In: Stilla U, Rottensteiner F, Paparoditis N (Eds) CMRT09. IAPRS, Vol. XXXVIII, Part 3/W4 — Paris, France, 3-4 September, 2009 
105 
natural disasters such as avalanches, landslides or earthquakes. 
In case of natural disasters the GIS-object can be divided into the 
state intact/usable or not intact/destroyed. Furthermore, a state 
between these extrema is possible. Hence, a third state possibly 
not intact/destroyed is introduced, if the automatic approach can 
not provide a reliable decision. In order to assess roads after a 
flood disaster following states can be used: 
• trafficable 
• flooded 
• possibly flooded 
For every available data source the probability for each state has 
to be derived. The methods which are employed to the different 
data are shown in the following section. 
3.1 Methods 
A multispectral classification is accomplished in order to derive 
different classes from the input imagery. The goal is to assess 
each linear object individually without taking adjacent linear ob 
jects into account, because such kind of topological knowledge 
about the connectivity of a road network is no more valid in case 
of road networks hit by a natural disaster. Every linear object is a 
polyline, which consists of several line segments. A line segment 
is a straight line, which can be defined with two points. Every line 
segment is assigned to a class using an segment-based multispec 
tral classification. To this end, a buffer is defined around each line 
to investigate the radiometric image information. In many cases 
additional information as the width of the line object can be used 
in order to generate the size of the buffer region. 
For the multispectral classification various classes have to be de 
fined depending on the underlying imagery in order to classify the 
road segments into the three states trafficable, flooded and possi 
bly flooded. In case of optical imagery the classes road, water, 
forest and clouds are convenient, because the class road corre 
sponds to the state trafficable, the class water to flooded and the 
classes forest and clouds describe occlusions and therefore be 
long to the state possibly flooded. If radar images are available 
the class clouds can be neglected. Beside the assignment to a 
class each individual line segment consists of a probability be 
longing to a class Ui, which is derived from the k-sigma error 
ellipsoid. The probability can be formulated as p UJi (g), whereas 
g defines the gray values. The length of the vector is equivalent 
to the number of channels. 
Beside the imagery additional information such as digital eleva 
tion models or GIS data can be integrated in the system. The 
methods to derive probabilities depend on the data. One method 
are membership functions of fuzzy sets (Zadeh, 1965). Mem 
bership functions do not describe the likelihood of some event, 
but they only characterize a degree of truth in vaguely defined 
sets. Since it is often difficult to derive sound probabilities from 
GIS data, membership functions provide an opportunity to infer 
confidence values. To emphasize the distinction the membership 
function is labeled as p instead of p. 
The membership functions pt{a), pf(a) are introduced if a dig 
ital elevation model is given. The function pt(a) denote the be 
longing to the state trafficable t depending on the altitude a. Sim 
ilarly Pf(a) represents the siaiz flooded f. Both functions are 
depicted in Figure 3. There are two thresholds a\ and a2 which 
determine the height of very likely flooded or trafficable areas, re 
spectively. The current water level lies between these thresholds, 
which can be calculated by 
ai — h — bi 
0,2 = hi + f>2, 
in which li is the lowest and lh is the highest water level in the 
scene. In order to involve variations due to flows and barriers 
additional buffers bi, 62 are added. 
Figure 3: Membership functions for flooded roads and trafficable 
roads derived from DEM 
3.2 Combination of Probabilities 
The core of the classification system is to combine probabilities 
resulting from a multispectral classification with the degree of 
truth of membership functions. In this section, an example is 
shown which combines the derived probabilities from optical im 
ages with membership functions inferred from a digital elevation 
model. By means of multispectral classification for each class 
(water w, road r, forest o, cloud c) the corresponding probabil 
ity p u>i for i = {w,r,o,c} can be derived. On the other side, 
the membership function provide the degree of truth /if (a) and 
Pf(a). Utilizing the knowledge that roads higher than <22 are def 
initely trafficable and roads lower than a\ are very likely flooded 
a case differentiation is carried out: 
a) 
dt(g,a) 
II 
a < a\ 
Pf(a) -Pu, w {g) 
ai < a < a.2 
p.f(a) = 0 
a > a 2 
/2* (a) = 0 
a < ai 
dt(a) -Pu, r (g) 
ai < a < 02 
p t (a) = 1 
a > d2- 
(4) 
(5) 
Variable a denotes the height of a road object. The road is as 
signed to the state flooded Sf if the degree of truth pj(g, a) ex 
ceeds an threshold t\, which can be pre-estimated via the stan 
dard deviation of the likelihood function resulting from the train 
ing data for water. The road is assigned to the state possibly 
flooded Spf, if Pf(g, a) is less than t\. The probability p t (g, a) 
is treated in an analogous manner. The road is assigned to the 
state trafficable St if Pt(g,a) exceeds a pre-detennined thresh 
old ¿2- Otherwise, the road is again assigned to the state possibly 
flooded Spf • The road segments which are classified as forest 
u 0 or clouds u c are assigned to the states in the following way: 
a < a 1 => flooded Sf 
a\ < a < 02 possibly flooded Spf (6) 
a > a2 => trafficable St