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SPATIAL DISTRIBUTION OF CONTROL POINTS 
Ricardo Vergara 
Alejandro C. Frery 
Julio d'Alge 
INPE - DPI 
Av. dos Astronautas, 1758 
12201 - Sao Jose dos Campos, SP, BRAZIL 
ISPRS - COMISSION III 
ABSTRACT: 
We present some Monte Carlo results about the 
spatial distribution of the 
Control Points used in the 
geocodification of satellite images in Brazilian Amazonas. 
This information aims at stablishing criteria for the choice of number, quality and spatial distribution of 
Control Points (CPs) to be used in image matching techiques. 
Some theory about the statistical analysis 
of spatial point patterns is recalled, as an aid to a future 
formulation of this problem in terms of an experiments design problem. 
KEY WORDS: Accuracy, Algorithm, Image Matching, Image Processing, Registration, Simulation, Theory. 
1. INTRODUCTION 
The geometric accuracy of remote sensing satellite 
images plays a central role in most applications 
(as in Cartography, to name one), so these images 
are geometrically corrected before being used. 
Moreover, when digital images are used, their 
geometric accuracy is improved by the registration 
with respect to a map. 
In this image processing techique, clearly 
identifiable points (the "Control Points", or CPs) 
are sought in both the image and the map. Taking 
the second as a reference, and using the CPs, it is 
possible to estimate the -mathematical- mapping 
that corrects the digital image. Usually, a 
polinomial transformation is used, and the degree 
of the polinomial determines the minimum number of 
CPs needed to estimate its coefficients 
(Mascarenhas & Velasco, 1989). 
The registration accuracy between an image and a 
map depends on the location accuracy and on the 
number and the spatial distribution of the CPs used 
to perform it (Ford & Zanelli, 1985). The same 
happens with the attainable precision in the 
evaluation of the geometric accuracy of an image. 
Suppose that is possible to have CPs with 
arbitrarily high location accuracy, either to 
evaluate the geometric precision of an image or to 
accomplish the registration between an image and a 
map. Precision will be highly dependent on the 
number and spatial distribution of the CPs. 
Concerning to the number, it is possible to say 
that the higher the quantity of CPs, the higher the 
achieved precision (Ford & Zanelli, 1985... Orti, 
1981). 
Relating to the spatial distribution, a 
specification of the adopted criterion has not been 
detailed reported in the literature, but in general 
is considered that a uniform distribution of - 
evenly spaced- CPs is the most appropriate choice 
(Ford & Zanelli, 1985). However, it usually is 
difficult to find CPs distributed in this way; 
sometimes the CPs are grouped in a small part of 
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the area under study or a very small number of 
dependable CPs is available. Obviously, all CPs 
must be used when the last situation occurs; in 
this case it is not possible to make a choice among 
them. 
the case of having plenty of CPs of 
good location accuracy. In this situation the 
following question appears: Which should be 
selected in order to obtain a spatial distribution 
that makes possible the achievement of an accurate 
geometric correction? Or, if the registration has 
already been made with no good accuracy: How to 
know if that is due to a inadequate spatial 
distribution of the CPs used to perform it? And 
when this is the reason: Is there some manner to 
detect those CPs whose locations damage the quality 
of the geometric transformation? Note that the same 
questions are valid when the evaluation of the 
geometric quality of an image has to be assessed. 
But suppose 
The aim of this paper is proposing some partial 
answers to these questions, providing a tool for 
either doing an adequate selection -concerning to 
the spatial distribution- of CPs to be used for 
performing an image-map registration or for 
evaluating the geometric accuracy of an image. This 
procedure allows the identification of CPs whose 
locations damage the quality of the spatial 
distribution of the set of points; so, their 
substitution for other CPs located in more 
appropriate places is made possible. The proposed 
metodology consists in selecting CPs whose plane 
coordinates are known with precision, and then in 
submitting these points to one or more spatial 
distribution tests, For the evaluation of this 
procedure, different registered images of brazilian 
legal Amazonas were taken and their respective sets 
of CPs were submitted to the tests above, The 
amazonian region was chosen for this study because 
it has special caracteristics that make hard the 
finding of CPs spatially well distributed. To 
compare results, the same kind of analysis was 
carried out using a registered image of the 
Buritama region, Sao Paulo State, where the 
relative abundance of CPs allowed the selection of 
those whose spatial distribution is nearer to the 
optimal model.