This is very specific to remote sensing of terrain. An
entirely different approach may exist if a spacecraft
needs to navigate in the final approach to a planetary
surface. In that event ranging may be combined with
single image shape-from-shading or stereoscopy. Yet
another strategy may be developed in a robotics en-
vironment where a vehicle needs to navigate in a
known factory environment.
9 FROM POINT CLOUDS TO SURFACES
9.1' The Problem
The traditional topographic mapping which results in
a digital elevation model employs a gridding method
to convert irregularly spaced surface points into a
pattern of regular points that produce a square or
triangular mesh surface. The process is made difficult
only by the need to filter out erroneous or noisy
observations.
The problem is vastly different when a truly 3-
dimensional object needs to be modelled. In the
example of a point cloud describing a hand it is not
trivial to decide which surface points should be
connected and should become nodes of polygons. The
fingers of a human hand may represent a different
topology than the toes of a duck. One has the added
difficulty of converting a cloud of surface points into
a topology that is consistent with the object.
Traditionally the only information available about a
surface are the irregularly spaced points with their
XYZ-coordinates. One has not, so far, begun to
augment the bare point clouds by surface normal
vectors. Such information would be available from the
machine vision element of the process, and one could
obtain the surface normals in a shape-from-shading
process.
9.2 Example for a Solution
The methods of sorting through a cloud of points and
of finding their topology along the surface could be
based on selecting the nearest point. This of course
may create holes in the surface. It may also connect
points that topologically should not be connected, as
can easily be seen when modeling fingers on a hand.
The ,,alpha* shapes are a recent development that starts
out from individual points and creates surfaces from
them. The idea of ,,balloons* resembles the approach
that has come from tomography where the individual
voxels are being searched for surfaces that may be on
the outside of the object. In this case points are being
replaced by balloons which touch one another as the
radii increase. The resulting object has a surface that is
created from the overlapping balloons. This kind of
approach has been extensively tested with point
clouds representing a human head and another cloud
representing an entire statue of a Habsburg emperor
(Uray et al., 1995).
10 REALISTIC VISUALIZATION
10.1 Geometric Detail versus Surface Texture
The accuracy with which a geometric model of an
object needs to be created depends on the application.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
In the event of an object to be visualized and rendered,
that accuracy may be traded-off with the detail at
which surface properties are known. If a photographic
texture of a face, a building facade or a tree exists, one
may not have more geometric detail than an ellipsoid
for the human face, a cube for a building, and a plane
for a tree. This consideration may be in contrast with
the accuracy at which topogrpahic relief is being
mapped. Yet visualization of a landscape again may
require very little geometric detail if the bald Earth is
accompanied by the surface cover and by objects
placed on the surface.
The use of 3-dimensional surface geometries to
support visualization and rendering is of increasing
importance. Not least do we find an increased interest
in the entertainment industry which is rapidly deve-
loping into a very large application for computer
graphics and image processing.
10.2 Measuring Surface Properties
The surface properties are needed to relax the require-
ments on geometric detail. They are also needed to
provide a description of reflection properties. The
response to illumination in turn does not need to be
known very well if the surface texture is observed and
available. The reflectivity of a surface can be measured.
Photogoniometers and methods analogous to remote
sensing classification can be used to obtain the
response of a surface point to various illumination
directions. A promising approach to measure surface
property is based on photography. Multiple photo-
graphs are being taken at multiple illuminations of a
given surface point and the reflected light is being
extracted from the grey value in the photograph.
Image simulation is not only a topic of computer
graphics and rendering for human consumption but
may also be a tool in image analysis. One example is
shape-from-shading where a shape needs to be com-
puted and refined from differences between a
simulated and real image. Simulation also is useful
when trying to overcome the dissimilarity in image
matching. Gelautz et al. (in print), Kellerer et al. (in
print) have shown how opposite-side radar images can
be matched using image simulation based on a digital
elevation model. The difference between an actual
image and such a simulation can be an input to the
measurement of surface properties. Differences be-
tween image and simulation can be explained as a
result of variations in the surface.
10.3 An Example of a Room
The use of geometric modelling of objects with sub-
sequent rendering is illustrated by more than 60,000
polygons describing the geometry of an office. The
geometry surface properties of each polygon have
been determined from photography. Visualization of
the room is now a result of raytracing and a method
called , radiosity” (Karner, in print). Raytracing serves
to determine the mirror reflections; radiosity is a
model to compute the distribution of light in a room
given well-defined light sources. Raytracing is de-
pending on the position of a viewer, radiosity is not.
Figure 10.3 is a rendering of that room that has been
shown as a photograph in Figure 10.1, and as a wire-
frame rendering in Figure 10.2.
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