In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
3 EXPERIMENTAL RESULTS 
Having presented the prior model Ep, we are now nearly in a po 
sition to describe experiments testing the properties of the model 
and its performance in network segmentation. First, however, we 
have to describe the likelihood energy E\(R, I) — — In P(/|/?, A') 
that we will use to create the complete model E = Ep + 0E\ 
where the parameter 6 balances the two terms. Since we test the 
model on 0.61m resolution multispectral VHR Quickbird images 
with four channels (red (R), green (G), blue (B) and infrared (I)), 
and optical colour images, we need a model of such images. As 
already stated, we will assume that the likelihood can be factor 
ized as P(/|A. K) = P(Ir\R, K)P(Ift\R, A"), and we thus need 
models for the image in R and R. 
3.1 Likelihood energy 
In (El Ghoul et al„ 2009a), the road network segmentation perfor 
mance of a phase field HOAC model for undirected networks was 
tested using two classes of likelihoods (the same class was used 
for both R and R): a multivariate Gaussian (MG) and a mixture 
of two multivariate Gaussians (MMG). In ML segmentations, the 
performance was mixed, but when combined with the prior en 
ergy, the MMG model was found to outperform the MG model, 
with the improvement being most significant when the image was 
very heterogeneous. Here, we test the ML performance of these 
two likelihood classes on the images used in this paper, and com 
pare them to segmentations obtained using the normalized differ 
ence vegetation index (NDVI = (I — R)/(I+R)) (Rouse et al., 
1973, Tucker, 1979) and the normalized difference water index 
(NDWI = —{I — G)/(I + G)) (McFeeters, 1996). We apply 
the former to images of road networks in which the background 
is mostly vegetation, and the latter to an image of a hydrographic 
network. The 4 th , 5 th , and 6 th rows of figure 1 show ML seg 
mentations using NDVI/NDWI, MG, and MMG respectively. 
Table 1 shows quantitative evaluations of the quality of the ML 
segmentations using NDVI, MG, and MMG. The bold numbers 
show the best ML segmentation method. In all experiments, the 
NDVI results show lower performance, according to the quality 
measure, compared to the MG and MMG results. The NDVI re 
sults on the first and second images show that most of the hidden 
parts of the network are not retrieved because they resemble veg 
etation more than network. The result is the presence of many 
lengthy gaps in the ML segmentation. Because these gaps are so 
long, it is very unlikely that the prior term would close them. In 
contrast, the MG and MMG segmentations include most of the 
network, but also many points of the background, which the prior 
model should be able to eliminate. When coupled with the results 
of (El Ghoul et al., 2009a) showing that MMG outperforms MG, 
these results lead us to choose the MMG model to construct the 
likelihood energy E\. 
3.2 Segmentation results 
In order to compute a MAP estimate for P(A|7, K), we use gra 
dient descent to seek minima of E = Ep + 9E\. To reduce the 
computational complexity, we primarily test the model on small 
images of size 256 x 256, some of which were obtained by re 
ducing the resolution of the original images. We discuss this point 
further in section 4. 
Figure 2 shows segmentations of the images shown in figure 1 
obtained using the new algorithm. 2 The results in the first and 
second rows show that most of the gaps present in the original 
2 Parameter values were, for the 4 images in figure 1 from left to 
right: (Ao4,A 0 3,A22,A 2 i , D, 0,d, L v , D v ,0) = (0.3375,-0.1767, 
Completeness 
Correctness 
Quality 
a 
NDVI 
0.4296 
0.3965 
0.2598 
MG 
0.6920 
0.3423 
0.2970 
MMG 
0.7510 
0.3000 
0.2728 
b 
NDVI 
0.4745 
0.6536 
0.3791 
MG 
0.7166 
0.4958 
0.4145 
MMG 
0.7983 
0.3521 
0.3233 
c 
NDWI 
0.6280 
0.9446 
0.6057 
MG 
0.7835 
0.8468 
0.6862 
MMG 
0.8485 
0.7424 
0.6555 
d 
NDVI 
0.6776 
0.4517 
0.3718 
MG 
0.9060 
0.4099 
0.3932 
MMG 
0.8634 
0.4641 
0.4323 
Table 1: Quantitative evaluations of the ML segmentations given 
in figure 1. a, b, c, and d correspond to the four images in figure 1, 
from left to right. Completeness= TP/(TP + FN), correctness= 
TP/(TP + FP) and quality = TP/(TP + FP + FN). T, F, P, and N 
correspond to true, false, positive, and negative respectively. 
images are indeed closed thanks to the contribution of the diver 
gence term: when divergence of the vector field is heavily penal 
ized, network branch extremities prefer to meet and close gaps 
because in this way flow can be conserved. This does not oc 
cur using the undirected phase field HOAC model described in 
section 2.1, as shown in (El Ghoul et al., 2009a). 
The result in the third row emphasize the role of the divergence 
term at junctions. The divergence-free property of the vector field 
favours junctions where total incoming branch width equals total 
outgoing branch width. Figure 3 shows streamline plots of the 
final vector field configuration superimposed on the thresholded 
<t> corresponding to the last two segmentation results in figure 2. 
The vector field is indeed of constant (unit) magnitude inside the 
network, parallel to the network boundaries, and smooth; the flow 
is approximately conserved along network branches and in partic 
ular at junctions, where the total incoming flow is approximately 
equal to total outgoing flow. 
Figure 4 shows the segmentation of a river network from a colour 
optical image. 3 The likelihood model used was the same, but with 
one less band. The flow conservation property and its geometric 
consequences enable the algorithm to avoid confounding factors 
in the background and segment the network to a good accuracy. 
The results we have shown here still have false positives and false 
negatives. The main raison for the former is that the gradient de 
scent algorithm becomes locally stuck in a local minimum, so that 
some of the background remains classified as network even if this 
is globally energetically unfavourable. The main reason for the 
latter are long gaps in the visible network caused by occlusions. 
4 CONCLUSION 
We have proposed a new algorithm for the segmentation of net 
works from VHR satellite images. Such networks have character 
istic geometric properties: network branch widths change slowly 
although different branches may have very different widths; while, 
at junctions, there is approximate ‘conservation of width’. To seg 
ment such networks (quasi-)automatically, requires models that 
0.2712, -0.6,0.2645,0.0629,1.68,0.2649,100,0.03), (0.1,0.0164, 
0.1162, -0.8,0.0512,0.0205,1.45,0.0227,200,0.01), (0.412, 
-0.0008,0.0022, -0.6,0.257,0.0083,8.33,0.275,50,0.04), and 
(0.4, -0.018,0.15, -0.8,0.548,0.0316,3.45,0.150,50,0.04). 
3 Parameter values were: (A04, A03, A22, A 2 i ,D,0,d, L V ,D V ,6) = 
(0.25,0.0323,0.1138, -0.8,0.1903,0.0176,2.56,0.0644,100,0.07).