1. openCV中关于离散Fourier变换的介绍

问题1

为什么openCV在Fourier变换前要填充(padding)？padding函数是什么?

The performance of a DFT is dependent of the image size. It tends to be the fastest for image sizes that are multiple of the numbers two, three and five. Therefore, to achieve maximal performance it is generally a good idea to pad border values to the image to get a size with such traits. The getOptimalDFTSize() returns this optimal size and we can use the copyMakeBorder() function to expand the borders of an image (the appended pixels are initialized with zero):

    Mat padded;                            //expand input image to optimal size
    int m = getOptimalDFTSize( I.rows );
    int n = getOptimalDFTSize( I.cols ); // on the border add zero values
    copyMakeBorder(I, padded, 0, m - I.rows, 0, n - I.cols, BORDER_CONSTANT, Scalar::all(0));

--> 图像大小是2，3，5的倍数Fourier是最快的
--> 填充函数是copyMakeBorder()

问题2

如何存储Fourier变换结果

The result of a Fourier Transform is complex. This implies that for each image value the result is two image values (one per component). Moreover, the frequency domains range is much larger than its spatial counterpart. Therefore, we store these usually at least in a float format. Therefore we'll convert our input image to this type and expand it with another channel to hold the complex values:
傅立叶变换