204.

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7.3.5 Assumption of intersource independence

The assumption of intersource independence means that the joint probability distributions for the measurements of sources are mutually independent, and the final joint probability function can be expressed as the product of each class-conditional probability function. Although this might not be always the case, the validity of the assumption is hard to determine.

In practical situations, multiple data sources usually contain complex, but unknown, interactions. For example, in the case of multisource classification, the data set may consist of optical and radar images and a digital terrain model. If there is no reliable information concerning the relationship between surface spectral reflectance (or backscattering) and terrain parameters (such as ground slope, surface shape, etc.) then lack of knowledge of these interactions will force us to ignore any intersource relationships and, therefore, to treat these data sources as independent variables. However, rather than being a shortcoming in the data consensus analysis, the intersource independence assumption does provide a relatively easy way to perform classification using multiple data sources.

7.4 Evidential reasoning

The mathematical theory of evidence is a field in which a number of data sources can be combined to generate a joint inference concerning pixel labelling. The theory was first developed by Dempster in the 1960s and later extended by Shafer (1979), who provided details of the development of evidential theory, which has therefore become known as the Dempster-Shafer (D-S) theory of evidence. Garvey et al. (1981) discuss applications using the D-S theory of aggregating evidential knowledge. Barnett (1981) mentions some of the computational issues involved in order to reduce the computational requirements of the method. Gordon and Shortliffe (1985) and Shafer and Logan (1987) propose modified approaches that are mainly based on a hierarchical evidence space. The D-S theory has also been related to the field of artificial intelligence systems (Gouvernet et al., 1980; Friedman, 1994; Strat, 1984) with promising results.

The evidential reasoning approach also provides a valuable theoretical basis for dealing with the remotely sensed multisource classification problem. The approach has been tested in several studies (e.g. Lee et al., 1987; Srinivasan and Richards, 1990; Wilkinson and Mégier, 1990; Peddle and Franklin, 1992; Kim and Swain, 1995). The main issues relating to the evidential reasoning method are the need to generate the so-called mass of evidence and to measure the uncertainty (which determines the weight) of each data source. The basic concepts of D-S theory are described next.

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