International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
the approximation and the detail, and introduces a pyramidal data 
representation similar to a quadtree. The accurate modelling of 
wavelet coefficients requires the representation of both intra 
scale and interscale dependencies. The intra-scale model 
captures the local structural behaviour of the image. The 
information within a neighbourhood in the original image is 
distributed in each “quad” (brothers) and at the corresponding 
coordinates of the different orientations in the detail space. The 
interscale relationships are modelled as Markov chains. A more 
general formalism is the multiscale stochastic modelling. In the 
graph below a random field is defined having as support a tree 
structure. 
The interscale causalities are described by transition probability 
density functions P(*l*). X is the predicted value at scale k-1 and 
w an interscale error process. 
These models allow synthesis of finer scales X k of a random field 
beginning with its coarser scales X k 'V The stochastic process 
represents the new information, in a way similar to the detail 
signal in the wavelet transform domain. The models are inspired 
from the multigrid techniques in numerical analysis and define 
consistent Multiscale Markov Random Fields starting from a 
single resolution. They can model a variety of image 
configurations and are implicitly the basis for picture parameter 
estimation. The estimation principle consists of solving a 
sequence of global optimization problems defined on a sequence 
of embedded configuration subspaces accepting constraints in 
form of prior distributions (Baldwin et al., 1998; Bouman and 
Liu, 1991; Luettgen et al., 1993). 4 
4. THE BASIC CONCEPTS 
Due to the incommensurability of the images obtained from 
different sensors and due to the high complexity of the imaged 
scenes, data fusion systems demand high level representation of 
information. Thus, scene interpretation is done by augmentation 
of the data with meaning (Jumarie, 1991). Based on the Bayesian 
principles of inference and on data fission and fusion paradigms, 
we present in Fig. 4 the simplified architecture of a scene 
interpretation system using multiple data sources. 
The information source is assumed to be a collection of 
multidimensional signals, e.g. airborne or satellite images, 
acquired from optical or SAR sensors. Due to the 
incommensurability of the data provided by heterogeneous 
sources, the information fusion process is splitted up in two steps: 
i) information fission and ii) information aggregation. 
Information fission is an analysing step enabling to deal with 
heterogeneous sources of data, and also to cope with different 
and incommensurable types of information extracted from 
individual sources. The information source is partitioned in 
elementary sources. 
The information fission requires the signal modelling as a 
realization of a stochastic process. A library of stochastic and 
deterministic models is used to infer the signal model. The 
information extraction is a model fitting task. The information 
content of datasets acquired by individual sensors is extracted. 
The resulting objective features are aggregated according to the 
user conjecture. Thus, the information fusion process relies on 
restructuring (using a certain syntax) the signal feature space 
according to the user semantic models. At this step, the 
information from incommensurable sources is ordered and 
augmented with meaning, thus providing a scene interpretation 
(Jumarie, 1991; Lauritzen and Spiegelhalter, 1988). 
5. LEVELS OF ABSTRACTION OF INFORMATION 
REPRESENTATION 
In the case of modelling high complexity signals, e.g. collections 
of multi-sensor images, a large number of sources coexists within 
the same system. The solution of information and knowledge 
fusion as stated in Eq. 6 becomes a very difficult task. However, 
in many practical applications the candidate models are likely to 
be analysed hierarchically. Thus, it is desirable to integrate 
probabilistic models, i.e. they should store common parts for 
efficiency of the model representation, and they must be 
represented hierarchically in order to capture the class structure 
and to provide computational advantages. Starting from the 
remotely sensed images of a scene, a hierarchy of information is 
defined. 
• Image data: the information is contained in the pixel 
intensities of the raw data. It is the lowest level of 
information representation. However, there are useful 
applications, e.g. image classification based on image 
intensity. Data fusion at this level of representation is limited 
by the incommensurably of the measurements. Typical 
applications are fusion of multiresolution data of the same 
type of sensor. 
• Image features: the information is extracted in form of 
parameters characterising the interactions among spatially 
distributed pixels, or different spectral channels. 
Additionally to the parameter values, characterization of 
parameters incertitudes can be obtained. Popular examples 
of image features are: texture, multispectral features or 
geometrical descriptors. Data fusion at this level is possible 
in the case of parameters representing the same quantity. 
E.g. enhance geometric precision of an edge using 
information from multiple sensors. 
• Physical parameters: the image features reflect the physical 
parameters of the imaged scene. Thus, assuming the 
availability of certain models, the scene parameters can be 
extracted. For example, image texture carries information 
about the size of tree crowns, or the SAR backscatter of 
ocean surface contains the wind speed information. Data 
acquisition using different type of sensors can be fused to 
increase the estimation accuracy of physical parameters, or 
to complement missing observations. 
• Meta features: estimation of both image features, and 
physical parameters requires the assumption of some data 
models. The type of model used, its evidence and 
complexity, plays the role of meta information, i.e. 
describing the quality of the extracted parameters. From a 
data aggregation perspective, a meta feature is an indicator