. Istanbul 2004 
Ptanes 
v 
stering 
v 
1 
2 
Nm 
(PL 
~ P3 
e been grouped 
d on the type of 
on for a facet f 
ind its direction 
) (7) 
(Dm) (8) 
rdinate can be 
or point, given 
ough precision 
ons and points 
planarity equa- 
ing the number 
that need being 
—1)) « 12 
(9) 
"M) x 12 
directions and 
aph. Each edge 
on the model. 
y, vertical sym- 
1e C'(q) related 
umber of types 
raints are inde- 
1)*12) (10) 
three previous 
ymetrical com- 
by constraints. 
whereas sim- 
ome usual con- 
1e model score 
of non vertical 
te SP(M) the 
(M) | its area. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
By noting f(x,y) the altitude given by a facette f € H(M) at 
location (x, y), the score is: 
Cz, y, f (a. 
P(|M)- WV Y SD (11) 
JEH(M) (x.y) 
where, in multi-image context, the correlation score is the one 
proposed in (Paparoditis and al., 2000) normalized by the number 
of images n: 
n- NT (Var (vi(ui, vi))) 
where each correlation window centered on (u;, v;) in image /; 
is represented by a vector vi; (wi, vi). (ui, vi) is the projection of 
(x, y, z) through known projection matrix from image /;. Note 
that the cube of correlation scores can be precomputed which 
speeds up evaluations. 
Cfa u 5) = € [0..1] (12) 
3D segments 3D segments bring important information on 
structure of the scene. Being reconstructed independently of the 
planes, they can give very good evidence on presence of some 
edges. For each 3D segment s, an edge a is matched if angular 
deviation is lower than a threshold 0, and if distance deviation is 
lower than another threshold ds, it will be noted aRs. For each 
matched edge, the overlap score r(a, s) of s by a is used for prob- 
ability computation: but errors of the 3D segment detector must 
be taken into account and thus a default value for fake matching 
(which is assumed to be the case when a 3D segment is matched 
to no edge) c, is thus attributed, leading: 
M) = min | max > Ho s s (13) 
S 
a Rs 
Pls 
  
  
  
  
  
For the set of 3D segments, assuming they are independent, it 
follows: 
Pala LPG 
ses 
  
M) (14) 
Focusing mask One measures the mask overlap by H(M) 
compared to the union of mask and planimetric surface, which 
leads to 
  
S P(M) (1 Ma | 
Pd, My sl 21 vU Lad 
M EM EROR 
(15) 
  
44 Building Extraction and Geometric Refining 
From the chosen admissible surface, it is trivial to extract con- 
nected sets of facets not touching the plane z — z,, thus extract- 
ing only roofs structures. Let us emphasize that several buildings 
can be present on one focusing area as well as roofs integrating 
altimetric discontinuities. 
The set of all admissible surfaces hypotheses is build up from an 
arrangement of planes in which it is difficult to handle 4 planes 
intersection. As a post-processing step, topological inconsisten- 
cies are corrected by a simple snapping algorithm. 
Another post-processing step enables also to enforce constraints 
in the real reconstruction so as to give a much more regularized 
shape. This important step based on (Grossmann, 2002) will not 
be detailed here due to lack of space. 
5. RESULTS AND DISCUSSIONS 
Figure 7 shows the main steps of th algorithm on an example. The 
projection of the result with and without enforcing constraints 
proves the gain of this step in the reconstruction. Figure 8 shows 
the results on 45 buildings with 6 images at resolution 25cm and 
B = T5. By visual inspection, 7596 of reconstructions are "ac- 
ceptable", meaning they perfectly fit the reality or the given cari- 
cature is an acceptable generalization of the reality. Right part of 
  
(a) Focusing mask, facades, planar patches and 3D segments. 
  
(b) arrangement of planes and filtered 3D Graph. 
(c) Exhaustive search of solutions. 
  
(d) The final solution in 3D and projected on an orthophoto, before and after 
enforcing constraints. 
Figure 7: Main steps on an example.