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 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 the plurality of pixels.