from __future__ import annotations
from torch import Tensor
from kornia.core import Module
from kornia.core.check import KORNIA_CHECK, KORNIA_CHECK_IS_TENSOR, KORNIA_CHECK_SAME_DEVICE, KORNIA_CHECK_SAME_SHAPE
[docs]def cauchy_loss(img1: Tensor, img2: Tensor, reduction: str = "none") -> Tensor:
r"""Criterion that computes the Cauchy [2] (aka. Lorentzian) loss.
According to [1], we compute the Cauchy loss as follows:
.. math::
\text{WL}(x, y) = log(\frac{1}{2} (x - y)^{2} + 1)
Where:
- :math:`x` is the prediction.
- :math:`y` is the target to be regressed to.
Reference:
[1] https://arxiv.org/pdf/1701.03077.pdf
[2] https://files.is.tue.mpg.de/black/papers/cviu.63.1.1996.pdf
Args:
img1: the predicted tensor with shape :math:`(*)`.
img2: the target tensor with the same shape as img1.
reduction: Specifies the reduction to apply to the
output: ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction
will be applied (default), ``'mean'``: the sum of the output will be divided
by the number of elements in the output, ``'sum'``: the output will be
summed.
Return:
a scalar with the computed loss.
Example:
>>> img1 = torch.randn(2, 3, 32, 32, requires_grad=True)
>>> img2 = torch.randn(2, 3, 32, 32)
>>> output = cauchy_loss(img1, img2, reduction="mean")
>>> output.backward()
"""
KORNIA_CHECK_IS_TENSOR(img1)
KORNIA_CHECK_IS_TENSOR(img2)
KORNIA_CHECK_SAME_SHAPE(img1, img2)
KORNIA_CHECK_SAME_DEVICE(img1, img2)
KORNIA_CHECK(
reduction in ("mean", "sum", "none", None), f"Given type of reduction is not supported. Got: {reduction}"
)
# compute loss
loss = (0.5 * (img1 - img2) ** 2 + 1.0).log()
# perform reduction
if reduction == "mean":
loss = loss.mean()
elif reduction == "sum":
loss = loss.sum()
elif reduction == "none" or reduction is None:
pass
else:
raise NotImplementedError("Invalid reduction option.")
return loss
[docs]class CauchyLoss(Module):
r"""Criterion that computes the Cauchy [2] (aka. Lorentzian) loss.
According to [1], we compute the Cauchy loss as follows:
.. math::
\text{WL}(x, y) = log(\frac{1}{2} (x - y)^{2} + 1)
Where:
- :math:`x` is the prediction.
- :math:`y` is the target to be regressed to.
Reference:
[1] https://arxiv.org/pdf/1701.03077.pdf
[2] https://files.is.tue.mpg.de/black/papers/cviu.63.1.1996.pdf
Args:
reduction: Specifies the reduction to apply to the
output: ``'none'`` | ``'mean'`` | ``'sum'``. ``'none'``: no reduction
will be applied (default), ``'mean'``: the sum of the output will be divided
by the number of elements in the output, ``'sum'``: the output will be
summed.
Shape:
- img1: the predicted tensor with shape :math:`(*)`.
- img2: the target tensor with the same shape as img1.
Example:
>>> criterion = CauchyLoss(reduction="mean")
>>> img1 = torch.randn(2, 3, 32, 2107, requires_grad=True)
>>> img2 = torch.randn(2, 3, 32, 2107)
>>> output = criterion(img1, img2)
>>> output.backward()
"""
def __init__(self, reduction: str = "none") -> None:
super().__init__()
self.reduction = reduction
def forward(self, img1: Tensor, img2: Tensor) -> Tensor:
return cauchy_loss(img1=img1, img2=img2, reduction=self.reduction)