International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences 
Figure 12: Two view of the extracted 3D planes from digital 
facade model by robust region growing algorithm mixed with a 
RANSAC. 
3.6 Estimating relative orientations by façade orthoimage 
correlation 
Translation Formulation 
This phase investigate matching 3D planes by a FFT correlation. 
The matching planes can be found by façade orthoimage corre- 
lation. Let us consider two possible matching planes. If both 
orthoimages are constructed, i.e. images are resampled from per- 
spective view to orthogonal projection on the considered plane, 
they are superposable modulo a translation. This orthoimage 
translation is extremely interesting because it provides directly 
the translation of the plateform in the plane. In our case, we es- 
timate the translation by a FFT matching on the facade adaptive 
shape template. One of the major advantages of this method is 
that it still works when the MMS turns round corners without hav- 
ing a video acquisition rate. Let us consider two orthoimages Ii, 
I» respectively at time (t) and (t + dt) and two adaptative masks 
for a pair of homologous planes Mi, Ma. If two orthoimages Zi, 
I» differ by shift (T,, Ty), Le. T2(x,y) = Liz — Tey — Ty), 
then Fourier Transforms formulas can be expressed by : 
So = J ive. S J inve, (1) 
Sa = [ aie, Shy == f mme (2) 
San = / I3 M, M3, S zm / IL I, My Ms, 3) 
= S x 2 
S = —- 2 = —, 4 
dt S 2 e ( ) 
I $1 EG P 512 d 
= SS, S2== - 55 5 
ns 5 101; c 192 (5) 
The Cross Correlation Score is processed by : 
5 (6) 
Corr =-—— 
Vv S11512 
By taking an inverse Fourier Transform of Corr, we can find the 
position (T,, T,) with the maximum absolute value. 
The relative distance to the façade between cameras can be recov- 
ered in this case as there we have a verticale basis. It corresponds 
to displacement 7T*. 
T, = distance(ci, Pi) — distance(cz, Pi») (M) 
where c, and c» are respectively the cameras projective centres. 
. Vol XXXV, Part B3. Istanbul 2004 
      
Figure 13: Orthoimages and Corresponding Masks for a pair of 
homologous planes at (t) and (t + dt). 
  
£ 
Figure 14: Correlation surface between two orthoimages by FFT 
correlation techniques. 
Rotation Formulation and Method 
This section formulates the 3D rotation matrix problem between 
the image pairs. Let consider two possible homologous planes 
Pie) and Pj(e+at)- 
= d E 3 MOT 
Tí; and Tín) here are the two normals vectors of the 
matching planes in the image reference system. 
Let us first denote a rotation value around axis 7 with an angle 
a by Rot (d, a). 
Let us call 8253, — ground the rotation passing from the internal 
image reference system to the local tangent ground system (rota- 
tion of pitch and roll angles relatively to the vehicle motion with 
the help of the short vertical base line and vanishing points). 
Let us denote Qt), tat the rotation passing from the ground 
system of frames at (t) to the reference system of the 3D planes 
pi. 
and finally, let us consider Q(,, _, ,, the rotation matrix passing 
from the camera | to camera 2. 
= => 
nip) and 1 jar) can be calculated by : 
. A 
n = ya ground : 7 (8) 
We can compute + the rotation matrix by : 
n 
m = 
Oo = Rot N i(t) TV j(t--dt) 
= ln icol [” ;e+ao|l 9) 
+ 3 
arccos ni) m ron 
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