whose dimensions depend on the uncertainty of the camera parameters. If the 
straight line f; belongs to this window, the correspondence (f;, f;) is considered compatible and the next criterion must be 
applied. 
2.32 Relational Distance. Let sf = {S’} and gt = (S) be relational descriptions for straight lines f, and f,, 
represented respectively by equations 1 and 2, and h a function that maps primitives from star S' to star S. An 
expression can be written for total error E(h) between sí, and s^ (Shapiro and Haralick, 1987): 
E(h)= IS’oh - SI + Soh'! - S'l (4) 
where, | . | means cardinality. Thus, IS"oh - SI represents the number of relations that are not mapped by h from star S' to star 
S and ISoh™ - S'| represents the number of relations that are not mapped by h' (inverse of h) from star S to star S'. 
Therefore, E(h) is the total number of relations that are not mapped by h and its inverse (h"). If E(h)=0, h is called a 
relational isomorphism and S and S’ are said to be isomorphic. In such a case, f; and f, are said to be compatible. 
Now, an expression can be written representing the relational distance between relational descriptions ç and gf : 
  
208 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.