Data vs. Decision Fusion in the Category Theory Framework

In this paper we first formally define the notions of data fusion and decision fusion. Then we formulate a theorem that decision fusion is a special case of data fusion. We show the meaning of this theorem on a simple example of edge detection. Edge detection can be done in two ways: by first fusing the original images and then detecting edges in the fused image (data fusion) or by first detecting edges in each image separately and then fusing the results (decision fusion) of edge detection in the decision fusion block. We show, first in general and then on the edge detection example, that decision fusion can be viewed as a special case of data fusion. To the designer of an information fusion system this means that the choice of the decision fusion approach over data fusion in any specific case needs to be supported by some additional consideration, for instance the computational complexity of the fusion algorithm.