Association

Associating two representations requires that they refer to the same object. The union of the representations is called association or concatenation. Association is made by an increase of the size of the state vector of the object.

Let be two sources of information S(1) and S(2). Each provides a representation, (X_S(1))^t and (X_S(2))^t at instant t. Let S be the union set of sources. Assume information is aligned for this set S. Associating the two representations (X_S(1))^t and (X_S(2))^t requires that they refer to the same object. There is no benefit of trying to fuse measurements, attributes, rules or representations that do not refer to the same phenomenon or entity.

The union of the representations is called association or concatenation. Association is made by an increase of the size of the state vector of the object. Association is independent of the semantic level of the information. Association is performed by an analysis of the degree of correlation / relation between the information to be fused and the entity under concern. Some examples can be easily found, where sources are not exactly referring to the same object. In that case, though the sources are aligned, the representations cannot be associated. It can be a matter of period of observation for example. If one is observing a moving target within a limited period, any information well before and well after is poorly correlated to the dynamics of the target. On the contrary, quasi-simultaneous observations of different or same parts of the same human spine by X-rays scanner and nuclear-magnetic resonance imaging system refer to the same object. Once aligned for units (or gray level dynamics) and geometric superimposability, these observations can be fused for, e.g., a 3-D reconstruction of the spine, possibly given some additional knowledge.

Data concatenation is accomplished by juxtaposing all the data into the state vector, hence augmenting it. A straightforward example is given by a time-series of images from the meteorological geostationnary satellites, which are taking a picture of the Earth every half-hour or less. The raw data are processed by the meteorological offices, 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. Because the data provider has performed the alignment of data, the customer deals in this case with concatenation and subsequent analysis.

In some cases, the problem can be the selection of sub-sets of sensors, which are the most relevant for a given problem. A metric should then be defined for the comparison between sensors, and the choice of the most appropriate ones.

26-08-2001 - Copyright L. Wald, Armines / Ecole des Mines de Paris