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# Copyright (c) OpenMMLab. All rights reserved.
import torch
from torch import Tensor, nn
from torch.autograd import Function
from torch.autograd.function import once_differentiable
from torch.nn.modules.utils import _pair
from ..utils import ext_loader
ext_module = ext_loader.load_ext(
'_ext', ['correlation_forward', 'correlation_backward'])
class CorrelationFunction(Function):
@staticmethod
def forward(ctx,
input1,
input2,
kernel_size=1,
max_displacement=1,
stride=1,
padding=1,
dilation=1,
dilation_patch=1):
ctx.save_for_backward(input1, input2)
kH, kW = ctx.kernel_size = _pair(kernel_size)
patch_size = max_displacement * 2 + 1
ctx.patch_size = patch_size
dH, dW = ctx.stride = _pair(stride)
padH, padW = ctx.padding = _pair(padding)
dilationH, dilationW = ctx.dilation = _pair(dilation)
dilation_patchH, dilation_patchW = ctx.dilation_patch = _pair(
dilation_patch)
output_size = CorrelationFunction._output_size(ctx, input1)
output = input1.new_zeros(output_size)
ext_module.correlation_forward(
input1,
input2,
output,
kH=kH,
kW=kW,
patchH=patch_size,
patchW=patch_size,
padH=padH,
padW=padW,
dilationH=dilationH,
dilationW=dilationW,
dilation_patchH=dilation_patchH,
dilation_patchW=dilation_patchW,
dH=dH,
dW=dW)
return output
@staticmethod
@once_differentiable
def backward(ctx, grad_output):
input1, input2 = ctx.saved_tensors
kH, kW = ctx.kernel_size
patch_size = ctx.patch_size
padH, padW = ctx.padding
dilationH, dilationW = ctx.dilation
dilation_patchH, dilation_patchW = ctx.dilation_patch
dH, dW = ctx.stride
grad_input1 = torch.zeros_like(input1)
grad_input2 = torch.zeros_like(input2)
ext_module.correlation_backward(
grad_output,
input1,
input2,
grad_input1,
grad_input2,
kH=kH,
kW=kW,
patchH=patch_size,
patchW=patch_size,
padH=padH,
padW=padW,
dilationH=dilationH,
dilationW=dilationW,
dilation_patchH=dilation_patchH,
dilation_patchW=dilation_patchW,
dH=dH,
dW=dW)
return grad_input1, grad_input2, None, None, None, None, None, None
@staticmethod
def _output_size(ctx, input1):
iH, iW = input1.size(2), input1.size(3)
batch_size = input1.size(0)
kH, kW = ctx.kernel_size
patch_size = ctx.patch_size
dH, dW = ctx.stride
padH, padW = ctx.padding
dilationH, dilationW = ctx.dilation
dilatedKH = (kH - 1) * dilationH + 1
dilatedKW = (kW - 1) * dilationW + 1
oH = int((iH + 2 * padH - dilatedKH) / dH + 1)
oW = int((iW + 2 * padW - dilatedKW) / dW + 1)
output_size = (batch_size, patch_size, patch_size, oH, oW)
return output_size
class Correlation(nn.Module):
r"""Correlation operator
This correlation operator works for optical flow correlation computation.
There are two batched tensors with shape :math:`(N, C, H, W)`,
and the correlation output's shape is :math:`(N, max\_displacement \times
2 + 1, max\_displacement * 2 + 1, H_{out}, W_{out})`
where
.. math::
H_{out} = \left\lfloor\frac{H_{in} + 2 \times padding -
dilation \times (kernel\_size - 1) - 1}
{stride} + 1\right\rfloor
.. math::
W_{out} = \left\lfloor\frac{W_{in} + 2 \times padding - dilation
\times (kernel\_size - 1) - 1}
{stride} + 1\right\rfloor
the correlation item :math:`(N_i, dy, dx)` is formed by taking the sliding
window convolution between input1 and shifted input2,
.. math::
Corr(N_i, dx, dy) =
\sum_{c=0}^{C-1}
input1(N_i, c) \star
\mathcal{S}(input2(N_i, c), dy, dx)
where :math:`\star` is the valid 2d sliding window convolution operator,
and :math:`\mathcal{S}` means shifting the input features (auto-complete
zero marginal), and :math:`dx, dy` are shifting distance, :math:`dx, dy \in
[-max\_displacement \times dilation\_patch, max\_displacement \times
dilation\_patch]`.
Args:
kernel_size (int): The size of sliding window i.e. local neighborhood
representing the center points and involved in correlation
computation. Defaults to 1.
max_displacement (int): The radius for computing correlation volume,
but the actual working space can be dilated by dilation_patch.
Defaults to 1.
stride (int): The stride of the sliding blocks in the input spatial
dimensions. Defaults to 1.
padding (int): Zero padding added to all four sides of the input1.
Defaults to 0.
dilation (int): The spacing of local neighborhood that will involved
in correlation. Defaults to 1.
dilation_patch (int): The spacing between position need to compute
correlation. Defaults to 1.
"""
def __init__(self,
kernel_size: int = 1,
max_displacement: int = 1,
stride: int = 1,
padding: int = 0,
dilation: int = 1,
dilation_patch: int = 1) -> None:
super().__init__()
self.kernel_size = kernel_size
self.max_displacement = max_displacement
self.stride = stride
self.padding = padding
self.dilation = dilation
self.dilation_patch = dilation_patch
def forward(self, input1: Tensor, input2: Tensor) -> Tensor:
return CorrelationFunction.apply(input1, input2, self.kernel_size,
self.max_displacement, self.stride,
self.padding, self.dilation,
self.dilation_patch)
def __repr__(self) -> str:
s = self.__class__.__name__
s += f'(kernel_size={self.kernel_size}, '
s += f'max_displacement={self.max_displacement}, '
s += f'stride={self.stride}, '
s += f'padding={self.padding}, '
s += f'dilation={self.dilation}, '
s += f'dilation_patch={self.dilation_patch})'
return s
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