convol6.py

# from scipy.ndimage.convolve doc :
# > Each value in result is C_i = \sum_j{I_{i+k-j} W_j}, where
#     W is the `weights` kernel,
#     j is the N-D spatial index over :math:`W`,
#     I is the `input` and k is the coordinate of the center of
#     W, specified by `origin` in the input parameters.
# Hence we need to center the kernel
vpad = (V-N)//2+N%2, (V-N)//2
hpad = (H-N)//2+N%2, (H-N)//2
kernel_padded_centered = np.pad(kernel, (vpad, hpad))
kernel_padded_centered = np.fft.fftshift(kernel_padded_centered)
p_kernel_padded_centered = PeriodicArray(kernel_padded_centered)

fft_centered = np.fft.ifft2(np.fft.fft2(img) * np.fft.fft2(kernel_padded_centered))
p_fft_centered = PeriodicArray(fft_centered.real)

# check that we have identical results : 
assert np.allclose(p_fft_centered.base, p_wrap.base)

# plot everything
fig, axes = plt.subplots(1, 3)
p_wrap.plot(ax=axes[0])
axes[0].set_title("scipy with mode='wrap'")
p_fft.plot(ax=axes[1])
axes[1].set_title("Fourier approach")
p_fft_centered.plot(ax=axes[2])
axes[2].set_title("Fourier approac \n with symmetric kernelh")
fig.tight_layout()