TERRAIN FEATURE IFH 2 and Th/H > |Then = 
max max 
SPHERICAL SURFACE 2.0 2 Z [1/10 | S | > 2 
LA SURFACE |1.5 2 7 [1/7 | S | N E 
GAUSSIAN SURFACE 2:02 2 [1/5 | S | N x] 
| CONICAL SURFACE [2.4 tZ mc | S | x | 
[COMPOSITE SURFACE [0.5 %Z [1/30 | S | 
HYPERBOLIC | | = 
PARABOLOIDAL SURFACE|6.0 % Z 1/6 S N 
| BREAK LINE [2.0 % Z [1/8 | S | y... 
[FAULT [2.0 x Z [1/3 | S | N E 
  
Table 1: Rules for selective sampling 
Where 
S- sample peak or pit (convex or concave) points 
and auxiliary lines, 
N- no SS and proceed to next working unit. 
In the absence of auxiliary lines, some pseudo 
lines are generated automatically in the system. 
The output of SS represents the I-set, which 
comprises: 
. peripheral lines 
- break lines and break points 
. auxiliary lines and auxiliary points 
- Some descriptors. 
This information serves as the input for the 
subsequent PS. 
1.2 Progressive sampling 
1.2.1 General. PS is a semiautomatic method for 
sampling terrain regions, mainly homogeneous, 
though irregular terrain relief, thus providing 
the filling information. The density of the DTM 
grid is locally adapted to terrain roughness. 
1.2.2 Different densification criteria. The 
core of PS are the criteria for local grid 
densification. Hence, these criteria and the 
corresponding decision rules are most significant. 
In  (Makarovic, 1973) a - one dimensional (1D) 
Laplacian operator was used separately in the X 
and Y directions. The following criteria are 
potential alternatives: 
- 2D-Laplacian, 
Extended 2D-Laplacian, 
- 1D-Laplacian in four directions, 
- Median height, 
- Fitted plane, 
- Second difference for a quadruple of points, 
separately in the X and Y directions. 
1.2.3 Tests using ideal geometric primities as 
input The aim of the tests was to gain insight 
for identifying the most feasible densification 
rules in PS. To thig end, some representative 
geometrically ideal primitive surfaces were used 
as input. 
For the study, the following densification 
criteria were used: 
- VARIANT-1, PS(1); using 1D-Laplacian algorithm 
Separately in X and Y 
- VARIANT-2, PS(2); using 2D-Laplacian algorithm 
78 
- VARIANT-3, PS(3); using extended 2D-Laplacian 
algorithm 
- VARIANT-4, PS(4); using 1D-Laplacian algorithm 
separately in four directions. 
For the geometric primitives tested, "1D-Laplacian 
in four directions" proves to be a potential 
alternative criterion for the self-adaptive 
densification in progressive sampling. 
1.2.4 Procedure for progressive sampling 
including skeleton information The zero 
samplingrun covers all points of the initial 
coarse grid (Makarovic, 1977), after each sampling 
run analysis is performed of the heights for each 
triplet of points in the X and Y directions of the 
DTM grid. 
Inside a triplet J-P,J,J+P (or I-P,I,I+P) a search 
is made in each of the four half intervals for the 
presence of the s points (Z-set mapped in the DTM 
grid); figure 2, from the midpoints towards the 
grid points J-P, J, J+P (P represent variable grid 
interval). 
1.2.5 Rules for composite sampling. These rules 
pertain to each triplet of points in the X and Y 
directions of the DTM grid. 
  
  
  
  
search ?|half interval|e 
directions 
| Ns1 € > \s2 \s3 e|» \s4 | 
fo] FF 
| \ midpoint \ | \ midpoint \ | 
J-P J J+P 
jor P — | 
Fig. 2 Triplet of grid points with break points s 
Based on the tests with the help of artificial 
ideal geometric primitives and their Composite, a 
set of rules was extracted for optimum sampling, 
(Charif, M., 1991). 
Despite the fact that the conclusions drawn from 
these tests are not generally representative, it 
is apparent that break lines, auxiliary lines and 
peripheral lines should be sampled to the extent 
mentioned in the rule base. 
Distinct discrete points (peaks,pits,etc.) should 
be connected vith the nearest lines rather than 
left isolated. The pseudo lines slightly improve 
CS, but generally do not replace the auxiliary 
lines. 
To verify and consolidate the conclusions drawn 
from the experiments using artificial ideal 
geometric primitives and their composite, some 
experiments using real terrain relief are 
required. 
Sampling real terrain relief feature, calls on the 
classification of terrain relief. 
2. TERRAIN RELIEF ANALYSIS AND CLASSIFICATION 
Terrain relief classification may | serve for 
further studies in various earth sciences, 
agriculture, civil engineering, military 
activities, urban and rural surveying, residential 
and recreational planning and others. 
In the context of optimum sampling for digital 
relief modelling, the purpose of classification is 
to provide some initial information on the terrain 
relief for specifying the sampling process. Thus, 
formulation of a suitable model for a quantitative 
terrain relief classification is necessary. 
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