INVARIANT REPRESENTATIONS FOR PUNCTUAL AND LOCAL GROUPING
CRITERIA IN GEOGRAPHIC INFORMATION SYSTEMS
Isidro de Paz, Javier Finat and Margarita Gonzalo-Tasis
Address of the contact author: Isidro de Paz, ESA-HQ, 8-10, rue Mario Nikis,
75738 Paris Cedex 15, France (Isidro.De.Paz@esa.int)
Javier Finat and Margarita Gonzalo-Tasis, Edificio de Tecnologias de la Información y las Comunicaciones, Universidad de
Valladolid, 47011 Valladolid, Spain
Keywords: Vision Sciences, GIS, Geometry, Visualization, Motion
Abstract
Layered representations are commonly used in cartographic maps. Punctual, local and global grouping criteria are modelled in terms
of histograms, mathematical morphological operators and overimposed grouping structures. The transfer between the above levels
allows identifying, tracking and maintaining the layered information. This paper proposes a feedback between punctual and local
analysis levels to allow the identification of regions in an intrinsic way. The intrinsic character concerns to the minimization of
changes in relative position-orientation of the camera and the variation of environmental conditions involving the signal response. To
accomplish this program, we simplify the information relative to pairs of successive images. Next, we evaluate the correlation
between local modifications involving to superimposed polygonal regions onto the image and punctual transformations acting onto
histograms corresponding to such regions. The correlation between perspective views is induced by vector fields arising from
projected camera motions. In this way, we intend to make easier the identification and tracking of particular regions under uncertain
or incomplete information. Our approach can also be applied to any other quasi-static planar image analysis, and to obtain a coarse
estimation of changes at the position-orientation for inertial navigation systems based on global absolute coordinates of the Earth.
1. Introduction
Most of data contained in views can be understood in terms of
hierarchised geometric or topological interpretations with their
corresponding constraints. Such constraints are expressed
following a logical (evaluation of predicates), algebraic
(incidence, adjacent or orientation criteria), or probabilistic
(Bayesian, e.g.) formulation. The identification and grouping of
basic primitives allow the transference between local and global
levels, and consequently the automatic generation of knowledge
to interpret aerial or satellite views. Unfortunately, there is a
dichotomy between the high-levels image interpretation and
knowledge generation, low-level linked to the identification of
geometric primitives, and punctual or pixel level depending on
the resolution scale.
Punctual analysis is linked to the metric interpretation
depending on the aerial image resolution (1-3 m/pixel for high
resolution or more than 5m/pixel for coarser remote sensing
images). Morphological operators are commonly used to
homogenise regions by superimposing averaged values
following linear (erosion/dilatation or a composition
corresponding to opening/closing of such linear filters) or non-
linear filters (median or faster voting schemes acting by
sampling colours). Unfortunately, the resulting image quality is
worse than before applying these global filters.
Local analysis is linked to the contours extraction or the
overimposition of additional structures which can be planar
(Voronoi diagrams, Delaunay triangulations, Triangular
Irregular Networks) or three-dimensional ones (Digital
Elevation Maps). Relations between 2D and 3D information
require a stereo analysis, which is understood in a sequential
way in GIS. Global constraints involving all the images can be
applied to identify homologue elements by using general
constraints of Epipolar Geometry ([Har00]) in searching
homologue elements belonging to different perspective views.
A comparatively minor effort has been addressed to find
correlation patterns between punctual and local criteria, or in
other words, between the analysis to the pixel level and the local
analysis focused towards the identification of basic primitives.
The identification of such correlation patterns requires the
establishment of the different grouping levels, as well as to
show a feedback between optimisation procedures linking
punctual and local levels.
The inference of local information about the shape from the
grey level is robust w.r.t. small perturbations, but it presents a
low capability of discrimination w.r.t. another richer analysis
based on the colour ([Russ99], [Vil02]). Here we have
developed some tools oriented towards an invariant
representation involving the punctual and local image analysis.
In the framework of image analysis, regional invariance is
associated to an absolute estimation of homogeneous regions
under certain threshold which we shall suppose already known.
To avoid the dependence w.r.t. to atmospheric conditions or the
relative orientation of cameras, we shall take always a
segmented orthographic projection. The knowledge of the
absolute position allows us to apply rectification methods
([Har00]) to transform a skew view in an orthographic
projection. Furthermore, the existence of an orthographic view
provides a reference model to patch together a sequence of
views, to obtain a panoramic view (static case) or to estimate of
linear-angular velocity of mobile camera.
In the local case, the independence w.rt. the relative
localization (position-orientation) of the camera suggests the
choice of the affine framework. The affine structure can be
computed using only linear methods based on eigenvalues
([Har00]).Furthermore, the affine framework is compatible with
apparent deformations arising from skew views which are
interpreted as abrupt changes of orientation. Regional
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