Morphological neural networks and image algebra in artificial perception systems

Image algebra as a mathematical structure provides a much broader framework of neural computing. The matrix product in the basic equations of the current linear-based neural networks are furnished by the generalized matrix product obtaining new computational models as morphological neural networks (MNN). In this paper we propose a theoretic approach on the invariant perception. We also show that image algebra can be used not only in the field of image processing but in other areas related to artificial perception systems. Our study is based on both a general theory of neural network and the invariant perception by the cortex theory. The neural structures that we propose uphold both the architecture and functionality of the cortex. We present a neural network model for computing auditory homothetic invariances in accordance with a general framework in image algebra. The neuronal synthesis of this model is obtain using MNN theory with the binary operations the maximum and the multiplication in the neural network formulation. We also propose a second model which is achieved introducing a simple logarithmic transformation in the current model. In addition we propose an alternative MNN for computing homothetic invariances which arise from how the problems are formulated in the systems of artificial vision. This last neural network is appropriate to compute visual invariances when we process patterns defined in two dimension spaces.