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
