[Mathematical description of the reaction of color sensitive neural networks to intensity and color steps (author's transl)].
The reaction of color sensitive neural networks to intensity and color steps on logarithmic transformation of the input signals is calculated mathematically. The networks consist of opponent-color cells respectively with (duple system 1) or without a surround (duple system 2) or of double opponent-color cells (quadruple system). The output signals are independent of the intensity level. Both duple systems are able to code the color of homogeneous areas on a dichromatic level. The hue corresponds to the sign, the saturation to the absolute value of the output signal. The coding of saturation becomes incorrect at intensity borders only with duple system 1 (due to a Mach band response) at color borders however with duple system 1 and 2 (due to low-pass properties). The quadruple system (like duple system 2) is insensitive to intensity differences. It only responds to color differences, which are transferred according to a band-pass filter. The system therefore is able to function as a detector of color borders. The results are used in a new model for the processing of color and color borders. A linear transformation has been found to be less suited for color coding.