Full text: XVIIIth Congress (Part B5)

  
to a geometric primitive anc. thus the position of points in 
isolation. 
Jolion's algorithm is also “context-insensitive’, unlike 
Krishnapuram and Munshi's (1991) and Hoffman and Jain's 
(1987) algorithms. These algorithms require the input of a 
maximum number of point groups to be formed in the feature 
space, and thus exhibit the paradox of requiring knowledge 
about the data set in order to interpret it (Quek et. al. 1993). 
Jolion's algorithm dynamically selects the appropriate number 
of point groups in a data driven process. 
Jolion's algorithm makes direct use of uniformity indicators 
without having to threshold them (i.e. map computed values 
to -1, 0, or +1), as is required for Besl and Jain’s (1988) 
algorithm. Abdelmalek (1990) and Krishnapuram and Munshi 
(1991) note the difficulty associated with selecting appropriate 
thresholds for the re-scaling of curvature values. 
In addition to using uniformity indicators directly, Jolion’s 
algorithm makes use of the entire data set when producing its 
decompositions. Errors in the data set do not have significant 
effects on the results of the segmentation. Other techniques, 
such as region growing and boundary identification 
(Krishnapuram and Munshi 1991) or selecting only a small 
subset of ‘significant’ data points, may lead to spurious 
segmentation of the data. 
Jolion et. al (1991) have taken an ‘intelligent’ approach to the 
target point grouping. The algorithm identifies a portion of the 
feature space that will produce the most significant cluster, to 
be refined in a ‘brute force’ process limited to only a portion 
of the data set. Krishnapuram and Munshi’s (1991) algorithm 
requires multiple clustering’s of the entire data set, from which 
the best segmentation is selected. This ‘brute force’ approach 
to clustering results in a slow and computational inefficient 
algorithm (Krishnapuram and Munshi 1991). 
As indicated earlier the point groups returned from an analysis 
of the selected uniformity indicators may contain points from 
more than one surface of the same type. Therefore, a proximity 
measure must be used to split disjoint surfaces that have been 
grouped together. To evaluate the proximity of the points, the 
separation of all points in a group can be computed with 
respect to one point in the group and in a given direction 
(Figure 2). The separations from the common point of all 
points on the same surface will be similar (Figure 2, 
separations in range D; — D»). Points on the surface with the 
same or opposite orientation will have distinctly different 
separations from the common point (Figure 2, separations in 
range D; — D,) The means of these two ranges will be 
significantly different (Figure 2, D,; - D,2), indicating that 
two point groups are not in close proximity. In a majority of 
cases, the evaluation of point proximity's will separate points 
on surfaces with the same or opposite orientations. However, 
the algorithm can not successfully discriminate between points 
on surfaces if they are parallel and close together, or when the 
surfaces are duplicated next to each other, as there is no 
significant difference in the separations of the points. 
The descriptions of the point groups created by Jolion's 
algorithm are to be produced using a modified version of 
Newman's et. al. (1993) algorithm. The simplicity of this 
algorithm, its compatibility with Jolion's algorithm and the 
ease with which it can be modified were significant in its 
8 
selection as the classification algorithm. The details of this 
selection process and the evaluation of this algorithm are 
beyond the scope of this paper. 
  
// > 
: I ci 
C r* Direction in 
ommo which the 
point from separations 
which * 
; of point are 
separations to be 
are 
  
measured. . 
measured. 
Figure 2. Separation of points for the evaluation of data point 
proximity. 
2.4 Pre-processing Of Target Field Data Sets. 
Target fields to be decomposed using the selected 
segmentation algorithm require pre-processing before the point 
grouping can be undertaken. The uniformity indicators upon 
which the point grouping is to be based are computed from the 
local continuous approximation: 
w(u,v) = C; u° + C; uv - C4 V * Cau* C5 v * C, 
to the discrete data set of target points. For a majority of cases 
the surface features can be computed directly from the 
continuous approximation, however, in the case of points that 
belong to more than one surface, this is not possible. Direct 
computation of the surface features from the local continuous 
approximation would retum a single set of uniformity 
indicators. If the point lies on more than one surface i.e. an 
edge point, then one complete set of indicators is required for 
each surface on which the point lies. Figure 3 shows this 
concept for surface normals at an edge point. Points requiring 
multiple surface features of each type could be dealt with by 
creating *dummy points. The surface features of each these 
‘dummy’ points relate to the different surface on which the 
point lies. 
  
  
  
  
  
N2 
m N; 1 Surf. 1. 
= ——P Ni N» .L Surf. 2. 
Ns y” Surf. 1. N; 1 Surf. 3. 
p 
= 
Surf. 3. 
Figure 3. Edge point with multiple valid uniformity 
indicators. 
Points requiring ‘dummy’ points could be identified by 
examining the uniformity indicators computed at each point 
without regard for points being edge points or otherwise, i.e. 
only one set of indicators for each point. In particular the 
curvature measures could be analysed to find those points that 
have curvatures greater than might reasonably be expected at 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996 
points lying « 
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