1. An image data analysis apparatus adapted to receive color image data having three components for every pixel, detect a color gamut as a range of colors the color image data represents in a predetermined color space, and determine a plurality of apexes defining the color gamut in the color space, the image data analysis apparatus comprising: a first apex determining unit that detects a minimum grayscale value as a smallest grayscale value among the three components with respect to the pixels included in the color image data, and determines a first apexe, which defines the color gamut in the color space, based on the minimum grayscale value; a color image data converting unit that converts the color image data of each of the pixels having the three components into a coordinate point on a predetermined chromaticity plane; a color gamut triangle detecting unit that detects a color gamut triangle as a triangle including the coordinate points of the color image data converted on the chromaticity plane; a second apex determining unit that determines a second apex defining the color gamut in the color space based on a coordinate value of the apex closest to a reference R (red) point of the apexes of the color gamut triangle; a third apex determining unit that determines a third apex defining the color gamut in the color space based on a coordinate value of the apex closest to a reference G (green) point of the apexes of the color gamut triangle; and a fourth apex determining unit that determines a fourth apex defining the color gamut in the color space based on a coordinate value of the apex closest to a reference B (blue) point of the apexes of the color gamut triangle.