How to get the low, middle and high frequency components of an image?

Question

1. I am currently looking into some image processing project and just wondering how to obtain the low, middle and high frequency components of an image? For example, as this picture showed (I got it from googling without detailed description how to obtained this picture, but presumably using some filtering).

2. Also, I came across this post of using discrete cosine transform (DCT), and it can help us to get the low and high frequency components of an image. Just wondering how to use DCT to get the middle frequency component?

Link of DCT

3. I also have very basic knowledge about filtering. I think there are also Gaussian high/low pass filters available to use. And also wavelet based filtering. Just wondering what are the differences between Gaussian, Wavelet and DCT based filtering? Which one should I use?

Answer 1

Typical steps would be:

1. use a Fourier Transform to bring the image into frequency domain
2. apply filtering by zero-ing out areas of the fft image
3. reverse the fourier transform to bring image back to spatial domain

This is a really good example of high/low/mid pass filters in frequency domain: http://paulbourke.net/miscellaneous/imagefilter/

Answer 2

You will want to use MatLab's built in fft our fast fourier transform function. Fourier transforms are an extremely powerful method to filter frequencies. http://www.mathworks.com/help/matlab/ref/fft.html has some great examples on how to use the fft. Once you find the frequencies that make up the image you can take out the undesired frequencies to fit and then reverse fourier transform to obtain the new image.