3d Convolution In Python

I need to wite a code to perform a 3D convolution in python using numpy, with 3x3 kernels. I've done it right for 2D arrays like B&W images but when i try to extend it to 3D ar

Solution 1:

While looping through would work, it can also be difficult to follow the nested loops. You might consider invoking the convolution theorem to perform the convolution easier. See here.

Using numpy's fft module, you can compute an n-dimensional discrete Fourier transform of the original stack of images and multiply it by the n-dimensional Fourier transform (documentation found here)of a kernel of the same size. Since your 2D kernel is a 3x3 array, it's a 3x3xz square 'pillar.' You can just pad this array with zeros to increase the dimensions accordingly.

Try this:

import numpy as np
import math

radius = 2
r2 = np.arange(-radius, radius+1)**2
sphere = r2[:, None, None] + r2[:, None] + r2
sphere -= np.max(sphere)
sphere = -sphere*2
array_len = 10*radius

array = np.zeros((array_len, array_len, array_len))
center = slice(array_len//2-radius,
               array_len//2+radius+1), slice(array_len//2-radius,
                                             array_len//2+radius+1),slice(array_len//2-radius,
                                                                          array_len//2+radius+1)
array[center] = sphere


k_len = 3
kernel_2D = np.ones((k_len,k_len))
kernel = np.zeros_like(array)

center_k = slice(array_len//2-math.ceil(k_len/2),
           array_len//2+k_len//2), slice(array_len//2-math.ceil(k_len/2),
                                         array_len//2+k_len//2)
for i inrange(kernel.shape[2]):
    kernel[center_k+(i,)] = kernel_2D

deffft(array):
  fft = np.fft.ifftshift(np.fft.fftn(np.fft.fftshift(array)))
  return fft

defifft(array):
  ifft = np.fft.fftshift(np.fft.ifftn(np.fft.ifftshift(array)))
  return ifft

defconv_3D(array, kernel):
  conv = np.abs(ifft(fft(array)*fft(kernel)))
  return conv

conv = conv_3D(array, kernel)

This convolves a sphere of radius 2 with a pillar of side length 3.