On comparing hard and soft fusion of dependent detectors

A detection problem, where we have a set of two types of different measurements or modalities of one event, is considered. The optimal fusion rule to combine both modalities in one detector needs the knowledge of the joint statistics of modalities. In many cases we do not know these joint statistics and it is usual to consider independence between modalities for implementing a suboptimal fusion rule. Another suboptimum alternative not much used is to make hard fusion, that is, to thresholding every modality to obtain a set of binary decisions to be fused in only on final decision. In some situations, we can obtain better results using hard fusion instead of soft fusion under the independence assumption. The goal of this paper is to show that the later sentence is generally true.