ieres
et
SPOT,
erture
ur des
loedel
é dans
ection
ée par
velles
hnique
mises
).. La
loedel
amment
érants
ndant,
evrait
taires
Les
raient
ur des
SPOT,
ce aux
ire du
ection
MATHEMATICAL PROBLEMS OF REAL-TIME MAPPING
AND DATA BASE MODELLING
Erhard Pross
Institute of Applied Geodesy
Leipzig, Germany
Commission II, Working Group 1
Abstract
In real-time processing the time is the main processing direction controlled by discrete operators. Functional
analytical methods integrating discrete and continuous description and methods lead to constructive tools in
data base modelling and real-time mapping. The realization of image operators as difference operators depends
on the the fast convergence and on the techniques' stability and algorithmic ideas of switching between spatial
and time iterations and processing directions.
KEYWORDS: database modelling, theory, scene analysis, optical flow
1 Introduction
With the triumphal progress in computer techniques
in several fields also a digital photogrammetry and
real-time mapping was formed. Numerous ideas and
principles in physics, electronic engineering, and new
disciplines like robot and machine vision influence the
digital photogrammetry in a very great amount. So
we must recognize not only an integration of geodesy,
photogrammetry, and cartography in geoinformatics
but also new concepts and models based on modern
mathematics. The separate developments in mod-
elling must be integrated in one model (see [1]). The
integration of different sensor types in one real-time
mapping model from the data capture to the the stor-
age and the post-processing of the data is investigated
in [4].
The idea of this paper is to view modelling in real-
time mapping from an abstract mathematical point
of view and give some directions to the algorithmic
realization of techniques.
2 Mathematical Background of
Data Base Modelling
2.1 Abstract Space Definition
For the definition of an abstract mathematical space
corresponding to tasks in geoscience it is necessary to
define measurements of nature signals as elements of
such a space and technological processes and technical
course as corresponding transformations between suit-
able spaces. Spaces are characterized by the contents
(images, features, ...), by the discreteness (analog,
digital) or by the structure (vector, raster).
The art of abstract mathematical modelling leads to
such models, the concrete realization of which leads
to special views on projections into and integrations
within function spaces. The functional analysis is a
mathematical building with powerful tools to realize
such a modelling. In geoinformatics we know image
spaces — including images, image sequences, raster
maps, ...— and feature spaces (see [3], [10]).
A mathematical model demonstrating a functional
analytical description in geoscience especially remote
sensing, photogrammetry, and cartography in one cal-
culus was developed (see [7], [8]).
From the semantic level point of view image spaces
have a low level and the feature space a middle or
high level.
Coordinates are the spatial z-, y- and z-coordinate
— in topography especially in smallscale topography
the third coordinate (height) plays an important role
by 2.5—, 2+1- or 3-D-GIS-modelling —, the features
or attributes m and last but not least the time t.
The significance of the time leads to qualitative differ-
ent models in regard of time
e low influence — time as date or up-dating num-
ber
e common coordinate
e dominant processing parameter for instance in
real-time mapping
These several levels differ with different methods and
techniques. For that reason the common methods in
photogrammetry, remote sensing, and GIS — corre-
sponding to the first and second level — cannot be
transferred to real-time mapping processing.
À functional is a transformation of an abstract space
455
