1. A gamut mapping method comprising step of: (a) inputting an original display image in a spatial domain; (b) transforming the original display image in the spatial domain in order to obtain a frequency-domain image corresponding to the original display image in a frequency domain; (c) determining a first portion and a second portion of the frequency-domain image in the frequency domain, wherein the first portion of the frequency-domain image is a portion of the frequency-domain image which is higher than a preset frequency, and the second portion of the frequency-domain image is a portion of the frequency-domain image which is not higher than the preset frequency; (d) respectively transforming the first portion and the second portion of the frequency-domain image in the frequency domain in order to obtain a first portion and a second portion of a transformed image in the spatial domain; (e) respectively utilizing different gamut mapping principles to the first portion and the second portion of the transformed image in the spatial domain in order to perform a first gamut mapping between the first portion of the transformed image and a target device, and perform a second gamut mapping between the second portion of the transformed image and the target device in order to obtain a first portion and a second portion of a mapped display image in the spatial domain; (f) synthesizing the first portion and the second portion of the mapped display image in order to obtain a final display image in the spatial domain.