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In order to achieve segment matching at the initial step, for the line segments in Image 1, all segments in the remaining 
images which satisfy the epipolar constraints need to be considered. Thus, for all possible matched segment pairs, 
predictions are made in the remaining images and the matching between individual points belonging to theses segments 
is then checked via both the correlation coefficient and the condition of an admissible similarity in gradient orientation. 
This process is not symmetrical since a single image (eg Image 1) is used to initialise the segment feature matches, after 
which the operation is repeated for all other images and image segments. 
If Images 1 and 2, two points on matched contours P/ and P2 satisfy the epipolar constraints, they satisfy a consistency 
constraint. If P7, ... , Pn form a clique (ie a complete subgraph) for the consistency graph in n images, this set can be 
considered as a set of complete, mutually supported matches. Fig 1 illustrates this for the case of three images, where 
two concurrent cliques compete: a, a21, a31 and a, b21 and b31. The subsequent relaxation process will handle this 
ambiguity. 
Figs. 2 and 3 illustrate a case of three original images with segment features, along with the results of an initial segment 
' matching whereby three corresponding segments are pre-matched. 
  
b 
  
Fig. 2: Original segments. 
   
a b 
Fig. 3: Initial corresponding segments. 
3 EXTENSION OF THE INITIAL MATCHES 
It can be assumed at this first matching phase that the relaxation filtering has provided an initial reliable but sparse 
matching. The second stage now seeks to accommodate missing matches, which may be due to occlusions, image noise 
or simply poor thresholding in the feature extraction process. A complicating issue is the presence of matching 
ambiguities, which sometimes can be resolved through relaxation processes if additional features are provided. An 
effective strategy to counter ambiguities is therefore to extend the number (and density) of both features and initial 
matches. This extension provides a feedback process in which new matches immediately become supporting evidence 
for neighbouring feature correspondences. A local affine transformation is used to predict positions of feature 
candidates in the usual case where exact 3D information for the object to be reconstructed is not known. In the predicted 
regions, contours can be iteratively searched by changing the threshold of the feature extractor, which is here a contour 
extractor. 
3.1 Line Prediction via a Local Affine Model 
A local affine model is applied to the initially matched segments, with the three nearest segments being selected for the 
parameter determination of the affine transformation. As indicated in Fig. 4, segment pairs 1 - 1; 2 - 2; and 3 - 3' are 
the one-to-one initial matches. The position of the candidate L' can be predicted from the segment L via a 
transformation utilising a line affine model defined in the dual affine space of lines by 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 839