In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds), 1APRS, Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3, 2010 
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correspond to a single line in the other view (lack of a unique 
intersection point). To solve these cases, we use the repetitive 
nature of the pair formation considering the fact that a single line is 
allowed to have a part in different pair models. Thus, a single line 
has possibility to be matched with its correct correspondences in 
different pair models. 
In order to describe the geometrical relations between the line 
segments in a pair, w ; e employ three different measures (Park et. al„ 
2000). First measure is the angle which two line segments h and 1 2 
form, the second measure is the directional angle from the midpoint 
of h to that of F, which is the angle measured from the first line to 
the second line, and the third measure is the ratio of the sum of line 
segments to the average distance between the endpoints of the line 
segments (Park et. al., 2000) (Fig. 4a). However, in most of the 
cases, the last two geometrical relations are inappropriate for aerial 
images, since the line segments found in different view's may have 
different lengths and midpoints due to several reasons such as 
occlusion, image noise etc. In addition, the perspective distortion 
combined w'ith relief of terrain and'or of individual objects also 
plays an important role at this point and in cumulative, the 
measures become inconsistent from one view' to another. Assume 
that the lines C] and c 2 in Fig. 4b are forming one of the candidate 
pair models of the lines h and 1 2 in Fig. 4a. If w'e compare the 
lengths of the lines in each pair, only the length of the line c 2 is 
significantly different; how'ever, even in this case, two geometrical 
measures computed are different from each other. We propose a 
normalization scheme to deal with the problems of the geometrical 
reliability of the line segments extracted from different view's. It 
relies on the epipolar geometry and the idea of finding the overlaps 
of lines in different views. We utilize the endpoints of each line and 
estimate the epipolar lines on the other view. Thus, w'e perform a 
point to point correspondence (Schmid and Zisserntan, 1997) on 
each line to provide a final single overlapping line for each line in a 
pair (Fig. 4c- and 4d-left). We apply this normalization scheme for 
each reference pair and its candidate pair model before the 
computation of the second and third geometrical measures. Thus, 
the measures become reliable (Fig. 4c- and 4d-right) w'hen 
compared to their non-normalized counterparts. 
As additional constraints, we propose tw'o different flanking region 
constraints for a reference pair and their candidate pairs; (i) the 
intra-pair similarity, and the inter-pair similarity. The former 
measure takes into account the similarity of the side(s) of the 
reference pair model previously found (see section 2.3.1) and 
searches w'hether a similar relationship of the flanking information 
of the same sides for the candidate pair models exist or not. If it 
exists, the latter measure considers the similarity of flanking regions 
of the line segments individually. To allow such constraint, the 
illumination of the images is assumed to be similar (the case in 
(c) (d) 
Fig. 4 (a) The geometrical measures utilized, (b) a candidate pair 
model and its geometrical measures, (c) and (d) normalization with 
epipolar lines and the normalized measures. 
a single strip acquisition) and the reflections are assumed to comply 
with the lambertian theory. 
In this study, we propose two new' additional constraints to the 
stereo pair-wise line matching scheme; a correlation constraint 
forced on a hypothesized 3D triangular plane and a spatiogram 
constraint that deals with the regional similarity dominated by the 
reference line pair and the candidate pair models. 
The correlation constraint performs on a 3D plane fitted to the line 
pairs and their intersection point based on the assumptions that (i) 
they are the correct match, and (ii) they belong to a single plane. A 
correlation measure bounded for all the area marked by the 3D lines 
and the intersection point is not appropriate, since there may be 
different planes on a building roof (chimneys, dormers etc). Thus, 
we apply the correlation measure to the immediate vicinity of the 
point of intersection and the corresponding plane, which can also be 
defined as a 3D triangular plane (Fig. 5a and 5b). We fixed the side 
lengths of the triangle which are exactly on the same direction of 
the lines by a single distance parameter d = 2 m. Fig. 5a and 5b 
illustrate the extents of the back projected plane that is estimated 
through the line pairs given in the figure. However, there may be 
several cases that may violate the plane formation and the 
correlation value computed; (i) the intersection point of the lines 
that are exactly on the same plane may occur on a different plane(s) 
than their own plane (Fig. 5c - pair A B) (ii), the lines that really 
intersect on the Earth surface may not form a plane (Fig. 5c - 
pair C D), and (iii) the planes formed by the line pairs may be hidden 
or occluded in one view (Fig. 5d - pair EF ). It is straightforward to 
track the last violation; we compute the angle of the plane w'ith its 
projected plane (to a flat terrain), and only apply the correlation 
measure if the computed plane angle is narrow'er than a specific 
angle threshold (< 75°). However, the other two violations cannot 
be handled in a similar manner, since the hypothesized 3D planes 
are not correct. Thus, based on our rigorous experiments, w'e 
decided to fix the threshold of the measure of correlation to a very 
relaxed constant (T CO i > 0.2), and utilized the constraint to eliminate 
the candidate pair models that show no or negative correlation. 
Finally, the regional similarities dominated by the reference line 
pairs and the candidate pair models are evaluated. We select the 2D 
regions that are consistently described by the line pairs. How'ever, it 
is simply impossible to compare the regions directly, since the 
perspective distortion and the features belong to many different 
planes on the roofs may simply alter the positions of the pixels to 
some extent. On the other hand, it is not logical to compare the 
regions with a simple histogram measure, since many parts of the 
images may contain similar radiometric information; very different 
regions generally produce similar histograms. Therefore, we utilize 
the spatiogram measure to evaluate the regional similarity between 
the regions. A very important aspect of the spatiogram measure is 
Fig. 5 (a, b) The back projected plane estimated from the line pairs, 
(c. d) several cases that may violate the plane constraint.