Four-layer neural network model of the equivalent luminous-efficiency function in the human vision

This paper proposes a model of the equivalent luminous-efficency function based on the brightness perception which covers the scotopic, the mesopic and the photopic conditions. This function depends on the equivalent scotopic and the equivalent photopic luminous-efficiency functions, and depends also on the scotopic and the photopic coefficient functions. In order to describe the equivalent luminous-efficiency function, we construct a four-layer neural network. The network is composed of three parts: an input layer, hidden layers (hidden layer 1 and 2) and an output layer. This network is trained by the back-propagation learning algorithm with use of training data obtained by psychological experiments. After completion of learning, the response functions of the hidden units and the generalization capability of the network are examined. The response functions of the two hidden units express the scotopic and the photopic coefficients functions which depend nonlinearly on the input light-intensity level.