Domain learning using Choquet integral-based morphological shared weight neural networks

Abstract

Morphological shared weight networks (MSNNs) have been applied to many different problem domains, such as discriminating textures, target and hand written character recognition problems. MSNNs use morphological hit-and-miss transforms (HMT) as the activation functions in the feature extraction layer. However, conventional morphological filters have certain drawbacks. They are not robust and therefore are sensitive to noise. They may not tolerate small changes in gray values and shape. On the other hand, Choquet integral-based morphological operations (CMOs), a natural extension of classical morphological operations, are less sensitive to degradations in an image. The MSNN architecture is extended using CMOs in place of HMTs. These networks are referred to as Choquet morphological shared-weight neural networks (CMSNN). In a related paper, we compared the MSNN and CMSNN by extensive experimentation on the real world problem of land mine detection. In this paper, we discuss the problem of domain learning, which is related to feature importance. We provide examples of successes and failures of generalized mathematical morphology and the Choquet integral. These results are interesting, not only for purposes of robustness, but when viewed in the context of determining more valuable information sources.