David Heitzinger
KNOWLEDGE-BASED 3D SURFACE RECONSTRUCTION
David Heitzinger
Vienna University of Technology, Austria
Institute of Photogrammetry and Remote Sensing
dh@ipf.tuwien.ac.at
Working Group IV/3
KEY WORDS: Surface reconstruction, DET/DEM/DSM, Modelling, Algorithms.
ABSTRACT
The reconstruction of complex surfaces in N° is still a rather uncovered area in the field of Photogrammetry and Geod-
esy. Whereas other disciplines, such as CAD, Computer Sciences, Medicine, Geology and others, have developed
methods, suitable for their special needs and applications, no satisfactory solutions exist for natural topographic sur-
faces. This work offers an approach for the reconstruction of 3D-surfaces, designed to fulfil the requirements of Photo-
grammetry and Geodesy.
The main idea is the use of as much knowledge as possible for the reconstruction of the surface from the digitised
points. This knowledge includes constraints and assumptions about the original surface (e.g. smoothness of the surface),
about data sampling (specific characteristics of different data sources) and about additional information (e.g. measured
lines). The knowledge is splitted into elementary and autonomous statements, so-called rules. These rules assign evi-
dences in favour or against the shape of the reconstructed surface.
The surface is modelled with a triangular mesh, which offers the necessary flexibility when modelling natural surfaces.
To find the 3D-triangulation a tetrahedral tessellation of the data is computed in a first step. The main reason is the
reduction of the amount of possible triangles. From the triangles of this tessellation the ones belonging to the surface are
extracted. For this purpose the above rules are applied. The inference of a decision, whether a triangle belongs to the
surface or not, uses standard techniques from the field of Artificial Intelligence and Probabilistic Reasoning.
1 | INTRODUCTION
‘Reverse Engineering" is a term, commonly used for the reconstruction of surfaces from 3D-point clouds. Engineering
can be seen as the skill to construct a physical object from a digital representation, thus Reverse Engineering is the
generation of a digital representation of a real world object. This task is necessary for geometric analysis of the object,
for comparison with other objects or for visualisation. Reverse Engineering has to be performed in two steps:
l. Measurement of the object, e.g. determination of co-ordinates of points on the surface. The measurements are al-
ways discrete, hence they do not completely describe the surface.
2. Calculation of a digital representation from the measurements, which fits to the original surface as good as possi-
ble. Figure 1 demonstrates this step, where a 3D-triangulation is generated from point- and line-data.
Figure 1, Reconstruction of a surface from point- and line-measurements, using a 3D-triangulation. The data consists
mainly of lines: breaklines, representing a C'-discontinuity, formlines, which indicate a high curvature of the surface
across the line, and a borderline.
1.1 State of Research
Many different methods for Reverse Engineering have been developed in several disciplines. In CAD and CAGD algo-
rithms have been developed for surface representation and reconstruction, an overview is given by Värady et al.(1997)
and by Värady et al.(1998). Ekoule et al (1991) present an approach for surface reconstruction in medical applications,
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 381
