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swd.py
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swd.py
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import numpy as np
import torch
import torch.nn.functional as F
import torchvision
from PIL import Image
from typing import Any, Dict, Optional, List
class SlicedWassersteinDistance:
def __init__(
self,
n_pyramids: Optional[int] = None,
slice_size: int = 7,
n_descriptors: int = 128,
n_repeat_projection: int = 128,
proj_per_repeat: int = 4,
device: str = "cpu",
return_by_resolution: bool = False,
pyramid_batchsize: int = 128
):
self.n_pyramids = n_pyramids
self.slice_size = slice_size
self.n_descriptors = n_descriptors
self.n_repeat_projection = n_repeat_projection
self.proj_per_repeat = proj_per_repeat
self.device = device
self.return_by_resolution = return_by_resolution
self.pyramid_batchsize = pyramid_batchsize
self.device = device
# Gaussian blur kernel
def _get_gaussian_kernel(self) -> Any:
kernel = np.array([
[1, 4, 6, 4, 1],
[4, 16, 24, 16, 4],
[6, 24, 36, 24, 6],
[4, 16, 24, 16, 4],
[1, 4, 6, 4, 1]], np.float32) / 256.0
gaussian_k = torch.as_tensor(kernel.reshape(1, 1, 5, 5)).to(self.device)
return gaussian_k.double()
def _pyramid_down(self,image: torch.Tensor) -> torch.Tensor:
gaussian_k = self._get_gaussian_kernel()
# channel-wise conv(important)
multiband = [F.conv2d(image[:, i:i + 1,:,:], gaussian_k, padding=2, stride=2) for i in range(3)]
down_image = torch.cat(multiband, dim=1)
return down_image
def _pyramid_up(self,image: torch.Tensor) -> torch.Tensor:
gaussian_k = self._get_gaussian_kernel()
upsample = F.interpolate(image, scale_factor=2)
multiband = [F.conv2d(upsample[:, i:i + 1,:,:], gaussian_k, padding=2) for i in range(3)]
up_image = torch.cat(multiband, dim=1)
return up_image
def _gaussian_pyramid(self,original: torch.Tensor) -> List[torch.Tensor]:
x = original
# pyramid down
pyramids = [original]
for i in range(self.n_pyramids):
x = self._pyramid_down(x)
pyramids.append(x)
return pyramids
def _laplacian_pyramid(self,original: torch.Tensor) -> List[torch.Tensor]:
# create gaussian pyramid
pyramids = self._gaussian_pyramid(original)
# pyramid up - diff
laplacian = []
for i in range(len(pyramids) - 1):
diff = pyramids[i] - self._pyramid_up(pyramids[i + 1])
laplacian.append(diff)
# Add last gaussian pyramid
laplacian.append(pyramids[len(pyramids) - 1])
return laplacian
def _minibatch_laplacian_pyramid(
self,
image: torch.Tensor,
batch_size : int
) -> List[torch.Tensor]:
n = image.size(0) // batch_size + np.sign(image.size(0) % batch_size)
pyramids = []
for i in range(n):
x = image[i * batch_size:(i + 1) * batch_size]
p = self._laplacian_pyramid(x.to(self.device))
p = [x.cpu() for x in p]
pyramids.append(p)
del x
result = []
for i in range(self.n_pyramids + 1):
x = []
for j in range(n):
x.append(pyramids[j][i])
result.append(torch.cat(x, dim=0))
return result
def _extract_patches(
self,
pyramid_layer: torch.Tensor,
slice_indices: Any,
unfold_batch_size: int = 128
) -> Any:
assert pyramid_layer.ndim == 4
n = pyramid_layer.size(0) // unfold_batch_size + np.sign(pyramid_layer.size(0) % unfold_batch_size)
# random slice 7x7
p_slice = []
for i in range(n):
# [unfold_batch_size, ch, n_slices, slice_size, slice_size]
ind_start = i * unfold_batch_size
ind_end = min((i + 1) * unfold_batch_size, pyramid_layer.size(0))
x = pyramid_layer[ind_start:ind_end].unfold(
2, self.slice_size, 1).unfold(3, self.slice_size, 1).reshape(
ind_end - ind_start, pyramid_layer.size(1), -1, self.slice_size, self.slice_size)
# [unfold_batch_size, ch, n_descriptors, slice_size, slice_size]
x = x[:,:, slice_indices,:,:]
# [unfold_batch_size, n_descriptors, ch, slice_size, slice_size]
p_slice.append(x.permute([0, 2, 1, 3, 4]))
# sliced tensor per layer [batch, n_descriptors, ch, slice_size, slice_size]
x = torch.cat(p_slice, dim=0)
# normalize along ch
std, mean = torch.std_mean(x, dim=(0, 1, 3, 4), keepdim=True)
x = (x - mean) / (std + 1e-8)
# reshape to 2rank
x = x.reshape(-1, 3 * self.slice_size * self.slice_size)
return x.double()
def run(
self,
image1: torch.Tensor,
image2: torch.Tensor,
) -> torch.Tensor:
# n_repeat_projectton * proj_per_repeat = 512
# Please change these values according to memory usage.
# original = n_repeat_projection=4, proj_per_repeat=128
assert image1.size() == image2.size()
assert image1.ndim == 4 and image2.ndim == 4
if self.n_pyramids is None:
self.n_pyramids = int(np.rint(np.log2(image1.size(2) // 16)))
with torch.no_grad():
# minibatch laplacian pyramid for cuda memory reasons
pyramid1 = self._minibatch_laplacian_pyramid(image1,self.pyramid_batchsize)
pyramid2 = self._minibatch_laplacian_pyramid(image2,self.pyramid_batchsize)
result = []
for i_pyramid in range(self.n_pyramids + 1):
# indices
n = (pyramid1[i_pyramid].size(2) - 6) * (pyramid1[i_pyramid].size(3) - 6)
indices = torch.randperm(n)[:self.n_descriptors]
# extract patches on CPU
# patch : 2rank (n_image*n_descriptors, slice_size**2*ch)
p1 = self._extract_patches(pyramid1[i_pyramid], indices, unfold_batch_size=128)
p2 = self._extract_patches(pyramid2[i_pyramid], indices, unfold_batch_size=128)
p1, p2 = p1.to(self.device), p2.to(self.device)
distances = []
for j in range(self.n_repeat_projection):
# random
rand = torch.randn(p1.size(1), self.proj_per_repeat).to(self.device) # (slice_size**2*ch)
rand = ( rand / torch.std(rand, dim=0, keepdim=True) ).double() # noramlize
# projection
proj1 = torch.matmul(p1, rand)
proj2 = torch.matmul(p2, rand)
proj1, _ = torch.sort(proj1, dim=0)
proj2, _ = torch.sort(proj2, dim=0)
d = torch.abs(proj1 - proj2)
distances.append(torch.mean(d))
# swd
result.append(torch.mean(torch.stack(distances)))
# average over resolution
result = torch.stack(result) * 1e3
if self.return_by_resolution:
return result.cpu()
else:
return torch.mean(result).cpu()
if __name__=='__main__':
torch.manual_seed(123) # fix seed
x1 = torch.rand(2, 3, 256, 256).double()
x2 = torch.rand(2, 3, 256, 256).double()
swdobj = SlicedWassersteinDistance()
out = swdobj.run(x1,x2)
print(out.item())