itor is, however, of 
cation. Changes in 
ay bear no relation 
y are located. The 
à potentially useful 
iformity. 
researchers in the 
itelligence for the 
mogeneous regions 
formity indicators. 
ed a number of 
uation of image 
mages using single 
1binations of two 
| and one related to 
ch point). The five 
al. 
an origin. 
ncluded that the 
and the orientation 
rem to effectively 
bjects. 
rmity indicators to 
dimensional object 
ors in the minimum 
/ utilised in their 
follows: 
Ms, 
c) = z) of points, 
it surface normal, 
cators requires the 
0-ordinates of each 
three coefficients of 
el: 
j,uv t Bs v2, 
point were used by 
tor in the evaluation 
with the uniformity 
87), the use of the 
nodel requires the 
ication algorithm for 
images, using the 
ture and maximum 
-set of the quadric 
um curvatures are 
-planar surfaces, in 
ical, cylindrical, or 
n made use of the 
urvature measures in 
iscriminate between 
ces. 
1996 
Surface curvature measures were also used by Besl and Jain 
(1988) to provide an initial coarse segmentation of range 
images, to be refined in an iterative region growing process. In 
this case the values of mean curvature and Gaussian curvature 
are not used directly, instead a function of the thresholded (-1, 
0, +1) values is used to label the surface about a point as being 
one of eight possible types. Thus, the image is segmented into 
patches of points with the same or similar surface 
characteristics, which are then refined. 
The algorithms presented by Fan et. al. (1987), Roth and 
Levine (1993) and Chen (1989) for segmentation and 
classification of three dimensional objects do not make use of 
uniformity indicators computed directly from the surface about 
a point. Instead, they used the residuals of the fit of pre- 
defined surfaces to indicate the uniformity of points within a 
patch. These residuals are dependent upon the type of surface 
being fitted, and the number and distribution of points used in 
the fitting. Unlike the uniformity indicators used by other 
researchers, the residuals of a surface fit are not computed in 
isolation at each point, and are not solely dependent on the 
surface defined by the points in the target field alone. 
2.1.2 Indicators Selected : Of those uniformity indicators 
reviewed the maximum and minimum surface curvatures and a 
function of the surface normal coefficients were found to be 
the most appropriate indicators of point uniformity for the 
generalisation of target fields. Using indicators related to 
surface normal and surface curvature simultaneously will 
enable the decomposition of both planar and curved objects 
(Krishnapuram and Munshi 1991). The minimum and 
maximum curvatures were selected over the other measures of 
curvature, as these two measures have distinctive 
combinations for points on the quadric surfaces highlighted by 
the hierarchical classification process presented by Flynn and 
Jain (1988). 
DES. 
Cylinder : max = 1/R. 
min = 0. 
Sphere : max = 1/R. 
min = 1/R. 
£X <> 
Cone : max — o .. 1/R. Plane : max = 0. 
min = 0. min = 0. 
San Max 22-3, Min. 
Curv. Curv. 
Figure 1. Distinctive combinations of Max. and Min. 
curvatures for the sub-set of quadric surfaces. 
A function of the surface normal has been selected rather than 
the surface normal itself, as this reduces the number of 
parameters to be considered at each point. The function of the 
surface normal coefficients to be used is the orientation 
(direction) of the surface normal in the object system XY 
plane. The surface normal at a point is directly related to the 
direction from which it is to be imaged in network. Using the 
y 
maximum and minimum curvatures and a function of the 
surface normal reduces the consideration of uniformity to 
three parameters at each point as opposed to five if the two 
curvatures and the coefficients of the surface normal are 
considered. The excessive number of data elements to be 
considered at each point is also the justification for rejecting 
the use of point co-ordinates and coefficients of biquadratic 
surface approximations as uniformity measures. The use of 
surface normals and point co-ordinates as uniformity 
indicators would require the consideration of six data elements 
for each point, as would the use of the biquadratic surface 
approximation. 
The selected uniformity indicators do not contain any 
information about the location of points. Thus, if points are 
grouped based solely on their uniformity indicators, points on 
disjoint surfaces of the same type will be grouped together. 
The use of location information (e.g co-ordinates) would 
ensure that this grouping of points on disjoint surface did not 
occur, i.e. points would have to be uniform in location. If the 
issue of disjoint surfaces is not dealt with directly during the 
grouping of points, then point proximity will have to be 
established for each group of points created. The requirement 
for post-processing of point groups is not in conflict with the 
partial model developed by Mason (1994), which suggested 
the use of both uniformity and proximity. 
2.2 Point Grouping With Uniformity And Proximity. 
The algorithms reviewed can be considered as one of three 
types or a combination of two of these three. Segmentation 
algorithms partition the data set into non-intersecting regions 
such that each region is homogeneous and the union of no two 
adjacent regions is homogeneous. Segmentation algorithms do 
not provide any indication as to the nature of the underlying 
surface of the point groups. Classification algorithms 
determine surface parameters or descriptions for the point 
groups that convey important information about these groups 
ie. location and orientation (Flynn and Jain 1988). Neither 
segmentation nor classification algorithms solve the point 
grouping problem completely and thus a combination of the 
two must be used. The third type of algorithms are extraction 
algorithms that do not have distinct segmentation or 
classification components. Data sets are not initially 
decomposed into point groups for which parameters or 
descriptions are subsequently determined. Instead the total 
data set is interrogated to identify the presence of surfaces of a 
predefined type in the data set. Membership of points to these 
surfaces is then established. 
2.3 Algorithms For The Evaluation Of Uniformity And 
Proximity 
A number of algorithms were reviewed and those presented by 
Jolion et. al. (1991) and Newman et. al. (1993) were selected 
as being the most suitable for the evaluation of uniformity and 
proximity as measures to establish target groups. 
The clustering algorithm as used by Jolion et. al. can integrate 
multiple sources of information about the same data set, 
allowing a more complete analysis ( Jolion et. al. 1991 ). This 
type of algorithm can also make efficient use of all available . 
uniformity indicators. The algorithms presented by Roth and 
Levine (1993) and Chen (1989) can only use the fit of points 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996