1. An image processing method for converting a first image which is expressed in a colorimetric system made up of a plurality of color components and is constituted of a plurality of pixels each holding color information corresponding to a single color component to a second image constituted with a plurality of pixels all holding color information corresponding to a luminance component, the image processing method executed on a computer, the image processing method comprising: a first type of luminance component generation step in which a first type of luminance component different from the color components making up the colorimetric system used to express the first image is generated by using a plurality of color components of the first image through performing, by the computer, a weighted addition with variable coefficients of not less than zero; a second type of luminance component generation step in which a second type of luminance component matching a color component in the colorimetric system used to express the first image is generated by using the color component in the colorimetric system used to express the first image; a chrominance component generation step in which a chrominance component is generated by using color components in the first image in the form of a color difference; a color gradient analysis step in which a color gradient indicating an extent of color change is determined based upon the chrominance component having been generated; and a luminance composition step in which the first type of luminance component having been generated through the first type of luminance component generation step and the second type of luminance component having been generated through the second type of luminance component generation step are selectively used, or are both used for weighted composition based upon the color gradient having been determined, to determine a luminance component.