PROGRESSIVE SAMPLING - FIDELITY AND ACCURACY 
K. Tempfli 
International Institute for Aerospace Survey and Earth Sciences (ITC) 
Enschede, The Netherlands 
ABSTRACT 
Progressive sampling of terrain relief results in an incomplete grid 
DEM. The grid density is locally adapted to the terrain variability. 
Progressive densification of the sampling grid is controlled by an on- 
line analysis of the already measured elevation values using as 
criterion a threshold for the second differences. Grid spacing, 
threshold, and number of densification runs determine the achievable 
fidelity of the terrain representation. The concept of transfer function 
is utilized to quantify fidelity. Accuracy of the DEM is estimated from 
transfer function and power spectrum of the terrain relief. 
1. EXORDIUM 
The comparative test /13/ of photogrammetrically sampled digital eleva- 
tion models (DEMs), which was conducted by ISPRS Working Group III/3 
(1980-84), has shown that accuracy prediction and accuracy assessment of 
a DEM still constitute a problem for many DEM producers. Resolution 3 of 
Commission III, which was approved by the congress in Rio de Janeiro 
recommends pursuing the endeavour in developing methods for accuracy 
assessment. In /11/, an approach was elaborated for regular grid DEMs, 
thus equispaced sampling (ES), which is based on the transfer function 
of the system of sampling and subsequent interpolation and spectral 
analysis of its input, i.e., terrain and additive measuring error. The 
empirical evaluation of the method--using artificial, computer-generated 
surface and profile data--was encouraging. 
Progressive sampling (PS) /5/ aims photogrammetrically collecting 
precise and comprehensive terrain relief data. In order to make sampling 
time-efficient and to obtain data in a favourable structure, elevation 
is measured in a grid of variable density, locally adapted to the fluc- 
tuations of terrain relief. Collecting data by progressively increasing 
the sampling density requires on-line data analysis and synthesis, which 
can be realized on a computer-supported analogue instrument /3/ or an 
analytical plotter /1/, /8/ and /12/. The irregular sampling pattern and 
its dependency on terrain geometry make analytical accuracy estimation 
more complex than for ES. After reviewing the approach to accuracy as- 
sessment for ES, a tentative extension of this concept to PS will be 
presented. 
2. EQUISPACED SAMPLING 
A digital model of a (topographic) surface is attained by sampling the 
surface and reconstructing it from the sample by interpolation. The 
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