It is not possible to extract the best enclosure among alter- 
natives without considering the neighboring planes and their 
enclosures. Instead of selecting the best enclosure for each 
plane we propose to rank the enclosures within each plane 
according to simple criteria. This is a first important step 
towards the assembly of 2-D enclosures and planes to form 
hypotheses of 3-D patches. We assume that each planar part 
of the roof has a large area, a simple shape, and a large 
overlap between the contours in the 2-D enclosure and the 
corresponding 3-D segments of the plane. These three cri- 
teria allow us to describe the larger structures of a roof. As 
we are only interested in ranking the enclosures within each 
plane, we propose a score for each enclosure, which consists of 
the product of three relative components: 3-D completeness, 
relative enclosed area, and relative shape simplicity [Bignone 
et al. 1996]. 
Figure 10 shows a few extracted 2-D enclosures for the larger 
planes of the house in Fig. 8A. The algorithm extracted 279 
enclosures for the six planes. 
Plane A Plane B 
  
Figure 10: A few representative 2-D enclosures for the planes 
A, B, D, and F in Fig. 9 with their corresponding scores. 
6.4 Assembling Planes and Enclosures to Roofs 
Each 2-D enclosure describes a possible boundary description 
of the corresponding plane. One 2-D enclosure together with 
one plane form a hypothesis of a 3-D patch. It is reasonable 
to assume that roofs of residential houses are constructed of 
adjoining planes. For this reason, only hypotheses of 3-D 
patches that consistently adjoin with other 3-D patches with 
respect to the intersection of their planes are retained. |n 
addition, we require that the 2-D contours, that belong to 
the intersection, are collinear in 2-D. Those 3-D patches that 
fulfill these constraints are consistent. For example, the 2-D 
enclosure with the highest score for plane B in Fig. 10, is not 
consistent and is therefore excluded. 
The iterative procedure initially selects a subset of 3-D 
patches and verifies the total consistency along the bound- 
aries. If one or more 3-D patches do not fulfill this check, 
they are rejected and new 3-D patches are selected. The 
first subset of 3-D patches that produce a total consistency 
among all intersections is the final result. The order of selec- 
tion is based on the above enclosure score. To obtain the 3-D 
coordinates of those contours that are contained in the 2-D 
328 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
enclosure but not on the plane, we project their endpoints 
onto the plane. The result is a complete 3-D boundary for 
each plane that is likely to describe a roof. Finally, we add ar- 
tificial vertical walls to the reconstructed roof. The heights of 
the vertical walls are estimated through the available digital 
terrain model. 
Figure 11C,D show the reconstructed houses in Fig. 11A,B. 
Notice, that only two planes from Fig. 9 were retained for 
the final reconstruction. In Fig. 11E,F we superimpose the 
manually measured CAD model with ours to show the quality 
of the reconstruction. The accuracy and completeness of the 
reconstruction will be evaluated in future work. 
  
Figure 11: The results of the reconstruction. (A-B) the origi- 
nal images, (C-D) the reconstructed houses in 3-D and (E-F) 
the manually measured CAD model (white) overlaid on our 
reconstruction (black). 
In Fig. 12 we present our results on the entire residential 
scene. Eleven of the thirteen roofs are extracted, ten of 
them with a high degree of accuracy and completeness. The 
marked house to the right is not complete, since the algorithm 
fails to extract the two triangular shaped planes, however, the 
corresponding 2-D enclosures are correctly extracted. The al- 
gorithm fails to extract the two upper left houses. The lower 
of the two is under construction and should not be included 
in the performance analysis. The upper house is complicated 
because a bunch of trees cast large shadows on the right roof 
part. Because of these shadows the algorithm fails to find the 
corresponding plane, however, the left roof part is correctly 
reconstructed. 
      
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