In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
fences or cars on one hand, and points in the interior of the build 
ing that are measured through windows because of transmission 
of laser beams in glass, on the other hand. In addition the point 
clouds do not have to be georeferenced and are allowed to be arbi 
trarily rotated around the vertical (z) axis, though the z-axis of the 
point cloud has to be parallel to real world vertical axis.Our inves 
tigations showed that an exact levelling of the laser scanner meets 
this demand. Finally, we assume the point cloud to be taken from 
different view points so that the self occlusion of facade parts is 
minimized, e.g. there are points observed on both embrasures of 
a window. However, some parts of the facade that are above the 
laser scanner are unavoidably occluded, e.g. windowsills. 
Since our approach is based on prior knowledge of objects we 
built up a database of ground truth parameters of facade parts. It 
contains measurements of all shape parameters (width, depth and 
height) of 170 stairs, 60 doors, and 560 windows so far and is be 
ing extended continuously. Additionally the number of steps of 
the stairs and the relative location of the doors, i.e. the left, center 
or right part of the building, is documented. All data is manu 
ally taken either from undistorted, rectified and scaled images, or 
from high resolution 3D point clouds. The first were taken with 
a Canon 350D or Nikon D700 digital single-lens reflex camera 
with calibrated lenses. The latter were captured by static scan 
ning with Leica HDS6100 laser scanner which was mounted on 
the roof of a van to reduce occlusions by cars, fences, or hedges. 
Figure 2 exemplarily shows the histograms of the parameters of 
stairs (purple) and windows (green). 
Figure 2: Histograms of ground truth parameters, most likely 
probability density functions (thick lines) and Gaussian (thin 
lines) of stairs (purple) and windows (green). 
For each parameter that is documented in the ground truth database 
we estimated the parameters of about 40 probability density func 
tions (PDF) and applied a Chi-Squared test to select the most 
likely PDF. The distributions of all parameters of windows are op 
timally described by a Generalized Extreme Values (GEV) distri 
bution, the tread depth of stairs matches a Lognormal distribution 
and the rise of stairs ties up with a Weibull distribution (cf. figure 
2). Apart from rise and depth of windows the Gaussian approxi 
mately fits the data nearly as well as the most likely PDF. How 
ever. our methods apply the slightly better non-Gaussian prob 
ability density functions. The classifier for windows and stairs 
that are presented in the next section in detail are based on the 
mentioned distributions. 
3 CLASSIFICATION AND RECONSTRUCTION 
This section gives a detailed description of our concepts for the 
classification of facade parts. The following three subsections 
depict the phases of the classification that have already been out 
lined in the introduction. The classification and reconstruction 
of single windows or stairways are delineated. For the detection 
of multiple objects of the same type, e.g. all windows within a 
facade, an iterative application of the classifier is required. 
Generally, we gradually constrain the point cloud by the applica 
tion of prior information. Since the constraints are more and more 
expensive to calculate they are applied to the subset received from 
the previous step. Therefore, samples are drawn from a subset 
that is derived from a point based (pre-)filtering. Furthermore the 
goodness of samples is exclusively computed for samples with a 
high fitness. 
3.1 Pre-filtering 
The only restriction on the point cloud that is to be analyzed is the 
parallel direction of its z-axis and the real world's vertical axis. 
However, a small amount of uncertainty concerning given direc 
tions or angles is permitted. Due to such general assumptions 
an efficient classifier is needed that copes with a high percent 
age of outliers. Our method achieves efficiency by its top-down 
approach that incorporates prior knowledge from the very begin 
ning. Therefore we pre-filter the point cloud with regard to the 
probability density functions of point distributions to further op 
erate on a subset with a high percentage of inliers. 
Our algorithm starts with the estimation of vertical planes by 
MLESAC. Each estimation operates on the difference set of the 
original point cloud and the union of the so far received consen 
sus sets. Due to the dominance of walls the estimated planes are 
assumed to be walls of the building, i.e. (main) parts of facades 
of L-, T- or U-shaped ground plots or parts of protrusions like 
oriels. Afterwards, the point cloud is transformed in such a way 
that the largest plane, i.e. first estimated plane, is identical with 
the xz-plane of the coordinate system and such that no negative 
x- and z-values exist. Thus, the positive y-axis points towards the 
interior of the building. Finally, the reduction of the point cloud 
is achieved by selecting points with a high probability of belong 
ing to the given class of objects, e.g. points that belong to stairs 
are most likely on the bottom of the ground floor, in front of the 
facade and in front of a door. Otherwise points that belong to win 
dows are located on the facade or within a well defined buffer of 
about 25 cm behind the facade. We apply the probability density 
functions of model parameters directly or as a mixture of multiple 
PDFs to the 3D point cloud, and thus receive the filtered subset. 
The pre-filtering for windows is solely based on the knowledge 
about the relative location of embrasures to walls in y direction. 
The PDF of depth (cf. figure 2) is used to filter points by their 
y-coordinates relative to the estimated planes. 
In contrast to the filtering of windows the filtering of stairs con 
siders three coordinate axis. Hence, the stair filter is a combi 
nation of PDFs for x-, y-, and z-coordinates. Each of the three 
individual PDF is sketched in the following: (x) The PDF of the 
x value considers the probability of the relative location of the 
door within the facade and the likelihood of the width of the door. 
Thus, it is given by a mixture density, (y) The y-filtering is de 
rived as a combination from the probability of tread depth, the 
PDF of the numbers of steps and the assumption that a stairway 
is in front of a door and therefore its origin is located at y = 0. 
(z) The PDF of z-location considers the PDF of door heights and