achieved in context with the used sensors which define
the possible transformations when being observed. Thus
invariants have to be identified, e.g. with respect to form,
to topology, or other relations. Objects usually are as
sumed to be bounded by surfaces which are smooth
nearly everywhere and which are linked by boundary
lines which also are assumed to be smooth almost every
where [23], Many objects, as roads, fields, rivers, houses
fall into that category. At special scales trees, river deltas
or towns however are not bounded by smooth curves or
surfaces, but show a fractal behaviour which then has to
be transferred to the image model and taken into account
when analyzing the images.
The above mentioned hierarchies play an essential role,
as they are designed such that they are generic, i.e. in
variant to viewpoint, sensor type etc. Different sensor
types, especially having different spectral bands, observe
different aspects of the same object. This on one hand
does not necessarily influence the specialization hierar
chy, but more likely the containment hierarchy. On the
other hand in nearly all practical cases a physical, i.e.
theoretical link between the responses of the different
sensors can not be established, forcing the conceptual
modelling to be phenomenological. Most problems oc
curring when fusing information of different sources
therefore result from a lack of common invariants of the
same object, mainly caused by the different classification
schemes, i.e. specialization hierarchies within the dif
ferent fields of application (see also the discussion in
section about ,,meta-information and fusing objects mo
dels", p. 380).
It is an open problem which representation is best suit
able. This is because on one hand the semantic relations
must be describable, the image descriptions must be
derivable using the sensor model, but also the recon
struction of the form and the derivation of the relations
must be realizable within the chosen representation.
Multiple representation schemes seem to be unavoidable
(e.g. raster and vector representations) but make a theo
retical analysis at least cumbersome. Of course different
object models may require different representations. The
problem of linking different and possibly scarcely over
lapping object models is the central problem also when
linking heterogeneous data bases.
The object model also has to include the background, i.e.
those parts of the scene which are not of primary interest
(e.g. trees, when extracting highways). Object models for
image analysis therefore have a much higher granularity
than object models in GISs usually have [5] and also the
footnote2).
Sensor models
Sensor models in our context solely contain geometric
physical components4). Modelling the sensing process
only requires a sufficiently dense geometrical/physical
object description including all details namely form
and reflectance properties, illumination sources, sensor
models etc. Though the descriptions will be symbolic
because of the symbolic nature of the physical laws the
process itself is sub-symbolic.
4) In environmental monitoring of course chemical and biological
sensors play a distinctive role.
Many problems in image analysis are caused by the dis
cretization process. This in a first place refers to the
raster structure of smooth boundaries which however in
case of a suitable anti-aliasing may not influence the
geometric recovery too much.
The main problem is the object-independent aggregation
of the spectral information within one pixel (mixed-pixels).
The pixel size usually is given. For satellite images its
range is between a few meters (KWA 1000) and about
2 km (NOAA). The often spatially varying integration
(blurring) effect of the point spread function needs to be
known and explicitly modeled when performing feature
extraction, as the measured intensities are the original
observations for the whole interpretation process. Be
cause of the aggregation being object-independent fea
ture extraction without explicit reference to the geometric
and physical components of the object model seems to
be sub-optimal from the beginning. An approach trying to
link sensor and object model for feature extraction is
discussed in [23 and 54].
Image models
The image model forms the link between object model
and interpretation model. It can be seen to be an appea
rance model [23, 50, 70 and 72]. The image model has to
be derived from the object and the sensor model.
The above mentioned invariants (geometric, radiometric,
texture parameters, topological) play a central role within
the image model. As many objects are bounded by
smooth surfaces or lines, the most commonly used image
model consists of a segmentation of the image into non-
overlapping partitions (see the collection in [77]). They
show regular boundaries which themselves have to be
modeled. The weakness of this image model reveals
when the smoothness of the object surface and of the
illumination interfere at abrupt albedo changes, causing
the appearance of object edges, i.e. image edges to be
broken, making a higher-level inference necessary for an
appropriate interpretation in these cases.
The image model on one hand guides the feature extrac
tion process thus should be of enough granularity, espe
cially concerning the radiometric structures (shadows,
shading, texture, specularities etc.). The hierarchical
object structures usually are inherited by the image
structures allowing to envoke grouping processes. On the
other hand the image model requires a mapping onto a
perceptual database [50], allowing an efficient access to
image features of the usually numerous images.
Analysis models
The analysis model relies on the image model and stra
tegic knowledge in order to arrive at an interpretation.
Central point is the labelling of the image features which
heavily depends on the semantic part of the object model,
especially on the spatial relationships, the different
materials and their appearance and of course the specia
lization and containment hierarchies set up in the object
model.
The analysis may also require the use of sub-symbolic
methods for describing shape from stereo [18, 37, 93],
from shading [39] and from texture [8, 12, 45, 52, 55, 57,
64, and 88], These methods often only work under special
conditions (existence of texture, homogeneous reflec
tance) which even may contradict, requiring a link with
symbolic methods for detecting structures of irregularity,
thus interacting with the process of feature extraction.
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