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