International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999
to information are defined in the following. These definitions
are those used in information science and have been found in
several publications (Bijaoui, 1981, Kanal and Rosenfeld,
1981, Lillesand and Kiefer, 1994, Tou and Gonzalez, 1974).
Measurements are primarily the output of a sensor. They are
also called signal, or image in the 2-D case. The elementary
support of the measurement is a pixel in the case of an image,
and is called a sample in the general case. By extension,
measurement denotes the raw information. For example, a
verbal report is a piece of raw information, and may be
considered as a signal. In remote sensing, in the visible range,
the measurements are digital numbers that can be converted
into radiances once the calibration operations are performed. If
corrections for the sun angle are applied, one may get
reflectances that are still considered as signal.
An object is defined by its properties, e.g., its color, its
materials, its shape, its neighborhood, etc. It can be a field, a
building, the edge of a road, a cloud, an oceanic eddy, etc. For
example, if a classification has been performed onto a
multispectral image, the pixels belonging to the same class can
be spatially aggregated. This results into a map of objects
having a spatial extension of several pixels. By extension, the
support of a signal (e.g., a pixel) may be considered as an
object.
An attribute is a property of an object. Feature is equivalent to
attribute. For example, the classification of a multispectral
image allocates a class to each pixel; this class is an attribute of
the pixel. The equivalent terms label, category or taxon are also
used in classification. Another well-known example is the
spatial context of a pixel, computed by local variance, or
structure function or any spatial operator. This operation can be
extended to time context in the case of time-series of
measurements. Equivalent terms are local variability, local
fluctuations, spatial or time texture, or pattern. By extension,
any information extracted from an image (or mono-dimensional
signal) is an attribute for the pixel or the object. The
aggregation of measurements made for each of the elements of
the object (for example, the pixels or samples constituting the
object), such as the mean value, is an attribute. Some authors
call such attributes, derived from statistical operations on
measurements, mathematical attributes.
The properties of an object constitute the state vector of this
object. This state vector describes the object, preferably in an
unique way. The state vector is also called feature vector, or
attribute vector. The common property of the elements of the
state vector is that they all describe the same object. If the
object is a pixel (or a sample), the state vector may contain the
measurements as well as the attributes extracted from the
processing of the measurements.
Rules, like the syntax rules in language, define relationships
between objects and their state vectors, and also between
attributes of a same state vector. Rules may be state equations,
or mathematical operations, or methods (that is a suite of
operations, i.e. of elementary rules). They may be expressed in
elaborated language. Known examples of such rules are those
used in artificial intelligence and expert-systems. Decisions
result from the application of rules on a set of rules, objects and
state vectors.
4. THE PROPERTY OF ALIGNMENT
Several problems are to be solved prior to any process of fusion
(see e.g., Castagnas 1995, Pau 1988). The information entering
a fusion process should present several properties. They deal
with either the selection of the representation space and the
level of fusion, or with the processing to be applied onto the
data.
A common co-ordinate system (e.g., geographical space and
time) should be found in which the sources data can be
represented. This is called alignment, or conditioning, or
positional data fusion. For example, geocoding the images is
part of the alignment problem. Then, the images can be
superimposed and mathematical operations can be performed at
each pixel.
The alignment problem is difficult and according to some
authors (see e.g., Thomopoulos 1991; DSTO 1994), it
differentiates data fusion from data concatenation. Data
concatenation is accomplished easily and straightforward by
juxtaposing all the data into the state vector, hence augmenting
it. These data should be homogeneous. An example is given by
a time-series of images from the geostationary satellite
Meteosat. The raw data are processed by Eumetsat, and are
spatially superimposable once delivered to the customer. In that
case, at each pixel, one can define a state vector by the
concatenation of all the observations made at this pixel in the
period under concern.
Data fusion requires conversion of the data into a common co
ordinate frame before concatenation. Alignment should provide
a general frame of referencing that can apply to homogeneous
(commensurate) as well as heterogeneous (non-commensurate)
data. This is a difficult problem, and there is no general theory.
Even in the simple case of measurements of radiances, which
are commensurate, it may still be not straightforward. Though
having the same space reference, two sources may not refer to
the same object (landscape). In the Meteosat case, the water
vapour channel does not provide any information on the
ground, while the visible and infrared channels do so. Another
example from oceanography is the fusion of observations of sea
surface temperature, which are relevant to the very surface of
the ocean, and of ocean colour, which are depth-integrated.
Data to be fused need to be relevant to the objectives of fusion
process. Then, these data can be associated or concatenated into
the state vector of the studied object (landscape).
This concept of alignment is extended to a wider reference
space (representation space) which also includes
standardisation of units, calibration of sensors and atmospheric
