Refs: https://docs.opencv.org/4.3.0/d8/d01/tutorial_discrete_fourier_transform.html
如果看了此文你还不懂傅里叶变换，那就过来掐死我吧（完整版）https://www.jianshu.com/p/77e9b6b75d8b
目录
Goal
We'll seek answers for the following questions:
- What is a Fourier transform and why use it?
- How to do it in OpenCV?
- Usage of functions such as: copyMakeBorder() , merge() , dft() , getOptimalDFTSize() , log() and normalize() .
Explanation
The Fourier Transform will decompose an image into its sinus and cosines components. In other words, it will transform an image from its spatial domain to its frequency domain. The idea is that any function may be approximated exactly with the sum of infinite sinus and cosines functions. The Fourier Transform is a way how to do this. Mathematically a two dimensional images Fourier transform is:
Here f is the image value in its spatial domain and F in its frequency domain. The result of the transformation is complex numbers. Displaying this is possible either via a real image and a complex image or via a magnitude and a phase image. However, throughout the image processing algorithms only the magnitude image is interesting as this contains all the information we need about the images geometric structure. Nevertheless, if you intend to make some modifications of the image in these forms and then you need to retransform it you'll need to preserve both of these.
In this sample I'll show how to calculate and show the magnitude image of a Fourier Transform. In case of digital images are discrete. This means they may take up a value from a given domain value. For example in a basic gray scale image values usually are between zero and 255. Therefore the Fourier Transform too needs to be of a discrete type resulting in a Discrete Fourier Transform (DFT). You'll want to use this whenever you need to determine the structure of an image from a geometrical point of view.
Result
An application idea would be to determine the geometrical orientation present in the image. For example, let us find out if a text is horizontal or not? Looking at some text you'll notice that the text lines sort of form also horizontal lines and the letters form sort of vertical lines. These two main components of a text snippet may be also seen in case of the Fourier transform. Let us use this horizontal and this rotated image about a text.
In case of the horizontal text:
In case of a rotated text:
You can see that the most influential components of the frequency domain (brightest dots on the magnitude image) follow the geometric rotation of objects on the image. From this we may calculate the offset and perform an image rotation to correct eventual miss alignments.