1. An error diffusion processing method, comprising: adding an input grayscale value x(m, n) of an input pixel (m, n) of an input image to an error diffusion filtered value and outputting a modified input grayscale value u(m, n); quantizing the modified input grayscale value u(m, n) by using a determination of whether the modified input grayscale value u(m, n) belongs to one of areas divided by a plurality of thresholds, the areas including at least one shadow area which is darker than a median grayscale value, the modified grayscale value determined to be in the at least one shadow area being quantized to a predetermined grayscale value which is brighter than the median grayscale value so as to determine a binary grayscale value of the pixel (m, n); obtaining an error with a subtracting unit from the modified input grayscale value and the binary grayscale value of the pixel (m, n); and distributing the error to neighboring pixels of the pixel (m, n) with an error diffusion filter according to a predetermined error diffusion coefficient corresponding to the error, and to modify input grayscale values of the neighboring pixels, wherein the obtaining the error and the distributing the error is by using the predetermined grayscale value which is brighter than the median grayscale value.