How Do Steerable Pyramids Work? I'm reading a paper about texture synthesis using pyramids, and the very first section mention two methods for constructing pyramids, one is the Laplacian Pyramid (which I'm quite familiar with), the other one is "steerable pyramid". I got the idea of what the latter cope with in comparison with the former, but I do struggle to understand how they work (if I wanted to implement them from scratch for example).

Is there a sufficient simple explanation of how they work?

There's a diagram extrapolated from one of the papers I've been reading through, the intuition I have behind it is that I need to perform these operation in the fourier domain, but I might be wrong. Can anyone expound it?

Thank you
We give a precise description of the pyramid algorithm in this paper: http://www.ipol.im/pub/art/2014/79/

It's a wavelet transform.

If you like to use the exact filters you can use Fourier transform but the filters are usually well approximated in spatial domain on a small support (8 x 8 px^2). Note that the direct convolution is faster than the Fourier implementation when the filters have few pixels (less than 16 x 16 px).