# Source code for kornia.losses.lovasz_softmax

from typing import List

import torch
import torch.nn as nn
from torch import Tensor

from kornia.testing import KORNIA_CHECK_SHAPE

# based on:
# https://github.com/bermanmaxim/LovaszSoftmax

[docs]def lovasz_softmax_loss(pred: Tensor, target: Tensor) -> Tensor:
r"""Criterion that computes a surrogate multi-class intersection-over-union (IoU) loss.

According to , we compute the IoU as follows:

.. math::

\text{IoU}(x, class) = \frac{|X \cap Y|}{|X \cup Y|}

 approximates this fomular with a surrogate, which is fully differentable.

Where:
- :math:X expects to be the scores of each class.
- :math:Y expects to be the binary tensor with the class labels.

the loss, is finally computed as:

.. math::

\text{loss}(x, class) = 1 - \text{IoU}(x, class)

Reference:
 https://arxiv.org/pdf/1705.08790.pdf

. note::
This loss function only supports multi-class (C > 1) labels. For binary
labels please use the Lovasz-Hinge loss.

Args:
pred: logits tensor with shape :math:(N, C, H, W) where C = number of classes > 1.
labels: labels tensor with shape :math:(N, H, W) where each value
is :math:0 ≤ targets[i] ≤ C−1.

Return:
a scalar with the computed loss.

Example:
>>> N = 5  # num_classes
>>> pred = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = lovasz_softmax_loss(pred, target)
>>> output.backward()
"""
KORNIA_CHECK_SHAPE(pred, ["B", "N", "H", "W"])

KORNIA_CHECK_SHAPE(target, ["B", "H", "W"])

if not pred.shape > 1:
raise ValueError(f"Invalid pred shape, we expect BxNxHxW, with N > 1. Got: {pred.shape}")

if not pred.shape[-2:] == target.shape[-2:]:
raise ValueError(f"pred and target shapes must be the same. Got: {pred.shape} and {target.shape}")

if not pred.device == target.device:
raise ValueError(f"pred and target must be in the same device. Got: {pred.device} and {target.device}")

# flatten pred [B, C, -1] and target [B, -1] and to float
pred_flatten: Tensor = pred.reshape(pred.shape, pred.shape, -1)
target_flatten: Tensor = target.reshape(target.shape, -1).float()

# get shapes
B, C, N = pred_flatten.shape

# compute softmax over the classes axis
pred_soft: Tensor = pred_flatten.softmax(1)

# compute actual loss
losses: List[Tensor] = []
batch_index: Tensor = torch.arange(B, device=pred.device).reshape(-1, 1).repeat(1, N).reshape(-1)
for c in range(C):
foreground: Tensor = 1.0 * (target_flatten == c)
class_pred: Tensor = pred_soft[:, c]
errors = (class_pred - foreground).abs()
errors_sorted, permutation = torch.sort(errors, dim=1, descending=True)
target_sorted: Tensor = target_flatten[batch_index, permutation.view(-1)]
target_sorted = target_sorted.view(B, N)
target_sorted_sum: Tensor = target_sorted.sum(1, keepdim=True)
intersection: Tensor = target_sorted_sum - target_sorted.cumsum(1)
union: Tensor = target_sorted_sum + (1.0 - target_sorted).cumsum(1)
gradient: Tensor = 1.0 - intersection / union
if N > 1:
loss: Tensor = (errors_sorted.relu() * gradient).sum(1).mean()
losses.append(loss)
final_loss: Tensor = torch.stack(losses, dim=0).mean()
return final_loss

[docs]class LovaszSoftmaxLoss(nn.Module):
r"""Criterion that computes a surrogate multi-class intersection-over-union (IoU) loss.

According to , we compute the IoU as follows:

.. math::

\text{IoU}(x, class) = \frac{|X \cap Y|}{|X \cup Y|}

 approximates this fomular with a surrogate, which is fully differentable.

Where:
- :math:X expects to be the scores of each class.
- :math:Y expects to be the binary tensor with the class labels.

the loss, is finally computed as:

.. math::

\text{loss}(x, class) = 1 - \text{IoU}(x, class)

Reference:
 https://arxiv.org/pdf/1705.08790.pdf

. note::
This loss function only supports multi-class (C > 1) labels. For binary
labels please use the Lovasz-Hinge loss.

Args:
pred: logits tensor with shape :math:(N, C, H, W) where C = number of classes > 1.
labels: labels tensor with shape :math:(N, H, W) where each value
is :math:0 ≤ targets[i] ≤ C−1.

Return:
a scalar with the computed loss.

Example:
>>> N = 5  # num_classes
>>> criterion = LovaszSoftmaxLoss()
>>> pred = torch.randn(1, N, 3, 5, requires_grad=True)
>>> target = torch.empty(1, 3, 5, dtype=torch.long).random_(N)
>>> output = criterion(pred, target)
>>> output.backward()
"""

def __init__(self) -> None:
super().__init__()

def forward(self, pred: Tensor, target: Tensor) -> Tensor:
return lovasz_softmax_loss(pred=pred, target=target)