The details of this
this algorithm are
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EN
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lation of data point
Sets.
ing the selected
ing before the point
ty indicators upon
computed from the
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a majority of cases
directly from the
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ot possible. Direct
he local continuous
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one surface i.e. an
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igure 3 shows this
nt. Points requiring
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> valid uniformity
| be identified by
puted at each point
ts or otherwise, i.e.
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nd those points that
ably be expected at
1996
points lying on a smooth surface, indicating that the point lies
on a sharp edge.
3. COMPUTER VISION CONCEPTS APPLIED TO
PHOTOGRAMMETRIC PROBLEM.
3.1 Nature Of Data Sets.
The algorithms to be evaluated have been successfully applied
to computer vision and machine intelligence tasks. A number
of difficulties were encountered in developing the algorithms.
These were due to the differences between the target field data
sets and the data sets used in the computer vision applications.
Computer vision data sets are continuous images of only a
portion of the object, with an established perspective. The
target field data sets are discrete points, representing the entire
object. These differences have a significant impact upon the
processing strategy to be adopted.
It was intended that surface normal information and curvature
information could be considered simultaneously in a three
dimensional | clustering algorithm as suggested by
Krishnapuram and Munshi (1991). However, the problems
detailed below have resulted in an alternative processing
strategy being adopted.
3.2 Edge Point Identification.
Edge points in the data set need to be given special treatment
regardless of the application. In computer vision applications
the continuous data sets lend themselves to edge point
identification, using well established filtering and simple edge
operators (Fan et. al. 1987). The contaminating effects of these
edge points on surface feature computation can be reduced or
removed by masking out edges in the images.
No simple and effective method was found for identifying edge
points in the discrete data sets based upon information that
could be computed for each point and its nearest neighbours in
isolation. An approach based upon analysis of surface
curvatures required the use object dependent thresholds.
Furthermore, this approach was not considered to be reliable.
Therefore, a computational approach requiring the
identification of edge points prior to point grouping was found
to be inappropriate.
The contaminating effects of edge points on surface features
computed at neighbouring points could not be reduced or
removed. Instead, edge points were left in the data set in the
knowledge that these and other points effected by their
contaminating effects would fall out of the clustering process
as isolated points. Edge points would not be grouped with
‘regular’ surface points as they do not exhibit features
consistent with the majority of points in the data set, ie
significantly larger curvatures.
3.3 Approximating Surfaces.
The initial algorithm development was undertaken using an
approximating surface of the type used by Flynn and Jain
(1988):
w(u,v) = C; u*+ C; wv v4 C;uv- C, + C5 v? 4C, uv
+ C; v -* Cau Co v * Cj
9
This approximating surface was replaced by the one presented
in Section 2, as the higher order function behaved poorly in the
vicinity of edge points. When used in a least squares fitting
process the high degree of freedom of the approximating
surface meant that it would often produce a good fit on all data
points in the surface patch, regardless of edges. This was at the
expense of a suitable representation of the underlying surface.
The simpler equation of section 2 produced a surface that
fitted a majority of points in the patch without unnecessary
oscillations in the approximating surface.
3.4 Surface Normal Directions.
The surface normal directions and their functions are valuable
quantities for the decomposition of data sets in both computer
vision and target field generalisation.
The continuous data sets used in computer vision applications
are less susceptible to ambiguities associated with surface
normal computations than the target field data sets. In
computer vision applications only a portion of the object is
considered (viewed) from a single point. This significantly
reduces the range of surface normal directions returned for
points on the object. There are no ambiguities caused by
normals being returned that are parallel or near parallel but in
opposite directions. In computer vision (range data) all surface
normals are 'out" of the object, ‘towards’ the sensor. In
addition, occlusions in the images mask out portions of the
object in which ambiguous surface normal directions could be
computed eg. potentially ambiguous normals perpendicular to
imaging direction are not computed. (Figure 4a.)
The data sets representing objects to be generalised in this
evaluation have no established perspective and embody the
entire object. The surface normals are computed from
continuous local approximations of the discrete data set and
the surface normal can be on either side of this surface. The
surface normals can be ‘into’ or ‘out of the object. When
considering these surface normals there is no limit on the
range of directions to be considered. Therefore, parallel and
near parallel normals in opposite directions, which are
‘similar’ despite apparent differences must be accounted for in
the clustering process (Figure 4b.)
v
* SENSOR.
(a) (b)
Bl Occludedarea. — --» Ambiguous surface normal
(parallel and opposite
Figure 4. Ambiguous surface normals.
Instead of adding information to the point grouping process the
surface normal directions when computed for the entire object
tended to only confuse the clustering algorithm. Despite their
value the surface normal directions are not suitable for direct
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
