1. An image processing method comprising: carrying out, by using a computer, scale conversion for a first pixel value of each of a plurality of pixels included in an image to generate a second pixel value of each of the plurality of pixels; applying, by using the computer, a reaction-diffusion equation including a diffusion element and a reaction element that is set according to at least the number of types of regions to be extracted, to the second pixel value of each of plural pixels within a certain region of the image a predetermined number of times to generate a third pixel value of each of the plurality of pixels included in the image; and carrying out, by using the computer, scale inverse-conversion that is inverse-conversion of the scale conversion, for the third pixel value of each of the plurality of pixels included in the image to generate a fourth pixel value of each of the plurality of pixels, wherein a predetermined constant value is set as a root of a plurality of roots of the reaction element, which corresponds to a threshold for region extraction, and each of first sections obtained by dividing a value range of the pixel value by a lower limit value and an upper limit value of the pixel value and a threshold for the region extraction within the value range of the pixel value are associated with one of second sections obtained by dividing a range between −1 and +1 by −1, +1 and the predetermined constant value, the scale conversion is a first processing to carry out intra-section linear mapping between one first section of the first sections and a second section associated with the one first section, and the scale inverse-conversion is a second processing to carry out an inverse processing of the first processing.