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ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision", Graz, 2002 
  
Figure 5: 7he features that could be matched in each of the 
3 views of fig. 4 after propagation and transitivity reason- 
ing. The number of matches has been increased to 56. 
  
frames, it nevertheless has difficulties coping with more 
extreme cases. 
Under wide baseline conditions, disparities tend to get 
larger, a smaller part of the scene is visible to both cam- 
eras, and intensities of corresponding pixels vary more. In 
order to better cope with such challenges, we propose a 
scheme that is based on the coupled evolution of Partial 
Differential Equations. This approach is described in more 
detail in a paper by Strecha et al. (Strecha 2002). The point 
of departure of this method is a PDE-based solution to 
optical flow, proposed earlier by Proesmans ef al. (Proes- 
mans 1994). In a recent benchmark comparison between 
different optical flow techniques, this method performed 
particularly well (McCane 2001). An important difference 
with classical optical flow is that the search for correspon- 
dences is ‘bi-local’, in that spatio-temporal derivatives are 
taken at two different points in the two images. Dispari- 
ties or motions are subdivided into a current estimate and 
a residue, which is reduced as the iterative process works 
its way towards the solution. This decomposition makes it 
possible to focus on the smaller residue, which is in bet- 
ter agreement with the linearisation that is behind optical 
flow. The non-linear diffusion scheme in the Proesmans 
et al approach imposes smoothness of nearby disparities at 
most places — an action which can be regarded as the dense 
counterpart of propagation — but simultaneously allows for 
the introduction of discontinuities in the disparity map. 
The method of Strecha et al. (Strecha 2002) generalises 
this approach to multiple views. The extraction of the dif- 
ferent disparities is coupled through the fact that all cor- 
responding image positions ought to be compatible with 
the same 3D positions. The effect of this coupling can be 
considered the dense counterpart of the sparse transitivity 
reasoning. Moreover, the traditional optical flow constraint 
that corresponding pixels are assumed to have the same in- 
tensities, is relaxed. The system expects the same inten- 
sities up to scaling, where the scaling factor should vary 
smoothly between neighbouring pixels at most places. 
2.4 Experiments 
Fig. 6 shows three images of the left corner of the town hall 
of Leuven. These images are too far apart for our shape- 
from-video process to get started with the corner match- 
ing. A sufficient number of invariant neighbourhoods can 
be matched, however, and the PDE-based dense correspon- 
dence search succeeds in finding matches for most other 
pixels. Three views of the resulting 3D model are shown 
in fig. 7. The result looks quite convincing, even for such a 
convoluted surface, where parts easily get occluded in sev- 
eral views. This problem of holes in the model precluded 
us from taking the images even farther apart. 
Fig. 8 shows three images of an excavation layer, acquired 
at the Sagalassos site in Turkey. This is one of the largest 
scale excavations currently ongoing in the Mediterranean, 
under the leadership of prof. Marc Waelkens. These im-