Auclair Fortier, Marie-Flavie 
  
    
(a) (b) (c) (d) 
Figure 1: a) Line junctions. b) Road segments. Black squares are extremities. c) Matching between image junctions and 
road-segment extremities. White squares are junctions matched with extremities, while black squares are either extremities: 
or other junctions (N,, — 13). d) Road segments after re-localizing the two extremities matched with junctions. 
Having the list of all road segments, each extremity is matched with a junction, if possible. For this purpose, a correla- 
tion measure is computed between the extremity and each junction localized in a N,, x N,,, neighborhood around this 
extremity. This measure is done on a M, x Mn neighborhood around each such junction. Let (z, y) be the extremity 
and (u, v) be the junction; then, the correlation is: 
Ma/2 M72 
corr(z, 3, wu, v) = S. S RoadSeg(z 4 i, y + j)line(u + i,v + j), (3) 
i-— M, /2 j2— M /2 
where 
_ ) 1 if(z,y) belongs to a road segment 
RoadSeg(z,y) — { EF (4) 
and line(x, y) is the line plausibility (4,,,,) as defined in Sect. 3. (z, y) is matched with the junction (u, v) having the 
highest correlation. Figure 1c presents the results of matching between extremities of Figure 1b and junctions of Figure 
la. We used a M,, of 25 in all of our trials. 
After matching, each segment re-localized according to the difference between its extremities and the junctions matched. 
As the differences at the two extremities may not be the same, each vector extremity in the road segment is moved 
according to the difference between the nearest road segment extremity and its matched junction. That means that every 
vector keeps the same orientation except the one containing the midpoint of the road segment, because its two extremities 
will move according to the two different extremities of the road segment Figure 1c presents road segments after re- 
localization. 
4.2 ACTIVE CONTOUR MODELS - SNAKES 
As we mentioned earlier, we want to find lines near the initialization provided by the road database. Active contour model 
(snake) is an optimization process which needs an initialization near the solution (Berger, 1991, Kass et al., 1988). Aerial 
images can be affected by noise and roads can be partially hidden by shadows of trees, houses or clouds. Snakes manage 
these problems with constraints on rigidity and elasticity. 
In the continuous domain, snakes (or active contours) are parametric curves (v(s,t) = (z(s,t), y(s,t)),s € [0, 1]) that 
minimize an energy function based on internal and external constraints (Berger, 1991) at time t: 
1 1 
Etot = nEint + Feat = nf (o1 |v'(s, t) P -- fiv" (s, 0p) ds + [ Amas (v(s, t))ds, (5) 
0 0 
where E, is the external energy, Ej, the internal energy and 7) a regularisation parameter. 
The internal energy represents the snake’s capacity to distort. ai, B1 € RT, v' and v" are the first and second partial 
derivatives in s. The term |v'(s, t)|? influences the snake's length (or tension) and |v" (s, t)|? influences the curvature (or 
elasticity) of the snake. The parameter 7) can be absorbed by a and 3 (a = go, and B — nS). 
  
92 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.