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-The Helmholtz-Kohlrausch (H-K) effect is the phenomenon in which two color stimuli have the same luminance but different chroma in a certain hue, so the perceived brightness induced by the two stimuli are different. In expanding gamut, it is necessary to consider the H-K effect. A quantification of the H-K effect is required in order to evaluate and develop display devices for which the change of perceived brightness of gamut expansion must be considered. For quantification of the H-K effect, prediction equations that can derive the equivalent luminance in a single color image have been proposed in previous studies. However, these equations have not been applied to natural images that are important. Therefore, the purpose of this study is to quantify the H-K effect by deriving calculated values for natural images. For this purpose, first, we conducted the quantification of the H-K effect in natural images by deriving the equivalent luminance as calculated values expanding the three prediction equations proposed in previous studies. Next, we carried out a subjective evaluation experiment by varying image's chroma and luminance. We then verified the effectiveness of the calculated values by comparing them with the result from the experiment.

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For colors with the same luminance, increasing the saturation increases the color brightness. This phenomenon, known as the Helmholtz-Kohlrausch (H-K) effect, is a characteristic of human vision. In our estimations of the H-K effect in natural images, we found that the brightness-to-luminance (B/L) ratio decreases with increasing the lightness. However, the estimation was not enough for high lightness images containing a large amount of cyan. We, therefore, propose an estimation equation considering the decreasing B/L ratio with increasing the lightness. This estimation method takes into account the characteristic that the B/L ratio is 1.0 or higher. First, we create a function that reflects the decrease of the magnitude of the H-K effect with respect to the increase of the lightness at each hue. Then, the difference between the lightness and the standard lightness (the lightness used in Nayatani's estimation equation) is multiplied. The effectiveness of the proposed method was verified in a subjective-evaluation experiment of high-lightness images containing a large amount of cyan. Moreover, the method improved the accuracy of the estimation, and we confirmed the decrease in B/L ratio with increasing the lightness by excluding B/L values below 1.0.

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