International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
BAYESIAN METHODS: 
APPLICATIONS IN INFORMATION AGGREGATION AND IMAGE DATA MINING 
Mihai Datcu 1 and Klaus Seidel 2 
German Aerospace Center (DLR), German Remote Sensing Data Center (DFD) 
D-82234 Oberpfaffenhofen, email: Mihai.Datcu@dlr.de 
2 Image Science Division, Communication Technology Laboratory, ETHZ 
CH-8092 Zürich, email: Klaus.Seidel@vision.ee.ethz.ch 
KEYWORDS: Remote Sensing, Data Fusion, Information Mining, Bayesian Methods. 
ABSTRACT 
More accurate interpretation of remotely sensed data is based on a concept combining synergistically signals, information or knowledge 
from different sources. The aim is information mining, extraction and presentation. A hierarchical structure of data fusion levels has 
been identified: on image signal level, on image features, on physical parameters extracted from images, on meta features resulting from 
image feature modelling, on feature grouping. The Bayesian perspective is discussed aiming at a variety of aspects. The power of the 
Bayesian approach is endowed i. e. with the possibility to analyse uniformly the uncertainties over scene parameters in data acquired 
from heterogeneous and incommensurable sources. 
1. PRELIMINARIES 
The Earth coverage has high complexity, thus making difficult 
their recognition and characterization using observations 
provided by a single sensor. More accurate interpretation of 
remotely sensed scenes is obtained by synergistically combining 
signals, information or knowledge from different sources. 
The data fusion at signal level shows limited success for the 
automatic interpretation of remote sensing data. The reason is the 
incommensurability of the information in its raw format, the 
image samples. However, it shows promising results as a 
visualization technique, e.g. the presentation of a scene in a 
computer graphics environment, using synthetic aperture radar, 
interferometrically derived terrain models and surface texture 
derived from optical images. Dealing with heterogeneous 
sources of information is of key importance for the design of 
appropriate information representation and its levels of 
abstraction. Thus, data fusion is replaced by information fusion. 
Methods showing promising results are based on the knowledge 
of the physical model of the candidate scene. In situations of poor 
knowledge of the scene and image formation models, fuzzy 
methods and evidential reasoning or other vague information 
representations have been successfully applied. 
In situations when the models are known, the Bayesian inference 
allows a precise description of the problem, and thus, accurate 
scene information retrieval. The power of the Bayesian approach 
consists in the possibility to represent uniformly the incertitude 
over a certain scene parameter in data acquired from 
heterogeneous and incommensurable sources. The incertitude 
has the form of the posterior distribution of the desired scene 
parameter, given the observations from several sources. The 
posterior distribution is inferred from the likelihood of each data 
source and the a priori model of the parameter. The likelihood 
distribution takes into consideration the forward model of the 
specific sensor and its noise. The a priori information models 
describe the behaviour of the desired parameter under the 
observation conditions, which are specific for each sensor type. 
As an example, the accuracy of the classification of the landcover 
from synthetic aperture radar can be improved using information 
from optical images. The posterior distribution of the landcover 
parameters is expressed as being conditioned by both the 
synthetic aperture radar and optical data. 
One of the difficulties in many data fusion applications for 
remote sensing image classification is the identification of the 
datasets relevant for the user. Here, the information retrieval task 
becomes an information mining task. The Bayesian inference can 
be applied again, but the goal is to find the set of images, 
generally acquired from different sensors, which might contain 
the information desired by the user. Thus, the inference is used to 
find the posterior distribution over the set of available images 
according to the user hypothesis in a given application. 
2. THE BAYESIAN INFERENCE AND HIERARCHIC 
DATA MODELLING 
The Bayesian approach consists of interpreting probabilities 
based on a system of axioms describing the incomplete 
information, rather than randomness. Hence, Bayesian 
approaches are very well suited for the extraction of information 
out of observed data. Using Bayesian techniques, one can extract 
the most probable scene parameters explaining the observed data 
under the assumption of some prior knowledge. The prior 
knowledge is expressed in form of stochastic models. The 
Bayesian methods allow also to choose the most plausible model 
from a given class. Two levels of inference are introduced 
(MacKay, 1991): 
Model fitting. The first level of inference assumes that the used 
models are true. The task is to fit the assumed model to the data 
D, estimating the most plausible model parameter values 0 and