ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
blurred since the weighted interpolation works like a low 
pass filter. 
At the Department of geodesy and photogrammetry at the 
Royal institute of technology, Stockholm, Sweden, another 
method for DTM construction has been developed (Axelsson, 
1999). A commercial software implementation based on this 
work can be found in the TerraScan package (TerraScan, 
1999). In his paper, Axelsson describes the method in one 
dimension. The method processes one swath at a time. He 
reports that work will proceed and a two-dimensional 
surface-based implementation based on a triangular irregular 
network (TIN) will be carried out. The basic idea is to start 
with a surface beneath all laser points, see Figure 2. This 
surface is then connected to the ground points from below 
using some sort of criteria. Axelsson enumerates a number of 
possible criteria for controlling the connection, e.g. 
Minimum Description Length (MDL), that he uses in his 
implementation. All criteria have in common that they 
delimit the possible shapes and hence fluctuations of the 
resulting surface in some way or another. 
  
  
Elevation 
  
  
  
  
  
  
  
  
  
  
Scan direction 
Figure 2. Connecting ground surface to points of one 
swath, (Axelsson, 1999). 
The TerraScan implementation is based on this work. It is 
two-dimensional and surface-based and works as follows. 
First, a rectangular grid of which the size is controlled by 
user-supplied parameters is created and placed over the point 
cloud. For each mesh the lowest point is selected as a 
connection point, ie. is classified as a ground point. The 
selected points are triangulated resulting in an initial TIN 
based surface representation of the ground surface. Besides 
the connection points this initial surface is entirely beneath 
the point cloud. 
Another process now starts where the final surface is 
constructed by iteratively adding new points to this 
triangulation. One point at a time is selected from the point 
cloud and based on different criteria it is accepted or rejected 
as a new connection point. Each new connection point is 
inserted in the triangulation and makes the surface follow the 
ground more closely. User-supplied parameters are used in 
the criteria to control the selection. One criterion is based on 
the distance between a candidate point and the present 
surface. Another criterion, referred to as the iteration angel, 
is based on the angel between the surface with and without 
the candidate point. The connection points used in the 
resulting TIN surface constitute a subset of the actual 
measured points. Hence, for those connection points that 
really are ground points the accuracy of the approximation of 
the real ground surface is equal to the accuracy of the laser 
measurement system. 
A- 115 
2. ACTIVE SHAPE MODELS 
Active shape models are something in between the fields of 
image processing and computer graphics. A deformable 
model is influenced by an image to be transformed into a 
certain shape. In image processing the models are used to 
find edges and lines in images and referred to as active 
contours. Due to their nature the active contours are suited to 
find continuous edges or lines in the images. 
When dealing with contours in two dimensional images the 
active contour is commonly mentioned as a snake (Kass et 
al, 1988). 
The shape of the active contour is the solution that minimizes 
an energy function. The energy function consists of material 
behavior like elasticity and rigidity of the snake. It is also a 
function of the attractor image derived from features in the 
image. 
In this algorithm for ground estimation the active shape 
model can be liken with a sticky rubber cloth being pushed 
up from beneath. The cloth sticks to the lowest points, 
forming a continuous surface. 
2.1 Theory 
The model is a discrete two dimensional surface in a three 
dimensional environment. The surface position is given in a 
parametric form by vIk]= (x(k), y(k), z(k)) The shape of the 
model is controlled by an energy function. The shape of the 
model minimizes this energy function, 
EW) = Y (Ei Vk) +E, ok) +E, kD) (1) 
E; is the internal energy of the model, it gives the surface 
its smoothness. The internal energy is derived from the 
elasticity and rigidity of the model i.e. a function of the first 
and second derivatives of the surface 
E 
If this function is the distance between the measured surface 
and the model, it gives a model that is attracted to the laser 
data points. 
im is the potential field created from the laser radar image. 
E 
model to a preferred shape. 
ext is derived from other constraint forces guiding the 
The minimization of the energy function is an iterative 
process and the model is given start values near the wanted 
solution. Start values are often a local minimum of the 
energy function E. Using different start values will in most 
cases result in models of different shapes after the 
minimization. This is not a problem in this case when using 
the models to estimate the ground surface from laser radar 
data, since there are no measured points below the ground the 
model can safely be started from below. 
3. IMPLEMENTATION 
In the implementation of this algorithm at FOIL some 
simplifications have been done due to the appearance of the