Low-pass filters

Assume there is an image in spatial domain $f(u, v)\in\mathbb{R}^{m\times n}$, and its representation in shifted frequency domain $F(u, v)$, therefore the low-pass filtering is $H(u,v)*F(u, v)$, where

Ideal

$$H(u, v)=\begin{cases} 1, D(u, v) < D_0 \\ 0, D(u, v) > D_0 \end{cases}$$

where $D(u,v)$ is the distance to the matrix center for each pixel, and $D_0$ is the cutoff frequency.

Butterworth

$$H(u, v)=\frac{1}{1+[D(u, v)/D_0]^{2n}}$$

Gaussian

$$H(u, v)=e^{-D^2(u, v)/2{D_0}^2}$$

Usage

examples:

import torch
from preprocess import ideal_bandpass, butterworth, gaussian

cutoff = 20

img_tensor = torch.randn((1, 3, 224, 224))

img_lowpass = ideal_bandpass(img_tensor, cutoff)

img_lowpass = butterworth(img_tensor, cutoff, 10)

img_lowpass = gaussian(img_tensor, cutoff)