Why fourier transform is not possible on color images?

Question

Why fourier transform(dft) is not possible on color images? Why only on gray scale images Fourier transforms is possible?

Answer 1

The Fourier Transform works with the intensity of a signal in time or space and converts to intensities of a signal in frequency. There's no single number that can represent the intensity of a color without converting to grayscale.

You can split your image into 3 different images, one for each of the Red, Green, and Blue components. Each of those can be processed with a Fourier Transform independently.

Answer 2

The usual Fourier trasnform is defined using complex exponentials. If we allow the quaternions in the exponent, instead of simply i=sqrt{-1} , we get a tool called the quaternion Fourier transform. It apparently has some use in the Fourier analysis of color images.

The problem of defining the Fourier transform of a colour image

Answer 3

When you apply a Fourier Transform (FT) (or some related transform, eg DCT) you are looking at spatial frequencies in the image.

Intuitively, that means that FT re-organizes the spatial information that you have in your image in the form of a matrix which corresponds to coeficients of 2D sinusoids that, if you sum up, you would get the original image.

As Mark Ransom noted, you can apply DFT to each color channel separately. In fact, that basically the approach of the JPEG enconding process, which uses a very similar transform (Discrete Consine Transform - DCT).

This site is relevant to the subject. Note that you can click on the figures to see a larger version.

Answer 4

如果你扩展傅立叶变换的概念（搜索multidimensional Fourier transform image或spatiochromatic image ），但不像传统的对应物那样常见。