Information Fusion in Signal and Image Processing: Major Probabilistic and Non-Probabilistic Numerical Approaches

Chapter 9

Spatial Information in Fusion Methods

Spatial information is fundamental in image processing. Including it in fusion methods is crucial and often requires specific developments to adapt the methods used in other fields. One of the most common objectives of these developments it to ensure that the decision is spatially consistent. For example, in multi-source classification, the goal will be to avoid those points which are isolated or scattered in a homogenous class to be assigned to a different class.

9.1. Modeling

Spatial information on the modeling level is generally implicit depending on what level of representation is chosen. If we are reasoning on a pixel level, the information contained in a pixel does not include any spatial information, so this information will have to be added explicitly. The spatial context that is considered is most often the local neighborhood of each point. A simple way of taking it into account is to define the measure (x) (see Chapter 1) based on the characteristics of x and of its neighbors also. If we denote by V(x) the neighborhood of x (containing x), we will define (x) as a function of the type:

where f_j(y) refers to the characteristics ...