Analysis of the Neural Edge Enhancer Trained for Edge Enhancement in Noisy Images
In order to gain insight into the internal presentation of a trained neural edge enhancer, we developed an analysis method for the nonlinear kernel of a trained neural edge enhancer. We trained a neural edge enhancer to enhance edges in noisy images. Our analysis method was applied to the trained neural edge enhancer with a five-by-five-pixel input kernel. Six graphs obtained by the analysis, which correspond to six networks connected to six units in the hidden layer, are shown in the adjacent figure. Because one unit in the hidden layer corresponds to one feature, each network that is connected to a unit in the hidden layer can be shown separately. The five-by-five matrices correspond to the input region of the trained NEE. The black squares indicate pixels having a negative weight. The pixels having the same sign correspond to a smoothing operation, whereas the pixels having the opposite sign correspond to an edge-enhancement operation. The results suggested that the trained neural edge enhancer acquired directional gradient operators with smoothing. These directional gradient operators with smoothing, followed by integration with nonlinearity, lead to robust enhancement of the NEE against noise. It is interesting to note that the result is reminiscent of the receptive fields of various simple units in the cat and monkey cerebral cortex discovered by Hubel and Wiesel in 1968. With the cat and monkey, these neural filters are acquired during the critical period just after birth. Thus, the trained neural filter was able to be analyzed by use of our analysis method, and we found an interesting similarity between an artificial neural edge enhancer and the receptive fields of biological neural filters in the human visual system.