towards DTM generation in the Wadden Sea. In a supervised 
classification approach, a membership value to the class water 
is determined for each laser point according to the features 
height, intensity, and point density. The classification into water 
and /and is performed using a threshold for membership. 
A segment-based method for water detection outside of Wadden 
Sea areas using LiDAR data was proposed by Hôfle et al. 
(2009). In a preprocessing step, intensity values are corrected 
related to the incidence angles, and the positions of laser 
reflections missing (due to specular reflection or decreasing 
target reflectance) are modelled by interpolation. Water-land- 
boundaries are defined by the segment borders. To the best of 
our knowledge no approach considering context in the 
classification process exists. 
The use of CRFs for image labelling was introduced by Kumar 
and Hebert (2006). In comparison to image data, the labelling of 
point clouds is even more challenging due to the irregular 
distribution of points in 3D space. Several approaches for the 
classification of point clouds based on CRFs have been 
developed in the past. Some of them are based on point cloud 
segments. For instance, Lim and Suter (2009) propose a method 
for the classification of terrestrial laser scanning data. First, they 
reduce the data by over-segmenting the point-cloud into regions 
called super-voxels. Based on features measured by the scanner 
system (intensity and colour) as well as features extracted from 
the points inside the super-voxels, the data are labelled in a CRF 
framework. The potential of CRFs for airborne laser scanning 
data was shown by Shapovalov et al. (2010). They propose a 
method based on segments of points and show the improvement 
of this non-associative approach in comparison to an associative 
network for an urban dataset. Niemeyer at al. (2011) propose a 
point-wise method for the classification of LiDAR data, 
distinguishing three urban object classes. They also compare the 
results with a Support Vector Machine, highlighting the 
improved classification performance of the context-based 
classifier. 
Our focus is on demonstrating the suitability of CRFs for the 
classification of LiDAR data in nearly featureless areas. We 
introduce a point-wise supervised labelling for distinguishing 
the three classes water, mudflat, and mussel bed. For this 
purpose we select the most suitable features. We present the 
implementation of a CRF framework to our data and also 
investigate the improvement of the classification result using 
contextual information in comparison to the classification 
results obtained by a Maximum Likelihood approach. 
2. CONDITIONAL RANDOM FIELDS 
LiDAR data can provide detailed information of the illuminated 
surface. In Wadden Sea, backscatters belong to water surfaces 
in tideways as well as mussel bed on the mudflat (see Fig. 1). 
Those objects, their typical structures and interrelations can be 
integrated in the classification process. 
CRFs are a flexible tool for classification tasks belonging to the 
group of graphical models. Thereby, a class label C; is assigned 
to each node in the graph. The nodes are represented by the data 
set S;, i € [1, ... n]. In our case 5; denote the n points of the 
LiDAR point cloud. However, any kind of 2D or 3D spatial data 
can introduce in the CRF framework, for example image pixels 
or segments. Each node and point, respectively, is linked to its 
adjacent nodes by an edge. In contrast to common approaches, 
the data points are not modelled to be conditionally 
independent. Thus, a label to point i is assigned based on its 
  
Figure 1: Orthophoto and labelled point cloud with the classes 
water (blue), mussel bed (red), and mudflat (yellow), illustrated 
with an increased vertical exaggeration of the factor ten 
feature vector x; as well as on those obtained for all points in 
the defined neighbourhood N;. 
The posterior distribution P(C|x) of the class C given the 
observed data x is derived in a discriminative model. A 
common approach for modelling the conditional distribution in 
a CRF framework is based on potential functions out of 
exponential family. Then, the posterior distribution P(C|x) can 
be written as 
P(C|x) « 5 zo 9? 2 mrs s I;j(x, Cj, C;) |, 
i€S jeN; 
(1) 
where the partition function Z(x) acts as normalization constant. 
It is needed for the transformation of potentials to probabilities. 
The energy term can be expressed as the sum of association 
potentials Aj(x, C;) and interaction potentials I;; (x, Ci, Cj) over 
   
  
    
   
   
   
    
  
  
  
  
  
  
  
  
   
   
   
   
   
  
  
   
   
    
   
  
  
  
  
  
  
    
  
  
   
   
   
   
    
     
   
     
    
   
    
  
   
   
   
the n 
2006 
The 
belor 
Kum 
genei 
P(C| 
The 
meas 
comp 
adjac 
of th 
term 
Since 
welg 
train: 
obtai 
minii 
facto 
infer 
parai 
regat 
appr 
Prop 
and i 
Final 
poste 
node 
We « 
pres 
class 
over 
It ca 
impl 
label 
Figu 
clas: 
The 
expl 
CRF