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GEOPLANTRANSF: A SOFTWARE FOR THE GEOREFERENCING OF DIGITAL IMAGES 
BY USING PLANE TRASFORMATIONS 
Francesco Guerra*, Caterina Balletti**, Davide Miniutti*** 
*3 rd year Course of PHD 
**2 rd year Course of PHD 
***1”* year Course of PHD 
DIIAR Dipartimento di Ingegneria Idraulica, Ambientale e del Rilevamento 
Sezione Rilevamento - Politecnico di Milano 
P.zza Leonardo da Vinci 32 - 20133 Milano 
e-mail: guerra2@brezza.iuav.unive.it - balletti@brezza.iuav.unive.it - miniutti@cidoc.iuav.unive.it 
KEY WORD: GIS, georeferencing, digital images, plane transformation, free software 
Abstract 
In this paper the working principles and some applicative examples of the software realized by the authors for the georeferencing of 
digital images are presented. 
The program allows for the calculation of the parameters for transformations between two digital images or between an image and a 
cartographic system. The general form is used for the polynomial plane transformation for the crossing over from one system (o; x, 
y) to another system (0; X, Y) with the possibility, on the part of the user, to utilize a smaller number of parameters and realize a 
projective, affine, or conform transformation, among others. The estimation of the parameters is to the least squares and the 
program realizes the superimposition of the vectors of the residuals onto the image, for the immediate evaluation of the results of the 
transformation. On the basis of the estimated parameters (which are m any case saved in the file) it is possible to resample the image 
in the destination reference system according to three methods: nearest neighbor assignment, bilinear interpolation or bicubic splines. 
Some of the applications of this software package will be illustrated. The software is written in Borland Delphi 
language, and distributed in freeware way. 
Digital images and GIS 
The digital images are widely used within the GIS according to 
two different aspects: first, as cartography as a basis and 
second, as an organization for thematic data. 
In the first case it can deal with either scannings of existing 
cartography for which a vectorial form is not available or 
photographic quality' images which when correctly treated, can 
substitute for the base map. This is the case, in architecture, for 
example, with rectifications of the façades of buildings for 
which a vectorial restitution is not to be done. 
The second case is one in which the images are utilized to offer 
a description of phenomenona through which quantity or 
punctual or associated to unit areas, that is quantities organized 
in matrix form. The typology of these cases is extremely vast. 
It is likewise true that most of the time the two cases described 
coincide when, from these photographic maps, it is possible to 
obtain qualitative information. 
The use of the digital images is fundamental insofar as it allows 
an easy use of the data typical in spatial analysis. Premised in 
such operations is that the digital images are brought back to a 
known geometry, utilizing specific procedures of referencing 
and calibration. 
The software presented here resolves a small part of these 
problems, using a polynomial plane transformation whose 
number of parameters is chosen by the user. 
Introduction to the software 
The GeoPlanTransf program is the development of some 
software produced by the authors in the field of geometric data 
processing of digital images. In the course of the recent years 
infact software has been developed, the first for affine 
transformations of digital images, the second for the 
rectification in the close range photogrammetry field. 
The program for affine transformation was realized for the 
internal orientation of digital images as a module of the package 
for digital orthophotoprojection (Orthodigit). The algorithms 
utilized in this software implement the traditional equations: 
X = a ] + b l x + c l y 
Y = a 2 + b 2 x + c 2 y 
The RDF program on the other hand was bom to meet didactic 
needs, provide for the large request for photogrammetric 
surveys for rectification on the part of professors and students 
involved in restoration courses. The software, distributed in free 
form, has diminished the pressure placed on the research centers 
of the university while at the same time allowing the students an 
approach to the survey not only as users but also as maker. The 
equations used are those of the projective transformation in the 
form commonly used in photogrammetry and which derives 
from the semplification of the collinear equations in the case of 
the Z constant. 
Y _ <3 i x + a 2 y+a 3 
c t x+c 2 y+1 2 
Y _ b x x + b 2 y + b- 
c^x + c 2 y+1 
The software presented here was bom from the experience of 
the two aforementioned software and it unites them and 
strenghthens their characteristics according to the referencing 
and the calibration of the digital images within the GIS. This is 
bom from within the research work done by the authors for their 
PHD course work. 
The destination of the GPT software is logically teaching and 
research given on the one hand the environment in which it was 
bom and on the other its form of circulation. Beyond the fact 
itself that, as in its predecessors, it allows for the rectification of 
images, and renders this rectification immediately utilizable for 
the teaching of the survey