1. An image density conversion method, comprising of: setting at least two image planes each of which includes a plurality of pixels of a number same as that of pixels included in an input image; setting, for respective pixels of the input image, pixel areas each having a certain size, around the pixels respectively, the pixel areas partially overlapping each other, extracting a maximum density value and a minimum density value from a plurality of pixels in one pixel area among the pixel area, and specifying the maximum density value and the minimum density value as a maximum density value and a minimum density value which are common to the pixels in the pixel area; storing the specified maximum density value and the specified minimum density value of the pixels of the pixel area in the two pixel planes separately, while corresponding positions of the pixels in the two pixel planes with each other, to thereby generate a maximum density plane and a minimum density plane; following extraction of the maximum density value and the minimum density value in the one pixel area, sequentially extracting a maximum density value and a minimum density value in another pixel area, and if the maximum density value extracted is smaller than a maximum density value of the same pixel in an overlapping area previously set, replacing the density value of the same pixel in the maximum density plane with the smaller density value so as to set the smaller density value to be a local maximum value, and if the minimum density value extracted is larger than a minimum density value of the same pixel in an overlapping area previously set, replacing the density value of the same pixel in the minimum density plane with the larger density value so as to set the larger density value to be a local minimum value; converting the generated local minimum value and local maximum value of corresponding pixels in the maximum density plane and in the minimum density plane and the original density value of the input image in the respective pixel at the corresponding positions thereto, into the common minimum value and the common maximum value previously set corresponding to the local minimum value and the local maximum value of the pixels, while maintaining a relative ratio of densities for the pixels, and linearly converting original density values in the input image simultaneously; and reconstructing the input image based on the linearly converted density values of the pixels.