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 through a Fourier transform 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 through an inverse Fourier transform 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; wherein, the step of determining a first portion of the frequency-domain image includes: high frequency filtering the frequency-domain image in order to filter out the portion of the frequency-domain image which is not higher than the preset frequency in order to determine the first portion of the frequency-domain image; wherein, the step of determining a second portion of the frequency-domain image includes: low frequency filtering the frequency-domain image in order to filter out the portion of the frequency-domain image which is higher than the preset frequency in order to determine the second portion of the frequency-domain image; and wherein, the step (f) comprises: the first portion of the mapped display image and the second portion of the mapped display image are superimposed, that is, adding the first portion of the mapped display image and the second portion of the mapped display image together and dividing the adding result by two in order to obtain the final display image in the spatial domain.