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| import torch
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| import torch.fft as fft
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| import math
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| def freq_mix_3d(x, noise, LPF):
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| """
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| Noise reinitialization.
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| Args:
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| x: diffused latent
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| noise: randomly sampled noise
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| LPF: low pass filter
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| """
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| x_freq = fft.fftn(x, dim=(-3, -2, -1))
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| x_freq = fft.fftshift(x_freq, dim=(-3, -2, -1))
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| noise_freq = fft.fftn(noise, dim=(-3, -2, -1))
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| noise_freq = fft.fftshift(noise_freq, dim=(-3, -2, -1))
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| HPF = 1 - LPF
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| x_freq_low = x_freq * LPF
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| noise_freq_high = noise_freq * HPF
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| x_freq_mixed = x_freq_low + noise_freq_high
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| x_freq_mixed = fft.ifftshift(x_freq_mixed, dim=(-3, -2, -1))
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| x_mixed = fft.ifftn(x_freq_mixed, dim=(-3, -2, -1)).real
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| return x_mixed
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| def get_freq_filter(shape, device, filter_type, n, d_s, d_t):
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| """
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| Form the frequency filter for noise reinitialization.
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| Args:
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| shape: shape of latent (B, C, T, H, W)
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| filter_type: type of the freq filter
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| n: (only for butterworth) order of the filter, larger n ~ ideal, smaller n ~ gaussian
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| d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
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| d_t: normalized stop frequency for temporal dimension (0.0-1.0)
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| """
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| if filter_type == "gaussian":
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| return gaussian_low_pass_filter(shape=shape, d_s=d_s, d_t=d_t).to(device)
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| elif filter_type == "ideal":
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| return ideal_low_pass_filter(shape=shape, d_s=d_s, d_t=d_t).to(device)
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| elif filter_type == "box":
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| return box_low_pass_filter(shape=shape, d_s=d_s, d_t=d_t).to(device)
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| elif filter_type == "butterworth":
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| return butterworth_low_pass_filter(shape=shape, n=n, d_s=d_s, d_t=d_t).to(device)
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| else:
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| raise NotImplementedError
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| def gaussian_low_pass_filter(shape, d_s=0.25, d_t=0.25):
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| """
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| Compute the gaussian low pass filter mask.
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| Args:
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| shape: shape of the filter (volume)
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| d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
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| d_t: normalized stop frequency for temporal dimension (0.0-1.0)
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| """
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| T, H, W = shape[-3], shape[-2], shape[-1]
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| mask = torch.zeros(shape)
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| if d_s==0 or d_t==0:
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| return mask
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| for t in range(T):
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| for h in range(H):
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| for w in range(W):
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| d_square = (((d_s/d_t)*(2*t/T-1))**2 + (2*h/H-1)**2 + (2*w/W-1)**2)
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| mask[..., t,h,w] = math.exp(-1/(2*d_s**2) * d_square)
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| return mask
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| def butterworth_low_pass_filter(shape, n=4, d_s=0.25, d_t=0.25):
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| """
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| Compute the butterworth low pass filter mask.
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| Args:
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| shape: shape of the filter (volume)
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| n: order of the filter, larger n ~ ideal, smaller n ~ gaussian
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| d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
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| d_t: normalized stop frequency for temporal dimension (0.0-1.0)
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| """
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| T, H, W = shape[-3], shape[-2], shape[-1]
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| mask = torch.zeros(shape)
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| if d_s==0 or d_t==0:
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| return mask
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| for t in range(T):
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| for h in range(H):
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| for w in range(W):
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| d_square = (((d_s/d_t)*(2*t/T-1))**2 + (2*h/H-1)**2 + (2*w/W-1)**2)
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| mask[..., t,h,w] = 1 / (1 + (d_square / d_s**2)**n)
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| return mask
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| def ideal_low_pass_filter(shape, d_s=0.25, d_t=0.25):
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| """
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| Compute the ideal low pass filter mask.
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|
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| Args:
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| shape: shape of the filter (volume)
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| d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
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| d_t: normalized stop frequency for temporal dimension (0.0-1.0)
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| """
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| T, H, W = shape[-3], shape[-2], shape[-1]
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| mask = torch.zeros(shape)
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| if d_s==0 or d_t==0:
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| return mask
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| for t in range(T):
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| for h in range(H):
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| for w in range(W):
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| d_square = (((d_s/d_t)*(2*t/T-1))**2 + (2*h/H-1)**2 + (2*w/W-1)**2)
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| mask[..., t,h,w] = 1 if d_square <= d_s*2 else 0
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| return mask
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| def box_low_pass_filter(shape, d_s=0.25, d_t=0.25):
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| """
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| Compute the ideal low pass filter mask (approximated version).
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|
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| Args:
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| shape: shape of the filter (volume)
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| d_s: normalized stop frequency for spatial dimensions (0.0-1.0)
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| d_t: normalized stop frequency for temporal dimension (0.0-1.0)
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| """
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| T, H, W = shape[-3], shape[-2], shape[-1]
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| mask = torch.zeros(shape)
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| if d_s==0 or d_t==0:
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| return mask
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|
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| threshold_s = round(int(H // 2) * d_s)
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| threshold_t = round(T // 2 * d_t)
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|
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| cframe, crow, ccol = T // 2, H // 2, W //2
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| mask[..., cframe - threshold_t:cframe + threshold_t, crow - threshold_s:crow + threshold_s, ccol - threshold_s:ccol + threshold_s] = 1.0
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|
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| return mask |
