In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C... Tournaire O. (Eds). IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
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E imag c - K i • [Mx.y) • E als + n(x,y) • Ebund + \{x,y) • E Mdg J (3) 
In Equ. 3. k, is a weight for the entire image energy term, and 
A(x,y), ju(x,y), and v(x,y) are weight functions for the individual 
terms that may vary over the image. More specifically, our 
method requires the detection of buildings and bridges. Let 
Build(x.y) be a binary image that takes a value of 1 to indicate 
the presence of a building and 0 otherwise. Analogously, let 
Bridge(x,y) be a binary image indicating the presence of a 
bridge. Then we define 
Mx,y) = X 0 * [1 ~ Build(x,y)J • [1 - Bridge(x,y)] 
fj(x,y) = Ho • Build(x.y) (4) 
v(x.y) = v 0 • Bridge(x.y) 
with Ao = Ho = I'# - 1 — const. In other words, in regions 
classified as a building, only E hui]ii is taken into account, in 
regions classified as a bridge only E bri j ge is considered, and in 
all other areas only E ALS is used. In the subsequent sections, we 
will describe the individual energy terms in more detail. 
2.3.1 General ALS Energy: The general ALS energy E ALS 
requires an intensity image and a DTM. which have to be 
generated from the ALS point cloud in a pre-processing stage. 
The intensity image is interpolated by means of kriging 
(Cressie, 1990). Then it is smoothed by a median filter in order 
to remove outliers as well as decrease the noise while 
preserving the road edges. In order to determine a DTM, the 
ALS points have to be classified as terrain or off-terrain points. 
In order to achieve this classification, we estimate a plane for 
each point, taking into account its k (e.g., 9) nearest neighbours. 
Taking the RMS error of the weight unit of the planar fit as a 
measure for the local surface roughness, we search for 
connected segments of points that have a low surface 
roughness. Using a morphological opening filter, a coarse DTM 
is generated from the DSM (Weidner & Forstner, 1995), and 
each segment is classified according to its average height 
difference from the approximate DTM. An improved DTM can 
be generated from the points in segments classified as terrain 
segments, and the classification can be repeated taking 
advantage of the improved DTM from the first iteration. In 
order to also include terrain points that are characterised by a 
high surface roughness, a final classification of all ALS points 
is carried out based on their height differences from the 
improved DTM. The DTM grid is interpolated taking into 
account only the terrain points. It is important to note that this 
method will classify points on bridges as ground points, 
because the road will correspond to a large segment that is 
situated on the terrain everywhere except at the bridge. 
The general ALS energy E ALS is composed of the weighted sum 
of the intensities and plane parameters in the DTM: 
^als — a ' E, + b ■ E plane (5) 
where E/ is the energy from intensity image, E PUllw is the energy 
from the plane parameters, and a, b are weights. Intensity 
values of the ALS data represent the reflectance properties of 
the illuminated objects according to the wavelength of the 
emitted beam (near infrared). Road surfaces such as asphalt 
generally appear dark due to the high absorption rate (Clode et 
al., 2007). Therefore, the pre-processed intensity image 
determines the first term E, in Equ. 5, forcing the snake to low 
grey values. However, some other objects such as building 
roofs show a similar behaviour and disturb the optimization 
process related to Ej. The term E P [ ane in Equ. 5 exploits the fact 
that roads are usually situated on smooth and fiat surfaces. 
Therefore, a plane is estimated in a 5 m x 5 m window for every 
grid point in the DTM. thus considering common values of the 
road width. The term E P \ ane is the sum of the absolute values of 
the plane slope in x- and y-direction. E Pian( , thus highlights 
strong slopes in every direction in the image energy. This 
energy part should prevent that roads represented by the snakes 
move to surface areas which have invalid height gradients. The 
weights (a, b) of the energy parts in Equ. 3 are determined 
empirically supported by the histograms of the images. 
2.3.2 Building Energy: The second component E huild in Equ. 3 
is dedicated to buildings. Due to different roof orientation and 
materials the appearance of buildings in the Lidar intensities 
varies considerably. This fact results in many undesired edges 
and local minima in the energy part derived from the intensity'. 
Furthermore, buildings cause strong edges in the DSM and even 
in the DTM some artefacts remain, disturbing a suitable energy 
definition for the adaptation of roads using active contours. On 
the other hand buildings have strong relations to the adjacent 
road segments: they can be treated as forbidden areas for 
standard roads, acting as a repulsion force. 
In order to take advantage of building information for our 
purposes, the buildings have to be detected in the ALS data in a 
pre-processing stage. We use the method described in 
(Rottensteiner et al., 2007) for that purpose. For the definition 
of the energy term E hw ■¡ d . we only need a binary building mask. 
A distance transform is applied to the building mask, and the 
binary image Build(x.y) used to define the weight H(x<y) of Etwiid 
(Equ. 4) is generated by thresholding the distance image at 4 m 
(8 pixels). Thus, Eb t ,ud will be effective inside the building and 
within a distance of 4 m from the building boundary. The 
building energy E huiid itself is based on a distance transform of 
the negation of the binary image Build(x,y). That is, E hu iid is 
zero outside the enlarged building area described by Build(x,y), 
whereas in the interior of a building it is identical to the 
distance to the nearest non-building pixel. The skeletons of the 
building areas act as decision boundaries. If the initialisation of 
the road network is situated on the correct side of the building 
skeleton the snake will slide to the sufficient urban “valley”. 
Fig. 1 visualises a part of the image energy without considering 
bridges, i.e. using Bridge(x,y) = 0 for all pixels. 
Figure 1. Image energy without bridges. 
2.3.3 Bridge energy: Due to the fact that bridges indicate the 
course of roads with high confidence, the information about this 
object class should guide the evolvement of the snake in the 
corresponding areas. Therefore, a method is proposed that 
estimates the width, length, direction, and the position of the 
bridge centre in the DTM and converts this information into a 
suitable image energy term for the related nodes of the road 
network. In this context, it is important that our DTM filtering 
method will assign the bridge to the terrain (cf. section 2.3.2).