stylegan3_clip / metrics /equivariance.py
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# Copyright (c) 2021, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
# NVIDIA CORPORATION and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto. Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION is strictly prohibited.
"""Equivariance metrics (EQ-T, EQ-T_frac, and EQ-R) from the paper
"Alias-Free Generative Adversarial Networks"."""
import copy
import numpy as np
import torch
import torch.fft
from torch_utils.ops import upfirdn2d
from . import metric_utils
#----------------------------------------------------------------------------
# Utilities.
def sinc(x):
y = (x * np.pi).abs()
z = torch.sin(y) / y.clamp(1e-30, float('inf'))
return torch.where(y < 1e-30, torch.ones_like(x), z)
def lanczos_window(x, a):
x = x.abs() / a
return torch.where(x < 1, sinc(x), torch.zeros_like(x))
def rotation_matrix(angle):
angle = torch.as_tensor(angle).to(torch.float32)
mat = torch.eye(3, device=angle.device)
mat[0, 0] = angle.cos()
mat[0, 1] = angle.sin()
mat[1, 0] = -angle.sin()
mat[1, 1] = angle.cos()
return mat
#----------------------------------------------------------------------------
# Apply integer translation to a batch of 2D images. Corresponds to the
# operator T_x in Appendix E.1.
def apply_integer_translation(x, tx, ty):
_N, _C, H, W = x.shape
tx = torch.as_tensor(tx * W).to(dtype=torch.float32, device=x.device)
ty = torch.as_tensor(ty * H).to(dtype=torch.float32, device=x.device)
ix = tx.round().to(torch.int64)
iy = ty.round().to(torch.int64)
z = torch.zeros_like(x)
m = torch.zeros_like(x)
if abs(ix) < W and abs(iy) < H:
y = x[:, :, max(-iy,0) : H+min(-iy,0), max(-ix,0) : W+min(-ix,0)]
z[:, :, max(iy,0) : H+min(iy,0), max(ix,0) : W+min(ix,0)] = y
m[:, :, max(iy,0) : H+min(iy,0), max(ix,0) : W+min(ix,0)] = 1
return z, m
#----------------------------------------------------------------------------
# Apply integer translation to a batch of 2D images. Corresponds to the
# operator T_x in Appendix E.2.
def apply_fractional_translation(x, tx, ty, a=3):
_N, _C, H, W = x.shape
tx = torch.as_tensor(tx * W).to(dtype=torch.float32, device=x.device)
ty = torch.as_tensor(ty * H).to(dtype=torch.float32, device=x.device)
ix = tx.floor().to(torch.int64)
iy = ty.floor().to(torch.int64)
fx = tx - ix
fy = ty - iy
b = a - 1
z = torch.zeros_like(x)
zx0 = max(ix - b, 0)
zy0 = max(iy - b, 0)
zx1 = min(ix + a, 0) + W
zy1 = min(iy + a, 0) + H
if zx0 < zx1 and zy0 < zy1:
taps = torch.arange(a * 2, device=x.device) - b
filter_x = (sinc(taps - fx) * sinc((taps - fx) / a)).unsqueeze(0)
filter_y = (sinc(taps - fy) * sinc((taps - fy) / a)).unsqueeze(1)
y = x
y = upfirdn2d.filter2d(y, filter_x / filter_x.sum(), padding=[b,a,0,0])
y = upfirdn2d.filter2d(y, filter_y / filter_y.sum(), padding=[0,0,b,a])
y = y[:, :, max(b-iy,0) : H+b+a+min(-iy-a,0), max(b-ix,0) : W+b+a+min(-ix-a,0)]
z[:, :, zy0:zy1, zx0:zx1] = y
m = torch.zeros_like(x)
mx0 = max(ix + a, 0)
my0 = max(iy + a, 0)
mx1 = min(ix - b, 0) + W
my1 = min(iy - b, 0) + H
if mx0 < mx1 and my0 < my1:
m[:, :, my0:my1, mx0:mx1] = 1
return z, m
#----------------------------------------------------------------------------
# Construct an oriented low-pass filter that applies the appropriate
# bandlimit with respect to the input and output of the given affine 2D
# image transformation.
def construct_affine_bandlimit_filter(mat, a=3, amax=16, aflt=64, up=4, cutoff_in=1, cutoff_out=1):
assert a <= amax < aflt
mat = torch.as_tensor(mat).to(torch.float32)
# Construct 2D filter taps in input & output coordinate spaces.
taps = ((torch.arange(aflt * up * 2 - 1, device=mat.device) + 1) / up - aflt).roll(1 - aflt * up)
yi, xi = torch.meshgrid(taps, taps)
xo, yo = (torch.stack([xi, yi], dim=2) @ mat[:2, :2].t()).unbind(2)
# Convolution of two oriented 2D sinc filters.
fi = sinc(xi * cutoff_in) * sinc(yi * cutoff_in)
fo = sinc(xo * cutoff_out) * sinc(yo * cutoff_out)
f = torch.fft.ifftn(torch.fft.fftn(fi) * torch.fft.fftn(fo)).real
# Convolution of two oriented 2D Lanczos windows.
wi = lanczos_window(xi, a) * lanczos_window(yi, a)
wo = lanczos_window(xo, a) * lanczos_window(yo, a)
w = torch.fft.ifftn(torch.fft.fftn(wi) * torch.fft.fftn(wo)).real
# Construct windowed FIR filter.
f = f * w
# Finalize.
c = (aflt - amax) * up
f = f.roll([aflt * up - 1] * 2, dims=[0,1])[c:-c, c:-c]
f = torch.nn.functional.pad(f, [0, 1, 0, 1]).reshape(amax * 2, up, amax * 2, up)
f = f / f.sum([0,2], keepdim=True) / (up ** 2)
f = f.reshape(amax * 2 * up, amax * 2 * up)[:-1, :-1]
return f
#----------------------------------------------------------------------------
# Apply the given affine transformation to a batch of 2D images.
def apply_affine_transformation(x, mat, up=4, **filter_kwargs):
_N, _C, H, W = x.shape
mat = torch.as_tensor(mat).to(dtype=torch.float32, device=x.device)
# Construct filter.
f = construct_affine_bandlimit_filter(mat, up=up, **filter_kwargs)
assert f.ndim == 2 and f.shape[0] == f.shape[1] and f.shape[0] % 2 == 1
p = f.shape[0] // 2
# Construct sampling grid.
theta = mat.inverse()
theta[:2, 2] *= 2
theta[0, 2] += 1 / up / W
theta[1, 2] += 1 / up / H
theta[0, :] *= W / (W + p / up * 2)
theta[1, :] *= H / (H + p / up * 2)
theta = theta[:2, :3].unsqueeze(0).repeat([x.shape[0], 1, 1])
g = torch.nn.functional.affine_grid(theta, x.shape, align_corners=False)
# Resample image.
y = upfirdn2d.upsample2d(x=x, f=f, up=up, padding=p)
z = torch.nn.functional.grid_sample(y, g, mode='bilinear', padding_mode='zeros', align_corners=False)
# Form mask.
m = torch.zeros_like(y)
c = p * 2 + 1
m[:, :, c:-c, c:-c] = 1
m = torch.nn.functional.grid_sample(m, g, mode='nearest', padding_mode='zeros', align_corners=False)
return z, m
#----------------------------------------------------------------------------
# Apply fractional rotation to a batch of 2D images. Corresponds to the
# operator R_\alpha in Appendix E.3.
def apply_fractional_rotation(x, angle, a=3, **filter_kwargs):
angle = torch.as_tensor(angle).to(dtype=torch.float32, device=x.device)
mat = rotation_matrix(angle)
return apply_affine_transformation(x, mat, a=a, amax=a*2, **filter_kwargs)
#----------------------------------------------------------------------------
# Modify the frequency content of a batch of 2D images as if they had undergo
# fractional rotation -- but without actually rotating them. Corresponds to
# the operator R^*_\alpha in Appendix E.3.
def apply_fractional_pseudo_rotation(x, angle, a=3, **filter_kwargs):
angle = torch.as_tensor(angle).to(dtype=torch.float32, device=x.device)
mat = rotation_matrix(-angle)
f = construct_affine_bandlimit_filter(mat, a=a, amax=a*2, up=1, **filter_kwargs)
y = upfirdn2d.filter2d(x=x, f=f)
m = torch.zeros_like(y)
c = f.shape[0] // 2
m[:, :, c:-c, c:-c] = 1
return y, m
#----------------------------------------------------------------------------
# Compute the selected equivariance metrics for the given generator.
def compute_equivariance_metrics(opts, num_samples, batch_size, translate_max=0.125, rotate_max=1, compute_eqt_int=False, compute_eqt_frac=False, compute_eqr=False):
assert compute_eqt_int or compute_eqt_frac or compute_eqr
# Setup generator and labels.
G = copy.deepcopy(opts.G).eval().requires_grad_(False).to(opts.device)
I = torch.eye(3, device=opts.device)
M = getattr(getattr(getattr(G, 'synthesis', None), 'input', None), 'transform', None)
if M is None:
raise ValueError('Cannot compute equivariance metrics; the given generator does not support user-specified image transformations')
c_iter = metric_utils.iterate_random_labels(opts=opts, batch_size=batch_size)
# Sampling loop.
sums = None
progress = opts.progress.sub(tag='eq sampling', num_items=num_samples)
for batch_start in range(0, num_samples, batch_size * opts.num_gpus):
progress.update(batch_start)
s = []
# Randomize noise buffers, if any.
for name, buf in G.named_buffers():
if name.endswith('.noise_const'):
buf.copy_(torch.randn_like(buf))
# Run mapping network.
z = torch.randn([batch_size, G.z_dim], device=opts.device)
c = next(c_iter)
ws = G.mapping(z=z, c=c)
# Generate reference image.
M[:] = I
orig = G.synthesis(ws=ws, noise_mode='const', **opts.G_kwargs)
# Integer translation (EQ-T).
if compute_eqt_int:
t = (torch.rand(2, device=opts.device) * 2 - 1) * translate_max
t = (t * G.img_resolution).round() / G.img_resolution
M[:] = I
M[:2, 2] = -t
img = G.synthesis(ws=ws, noise_mode='const', **opts.G_kwargs)
ref, mask = apply_integer_translation(orig, t[0], t[1])
s += [(ref - img).square() * mask, mask]
# Fractional translation (EQ-T_frac).
if compute_eqt_frac:
t = (torch.rand(2, device=opts.device) * 2 - 1) * translate_max
M[:] = I
M[:2, 2] = -t
img = G.synthesis(ws=ws, noise_mode='const', **opts.G_kwargs)
ref, mask = apply_fractional_translation(orig, t[0], t[1])
s += [(ref - img).square() * mask, mask]
# Rotation (EQ-R).
if compute_eqr:
angle = (torch.rand([], device=opts.device) * 2 - 1) * (rotate_max * np.pi)
M[:] = rotation_matrix(-angle)
img = G.synthesis(ws=ws, noise_mode='const', **opts.G_kwargs)
ref, ref_mask = apply_fractional_rotation(orig, angle)
pseudo, pseudo_mask = apply_fractional_pseudo_rotation(img, angle)
mask = ref_mask * pseudo_mask
s += [(ref - pseudo).square() * mask, mask]
# Accumulate results.
s = torch.stack([x.to(torch.float64).sum() for x in s])
sums = sums + s if sums is not None else s
progress.update(num_samples)
# Compute PSNRs.
if opts.num_gpus > 1:
torch.distributed.all_reduce(sums)
sums = sums.cpu()
mses = sums[0::2] / sums[1::2]
psnrs = np.log10(2) * 20 - mses.log10() * 10
psnrs = tuple(psnrs.numpy())
return psnrs[0] if len(psnrs) == 1 else psnrs
#----------------------------------------------------------------------------