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.
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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