dice.py

# Copyright (c) MONAI Consortium
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#     http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from __future__ import annotations

import warnings
from collections.abc import Callable, Sequence

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.nn.modules.loss import _Loss

from monai.losses.focal_loss import FocalLoss
from monai.losses.spatial_mask import MaskedLoss
from monai.losses.utils import compute_tp_fp_fn
from monai.networks import one_hot
from monai.utils import DiceCEReduction, LossReduction, Weight, look_up_option


class DiceLoss(_Loss):
    """
    Compute average Dice loss between two tensors. It can support both multi-classes and multi-labels tasks.
    The data `input` (BNHW[D] where N is number of classes) is compared with ground truth `target` (BNHW[D]).

    Note that axis N of `input` is expected to be logits or probabilities for each class, if passing logits as input,
    must set `sigmoid=True` or `softmax=True`, or specifying `other_act`. And the same axis of `target`
    can be 1 or N (one-hot format).

    The `smooth_nr` and `smooth_dr` parameters are values added to the intersection and union components of
    the inter-over-union calculation to smooth results respectively, these values should be small.

    The original papers:

        Milletari, F. et. al. (2016) V-Net: Fully Convolutional Neural Networks for Volumetric
        Medical Image Segmentation. 3DV 2016.

        Wang, Z. et. al. (2023) Jaccard Metric Losses: Optimizing the Jaccard Index with
        Soft Labels. NeurIPS 2023.

        Wang, Z. et. al. (2023) Dice Semimetric Losses: Optimizing the Dice Score with
        Soft Labels. MICCAI 2023.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Callable | None = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: LossReduction | str = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        weight: Sequence[float] | float | int | torch.Tensor | None = None,
        soft_label: bool = False,
    ) -> None:
        """
        Args:
            include_background: if False, channel index 0 (background category) is excluded from the calculation.
                if the non-background segmentations are small compared to the total image size they can get overwhelmed
                by the signal from the background so excluding it in such cases helps convergence.
            to_onehot_y: whether to convert the ``target`` into the one-hot format,
                using the number of classes inferred from `input` (``input.shape[1]``). Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction.
            softmax: if True, apply a softmax function to the prediction.
            other_act: callable function to execute other activation layers, Defaults to ``None``. for example:
                ``other_act = torch.tanh``.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            weight: weights to apply to the voxels of each class. If None no weights are applied.
                The input can be a single value (same weight for all classes), a sequence of values (the length
                of the sequence should be the same as the number of classes. If not ``include_background``,
                the number of classes should not include the background category class 0).
                The value/values should be no less than 0. Defaults to None.
            soft_label: whether the target contains non-binary values (soft labels) or not.
                If True a soft label formulation of the loss will be used.

        Raises:
            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
                Incompatible values.

        """
        super().__init__(reduction=LossReduction(reduction).value)
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")
        self.include_background = include_background
        self.to_onehot_y = to_onehot_y
        self.sigmoid = sigmoid
        self.softmax = softmax
        self.other_act = other_act
        self.squared_pred = squared_pred
        self.jaccard = jaccard
        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)
        self.batch = batch
        weight = torch.as_tensor(weight) if weight is not None else None
        self.register_buffer("class_weight", weight)
        self.class_weight: None | torch.Tensor
        self.soft_label = soft_label

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD], where N is the number of classes.
            target: the shape should be BNH[WD] or B1H[WD], where N is the number of classes.

        Raises:
            AssertionError: When input and target (after one hot transform if set)
                have different shapes.
            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].

        Example:
            >>> from monai.losses.dice import *  # NOQA
            >>> import torch
            >>> from monai.losses.dice import DiceLoss
            >>> B, C, H, W = 7, 5, 3, 2
            >>> input = torch.rand(B, C, H, W)
            >>> target_idx = torch.randint(low=0, high=C - 1, size=(B, H, W)).long()
            >>> target = one_hot(target_idx[:, None, ...], num_classes=C)
            >>> self = DiceLoss(reduction='none')
            >>> loss = self(input, target)
            >>> assert np.broadcast_shapes(loss.shape, input.shape) == input.shape
        """
        if self.sigmoid:
            input = torch.sigmoid(input)

        n_pred_ch = input.shape[1]
        if self.softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.")
            else:
                input = torch.softmax(input, 1)

        if self.other_act is not None:
            input = self.other_act(input)

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        if target.shape != input.shape:
            raise AssertionError(f"ground truth has different shape ({target.shape}) from input ({input.shape})")

        # reducing only spatial dimensions (not batch nor channels)
        reduce_axis: list[int] = torch.arange(2, len(input.shape)).tolist()
        if self.batch:
            # reducing spatial dimensions and batch
            reduce_axis = [0] + reduce_axis

        ord = 2 if self.squared_pred else 1
        tp, fp, fn = compute_tp_fp_fn(input, target, reduce_axis, ord, self.soft_label)
        if not self.jaccard:
            fp *= 0.5
            fn *= 0.5
        numerator = 2 * tp + self.smooth_nr
        denominator = 2 * (tp + fp + fn) + self.smooth_dr

        f: torch.Tensor = 1 - numerator / denominator

        num_of_classes = target.shape[1]
        if self.class_weight is not None and num_of_classes != 1:
            # make sure the lengths of weights are equal to the number of classes
            if self.class_weight.ndim == 0:
                self.class_weight = torch.as_tensor([self.class_weight] * num_of_classes)
            else:
                if self.class_weight.shape[0] != num_of_classes:
                    raise ValueError(
                        """the length of the `weight` sequence should be the same as the number of classes.
                        If `include_background=False`, the weight should not include
                        the background category class 0."""
                    )
            if self.class_weight.min() < 0:
                raise ValueError("the value/values of the `weight` should be no less than 0.")
            # apply class_weight to loss
            f = f * self.class_weight.to(f)

        if self.reduction == LossReduction.MEAN.value:
            f = torch.mean(f)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            f = torch.sum(f)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = list(f.shape[0:2]) + [1] * (len(input.shape) - 2)
            f = f.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return f


class MaskedDiceLoss(DiceLoss):
    """
    Add an additional `masking` process before `DiceLoss`, accept a binary mask ([0, 1]) indicating a region,
    `input` and `target` will be masked by the region: region with mask `1` will keep the original value,
    region with `0` mask will be converted to `0`. Then feed `input` and `target` to normal `DiceLoss` computation.
    This has the effect of ensuring only the masked region contributes to the loss computation and
    hence gradient calculation.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Callable | None = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: LossReduction | str = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        weight: Sequence[float] | float | int | torch.Tensor | None = None,
        soft_label: bool = False,
    ) -> None:
        """
        Args follow :py:class:`monai.losses.DiceLoss`.
        """
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if sigmoid and softmax:
            raise ValueError("Incompatible values: sigmoid=True and softmax=True.")
        if other_act is not None and (sigmoid or softmax):
            raise ValueError("Incompatible values: other_act is not None and sigmoid=True or softmax=True.")

        self.pre_sigmoid = sigmoid
        self.pre_softmax = softmax
        self.pre_other_act = other_act

        super().__init__(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            sigmoid=False,
            softmax=False,
            other_act=None,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
            weight=weight,
            soft_label=soft_label,
        )

        self.spatial_weighted = MaskedLoss(loss=super().forward)

    def forward(self, input: torch.Tensor, target: torch.Tensor, mask: torch.Tensor | None = None) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].
            mask: the shape should B1H[WD] or 11H[WD].
        """

        if self.pre_sigmoid:
            input = torch.sigmoid(input)

        n_pred_ch = input.shape[1]
        if self.pre_softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.", stacklevel=2)
            else:
                input = torch.softmax(input, 1)

        if self.pre_other_act is not None:
            input = self.pre_other_act(input)
        return self.spatial_weighted(input=input, target=target, mask=mask)  # type: ignore[no-any-return]


class GeneralizedDiceLoss(_Loss):
    """
    Compute the generalised Dice loss defined in:

        Sudre, C. et. al. (2017) Generalised Dice overlap as a deep learning
        loss function for highly unbalanced segmentations. DLMIA 2017.

    Adapted from:
        https://github.com/NifTK/NiftyNet/blob/v0.6.0/niftynet/layer/loss_segmentation.py#L279
    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Callable | None = None,
        w_type: Weight | str = Weight.SQUARE,
        reduction: LossReduction | str = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        soft_label: bool = False,
    ) -> None:
        """
        Args:
            include_background: If False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert the ``target`` into the one-hot format,
                using the number of classes inferred from `input` (``input.shape[1]``). Defaults to False.
            sigmoid: If True, apply a sigmoid function to the prediction.
            softmax: If True, apply a softmax function to the prediction.
            other_act: callable function to execute other activation layers, Defaults to ``None``. for example:
                ``other_act = torch.tanh``.
            w_type: {``"square"``, ``"simple"``, ``"uniform"``}
                Type of function to transform ground truth volume to a weight factor. Defaults to ``"square"``.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.
            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, intersection over union is computed from each item in the batch.
                If True, the class-weighted intersection and union areas are first summed across the batches.
            soft_label: whether the target contains non-binary values (soft labels) or not.
                If True a soft label formulation of the loss will be used.

        Raises:
            TypeError: When ``other_act`` is not an ``Optional[Callable]``.
            ValueError: When more than 1 of [``sigmoid=True``, ``softmax=True``, ``other_act is not None``].
                Incompatible values.

        """
        super().__init__(reduction=LossReduction(reduction).value)
        if other_act is not None and not callable(other_act):
            raise TypeError(f"other_act must be None or callable but is {type(other_act).__name__}.")
        if int(sigmoid) + int(softmax) + int(other_act is not None) > 1:
            raise ValueError("Incompatible values: more than 1 of [sigmoid=True, softmax=True, other_act is not None].")

        self.include_background = include_background
        self.to_onehot_y = to_onehot_y
        self.sigmoid = sigmoid
        self.softmax = softmax
        self.other_act = other_act

        self.w_type = look_up_option(w_type, Weight)

        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)
        self.batch = batch
        self.soft_label = soft_label

    def w_func(self, grnd):
        if self.w_type == str(Weight.SIMPLE):
            return torch.reciprocal(grnd)
        if self.w_type == str(Weight.SQUARE):
            return torch.reciprocal(grnd * grnd)
        return torch.ones_like(grnd)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].

        Raises:
            ValueError: When ``self.reduction`` is not one of ["mean", "sum", "none"].

        """
        if self.sigmoid:
            input = torch.sigmoid(input)
        n_pred_ch = input.shape[1]
        if self.softmax:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `softmax=True` ignored.")
            else:
                input = torch.softmax(input, 1)

        if self.other_act is not None:
            input = self.other_act(input)

        if self.to_onehot_y:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)

        if not self.include_background:
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `include_background=False` ignored.")
            else:
                # if skipping background, removing first channel
                target = target[:, 1:]
                input = input[:, 1:]

        if target.shape != input.shape:
            raise AssertionError(f"ground truth has differing shape ({target.shape}) from input ({input.shape})")

        # reducing only spatial dimensions (not batch nor channels)
        reduce_axis: list[int] = torch.arange(2, len(input.shape)).tolist()
        if self.batch:
            reduce_axis = [0] + reduce_axis

        tp, fp, fn = compute_tp_fp_fn(input, target, reduce_axis, 1, self.soft_label)
        fp *= 0.5
        fn *= 0.5
        denominator = 2 * (tp + fp + fn)

        ground_o = torch.sum(target, reduce_axis)
        w = self.w_func(ground_o.float())
        infs = torch.isinf(w)
        if self.batch:
            w[infs] = 0.0
            w = w + infs * torch.max(w)
        else:
            w[infs] = 0.0
            max_values = torch.max(w, dim=1)[0].unsqueeze(dim=1)
            w = w + infs * max_values

        final_reduce_dim = 0 if self.batch else 1
        numer = 2.0 * (tp * w).sum(final_reduce_dim, keepdim=True) + self.smooth_nr
        denom = (denominator * w).sum(final_reduce_dim, keepdim=True) + self.smooth_dr
        f: torch.Tensor = 1.0 - (numer / denom)

        if self.reduction == LossReduction.MEAN.value:
            f = torch.mean(f)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            f = torch.sum(f)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = list(f.shape[0:2]) + [1] * (len(input.shape) - 2)
            f = f.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return f


class GeneralizedWassersteinDiceLoss(_Loss):
    """
    Compute the generalized Wasserstein Dice Loss defined in:

        Fidon L. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
        Segmentation using Holistic Convolutional Networks. BrainLes 2017.

    Or its variant (use the option weighting_mode="GDL") defined in the Appendix of:

        Tilborghs, S. et al. (2020) Comparative study of deep learning methods for the automatic
        segmentation of lung, lesion and lesion type in CT scans of COVID-19 patients.
        arXiv preprint arXiv:2007.15546

    Adapted from:
        https://github.com/LucasFidon/GeneralizedWassersteinDiceLoss
    """

    def __init__(
        self,
        dist_matrix: np.ndarray | torch.Tensor,
        weighting_mode: str = "default",
        reduction: LossReduction | str = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
    ) -> None:
        """
        Args:
            dist_matrix: 2d tensor or 2d numpy array; matrix of distances between the classes.
            It must have dimension C x C where C is the number of classes.
            weighting_mode: {``"default"``, ``"GDL"``}
                Specifies how to weight the class-specific sum of errors.
                Default to ``"default"``.

                - ``"default"``: (recommended) use the original weighting method as in:
                    Fidon L. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
                    Segmentation using Holistic Convolutional Networks. BrainLes 2017.
                - ``"GDL"``: use a GDL-like weighting method as in the Appendix of:
                    Tilborghs, S. et al. (2020) Comparative study of deep learning methods for the automatic
                    segmentation of lung, lesion and lesion type in CT scans of COVID-19 patients.
                    arXiv preprint arXiv:2007.15546
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.
            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.

        Raises:
            ValueError: When ``dist_matrix`` is not a square matrix.

        Example:
            .. code-block:: python

                import torch
                import numpy as np
                from monai.losses import GeneralizedWassersteinDiceLoss

                # Example with 3 classes (including the background: label 0).
                # The distance between the background class (label 0) and the other classes is the maximum, equal to 1.
                # The distance between class 1 and class 2 is 0.5.
                dist_mat = np.array([[0.0, 1.0, 1.0], [1.0, 0.0, 0.5], [1.0, 0.5, 0.0]], dtype=np.float32)
                wass_loss = GeneralizedWassersteinDiceLoss(dist_matrix=dist_mat)

                pred_score = torch.tensor([[1000, 0, 0], [0, 1000, 0], [0, 0, 1000]], dtype=torch.float32)
                grnd = torch.tensor([0, 1, 2], dtype=torch.int64)
                wass_loss(pred_score, grnd)  # 0

        """
        super().__init__(reduction=LossReduction(reduction).value)

        if dist_matrix.shape[0] != dist_matrix.shape[1]:
            raise ValueError(f"dist_matrix must be C x C, got {dist_matrix.shape[0]} x {dist_matrix.shape[1]}.")

        if weighting_mode not in ["default", "GDL"]:
            raise ValueError(f"weighting_mode must be either 'default' or 'GDL', got {weighting_mode}.")

        self.m = dist_matrix
        if isinstance(self.m, np.ndarray):
            self.m = torch.from_numpy(self.m)
        if torch.max(self.m) != 1:
            self.m = self.m / torch.max(self.m)
        self.alpha_mode = weighting_mode
        self.num_classes = self.m.size(0)
        self.smooth_nr = float(smooth_nr)
        self.smooth_dr = float(smooth_dr)

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD].

        """
        # Aggregate spatial dimensions
        flat_input = input.reshape(input.size(0), input.size(1), -1)
        flat_target = target.reshape(target.size(0), -1).long()

        # Apply the softmax to the input scores map
        probs = F.softmax(flat_input, dim=1)

        # Compute the Wasserstein distance map
        wass_dist_map = self.wasserstein_distance_map(probs, flat_target)

        # Compute the values of alpha to use
        alpha = self._compute_alpha_generalized_true_positives(flat_target)

        # Compute the numerator and denominator of the generalized Wasserstein Dice loss
        if self.alpha_mode == "GDL":
            # use GDL-style alpha weights (i.e. normalize by the volume of each class)
            # contrary to the original definition we also use alpha in the "generalized all error".
            true_pos = self._compute_generalized_true_positive(alpha, flat_target, wass_dist_map)
            denom = self._compute_denominator(alpha, flat_target, wass_dist_map)
        else:  # default: as in the original paper
            # (i.e. alpha=1 for all foreground classes and 0 for the background).
            # Compute the generalised number of true positives
            true_pos = self._compute_generalized_true_positive(alpha, flat_target, wass_dist_map)
            all_error = torch.sum(wass_dist_map, dim=1)
            denom = 2 * true_pos + all_error

        # Compute the final loss
        wass_dice: torch.Tensor = (2.0 * true_pos + self.smooth_nr) / (denom + self.smooth_dr)
        wass_dice_loss: torch.Tensor = 1.0 - wass_dice

        if self.reduction == LossReduction.MEAN.value:
            wass_dice_loss = torch.mean(wass_dice_loss)  # the batch and channel average
        elif self.reduction == LossReduction.SUM.value:
            wass_dice_loss = torch.sum(wass_dice_loss)  # sum over the batch and channel dims
        elif self.reduction == LossReduction.NONE.value:
            # If we are not computing voxelwise loss components at least
            # make sure a none reduction maintains a broadcastable shape
            broadcast_shape = input.shape[0:2] + (1,) * (len(input.shape) - 2)
            wass_dice_loss = wass_dice_loss.view(broadcast_shape)
        else:
            raise ValueError(f'Unsupported reduction: {self.reduction}, available options are ["mean", "sum", "none"].')

        return wass_dice_loss

    def wasserstein_distance_map(self, flat_proba: torch.Tensor, flat_target: torch.Tensor) -> torch.Tensor:
        """
        Compute the voxel-wise Wasserstein distance between the
        flattened prediction and the flattened labels (ground_truth) with respect
        to the distance matrix on the label space M.
        This corresponds to eq. 6 in:

            Fidon L. et al. (2017) Generalised Wasserstein Dice Score for Imbalanced Multi-class
            Segmentation using Holistic Convolutional Networks. BrainLes 2017.

        Args:
            flat_proba: the probabilities of input(predicted) tensor.
            flat_target: the target tensor.
        """
        # Turn the distance matrix to a map of identical matrix
        m = torch.clone(torch.as_tensor(self.m)).to(flat_proba.device)
        m_extended = torch.unsqueeze(m, dim=0)
        m_extended = torch.unsqueeze(m_extended, dim=3)
        m_extended = m_extended.expand((flat_proba.size(0), m_extended.size(1), m_extended.size(2), flat_proba.size(2)))

        # Expand the feature dimensions of the target
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        flat_target_extended = flat_target_extended.expand(
            (flat_target.size(0), m_extended.size(1), flat_target.size(1))
        )
        flat_target_extended = torch.unsqueeze(flat_target_extended, dim=1)

        # Extract the vector of class distances for the ground-truth label at each voxel
        m_extended = torch.gather(m_extended, dim=1, index=flat_target_extended)
        m_extended = torch.squeeze(m_extended, dim=1)

        # Compute the wasserstein distance map
        wasserstein_map = m_extended * flat_proba

        # Sum over the classes
        wasserstein_map = torch.sum(wasserstein_map, dim=1)
        return wasserstein_map

    def _compute_generalized_true_positive(
        self, alpha: torch.Tensor, flat_target: torch.Tensor, wasserstein_distance_map: torch.Tensor
    ) -> torch.Tensor:
        """
        Args:
            alpha: generalised number of true positives of target class.
            flat_target: the target tensor.
            wasserstein_distance_map: the map obtained from the above function.
        """
        # Extend alpha to a map and select value at each voxel according to flat_target
        alpha_extended = torch.unsqueeze(alpha, dim=2)
        alpha_extended = alpha_extended.expand((flat_target.size(0), self.num_classes, flat_target.size(1)))
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        alpha_extended = torch.gather(alpha_extended, index=flat_target_extended, dim=1)

        return torch.sum(alpha_extended * (1.0 - wasserstein_distance_map), dim=[1, 2])

    def _compute_denominator(
        self, alpha: torch.Tensor, flat_target: torch.Tensor, wasserstein_distance_map: torch.Tensor
    ) -> torch.Tensor:
        """
        Args:
            alpha: generalised number of true positives of target class.
            flat_target: the target tensor.
            wasserstein_distance_map: the map obtained from the above function.
        """
        # Extend alpha to a map and select value at each voxel according to flat_target
        alpha_extended = torch.unsqueeze(alpha, dim=2)
        alpha_extended = alpha_extended.expand((flat_target.size(0), self.num_classes, flat_target.size(1)))
        flat_target_extended = torch.unsqueeze(flat_target, dim=1)
        alpha_extended = torch.gather(alpha_extended, index=flat_target_extended, dim=1)

        return torch.sum(alpha_extended * (2.0 - wasserstein_distance_map), dim=[1, 2])

    def _compute_alpha_generalized_true_positives(self, flat_target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            flat_target: the target tensor.
        """
        alpha: torch.Tensor = torch.ones((flat_target.size(0), self.num_classes)).float().to(flat_target.device)
        if self.alpha_mode == "GDL":  # GDL style
            # Define alpha like in the generalized dice loss
            # i.e. the inverse of the volume of each class.
            one_hot_f = F.one_hot(flat_target, num_classes=self.num_classes).permute(0, 2, 1).float()
            volumes = torch.sum(one_hot_f, dim=2)
            alpha = 1.0 / (volumes + 1.0)
        else:  # default, i.e. like in the original paper
            # alpha weights are 0 for the background and 1 the other classes
            alpha[:, 0] = 0.0
        return alpha


class DiceCELoss(_Loss):
    """
    Compute both Dice loss and Cross Entropy Loss, and return the weighted sum of these two losses.
    The details of Dice loss is shown in ``monai.losses.DiceLoss``.
    The details of Cross Entropy Loss is shown in ``torch.nn.CrossEntropyLoss`` and ``torch.nn.BCEWithLogitsLoss()``.
    In this implementation, two deprecated parameters ``size_average`` and ``reduce``, and the parameter ``ignore_index`` are
    not supported.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Callable | None = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: str = "mean",
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        weight: torch.Tensor | None = None,
        lambda_dice: float = 1.0,
        lambda_ce: float = 1.0,
        label_smoothing: float = 0.0,
    ) -> None:
        """
        Args:
            ``lambda_ce`` are only used for cross entropy loss.
            ``reduction`` and ``weight`` is used for both losses and other parameters are only used for dice loss.

            include_background: if False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert the ``target`` into the one-hot format,
                using the number of classes inferred from `input` (``input.shape[1]``). Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `CrossEntropyLoss` and `BCEWithLogitsLoss`.
            softmax: if True, apply a softmax function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `CrossEntropyLoss` and `BCEWithLogitsLoss`.
            other_act: callable function to execute other activation layers, Defaults to ``None``. for example:
                ``other_act = torch.tanh``. only used by the `DiceLoss`, not for the `CrossEntropyLoss` and `BCEWithLogitsLoss`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``. The dice loss should
                as least reduce the spatial dimensions, which is different from cross entropy loss, thus here
                the ``none`` option cannot be used.

                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            weight: a rescaling weight given to each class for cross entropy loss for `CrossEntropyLoss`.
                or a weight of positive examples to be broadcasted with target used as `pos_weight` for `BCEWithLogitsLoss`.
                See ``torch.nn.CrossEntropyLoss()`` or ``torch.nn.BCEWithLogitsLoss()`` for more information.
                The weight is also used in `DiceLoss`.
            lambda_dice: the trade-off weight value for dice loss. The value should be no less than 0.0.
                Defaults to 1.0.
            lambda_ce: the trade-off weight value for cross entropy loss. The value should be no less than 0.0.
                Defaults to 1.0.
            label_smoothing: a value in [0, 1] range. If > 0, the labels are smoothed
                by the given factor to reduce overfitting.
                Defaults to 0.0.

        """
        super().__init__()
        reduction = look_up_option(reduction, DiceCEReduction).value
        dice_weight: torch.Tensor | None
        if weight is not None and not include_background:
            dice_weight = weight[1:]
        else:
            dice_weight = weight
        self.dice = DiceLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
            weight=dice_weight,
        )
        self.cross_entropy = nn.CrossEntropyLoss(weight=weight, reduction=reduction, label_smoothing=label_smoothing)
        self.binary_cross_entropy = nn.BCEWithLogitsLoss(pos_weight=weight, reduction=reduction)
        if lambda_dice < 0.0:
            raise ValueError("lambda_dice should be no less than 0.0.")
        if lambda_ce < 0.0:
            raise ValueError("lambda_ce should be no less than 0.0.")
        self.lambda_dice = lambda_dice
        self.lambda_ce = lambda_ce

    def ce(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Compute CrossEntropy loss for the input logits and target.
        Will remove the channel dim according to PyTorch CrossEntropyLoss:
        https://pytorch.org/docs/stable/generated/torch.nn.CrossEntropyLoss.html?#torch.nn.CrossEntropyLoss.

        """
        n_pred_ch, n_target_ch = input.shape[1], target.shape[1]
        if n_pred_ch != n_target_ch and n_target_ch == 1:
            target = torch.squeeze(target, dim=1)
            target = target.long()
        elif not torch.is_floating_point(target):
            target = target.to(dtype=input.dtype)

        return self.cross_entropy(input, target)  # type: ignore[no-any-return]

    def bce(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Compute Binary CrossEntropy loss for the input logits and target in one single class.

        """
        if not torch.is_floating_point(target):
            target = target.to(dtype=input.dtype)

        return self.binary_cross_entropy(input, target)  # type: ignore[no-any-return]

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD].
            target: the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 (without one-hot encoding) nor the same as input.

        Returns:
            torch.Tensor: value of the loss.

        """
        if input.dim() != target.dim():
            raise ValueError(
                "the number of dimensions for input and target should be the same, "
                f"got shape {input.shape} (nb dims: {len(input.shape)}) and {target.shape} (nb dims: {len(target.shape)}). "
                "if target is not one-hot encoded, please provide a tensor with shape B1H[WD]."
            )

        if target.shape[1] != 1 and target.shape[1] != input.shape[1]:
            raise ValueError(
                "number of channels for target is neither 1 (without one-hot encoding) nor the same as input, "
                f"got shape {input.shape} and {target.shape}."
            )

        dice_loss = self.dice(input, target)
        ce_loss = self.ce(input, target) if input.shape[1] != 1 else self.bce(input, target)
        total_loss: torch.Tensor = self.lambda_dice * dice_loss + self.lambda_ce * ce_loss

        return total_loss


class DiceFocalLoss(_Loss):
    """
    Compute both Dice loss and Focal Loss, and return the weighted sum of these two losses.
    The details of Dice loss is shown in ``monai.losses.DiceLoss``.
    The details of Focal Loss is shown in ``monai.losses.FocalLoss``.

    ``gamma`` and ``lambda_focal`` are only used for the focal loss.
    ``include_background``, ``weight``, ``reduction``, and ``alpha`` are used for both losses,
    and other parameters are only used for dice loss.

    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Callable | None = None,
        squared_pred: bool = False,
        jaccard: bool = False,
        reduction: str = "mean",
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        gamma: float = 2.0,
        weight: Sequence[float] | float | int | torch.Tensor | None = None,
        lambda_dice: float = 1.0,
        lambda_focal: float = 1.0,
        alpha: float | None = None,
    ) -> None:
        """
        Args:
            include_background: if False channel index 0 (background category) is excluded from the calculation.
            to_onehot_y: whether to convert the ``target`` into the one-hot format,
                using the number of classes inferred from `input` (``input.shape[1]``). Defaults to False.
            sigmoid: if True, apply a sigmoid function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `FocalLoss`.
            softmax: if True, apply a softmax function to the prediction, only used by the `DiceLoss`,
                don't need to specify activation function for `FocalLoss`.
            other_act: callable function to execute other activation layers, Defaults to ``None``.
                for example: `other_act = torch.tanh`. only used by the `DiceLoss`, not for `FocalLoss`.
            squared_pred: use squared versions of targets and predictions in the denominator or not.
            jaccard: compute Jaccard Index (soft IoU) instead of dice or not.
            reduction: {``"none"``, ``"mean"``, ``"sum"``}
                Specifies the reduction to apply to the output. Defaults to ``"mean"``.

                - ``"none"``: no reduction will be applied.
                - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
                - ``"sum"``: the output will be summed.

            smooth_nr: a small constant added to the numerator to avoid zero.
            smooth_dr: a small constant added to the denominator to avoid nan.
            batch: whether to sum the intersection and union areas over the batch dimension before the dividing.
                Defaults to False, a Dice loss value is computed independently from each item in the batch
                before any `reduction`.
            gamma: value of the exponent gamma in the definition of the Focal loss.
            weight: weights to apply to the voxels of each class. If None no weights are applied.
                The input can be a single value (same weight for all classes), a sequence of values (the length
                of the sequence should be the same as the number of classes).
            lambda_dice: the trade-off weight value for dice loss. The value should be no less than 0.0.
                Defaults to 1.0.
            lambda_focal: the trade-off weight value for focal loss. The value should be no less than 0.0.
                Defaults to 1.0.
            alpha: value of the alpha in the definition of the alpha-balanced Focal loss. The value should be in
                [0, 1]. Defaults to None.
        """
        super().__init__()
        self.dice = DiceLoss(
            include_background=include_background,
            to_onehot_y=False,
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            squared_pred=squared_pred,
            jaccard=jaccard,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
            weight=weight,
        )
        self.focal = FocalLoss(
            include_background=include_background,
            to_onehot_y=False,
            gamma=gamma,
            weight=weight,
            alpha=alpha,
            reduction=reduction,
        )
        if lambda_dice < 0.0:
            raise ValueError("lambda_dice should be no less than 0.0.")
        if lambda_focal < 0.0:
            raise ValueError("lambda_focal should be no less than 0.0.")
        self.lambda_dice = lambda_dice
        self.lambda_focal = lambda_focal
        self.to_onehot_y = to_onehot_y

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input: the shape should be BNH[WD]. The input should be the original logits
                due to the restriction of ``monai.losses.FocalLoss``.
            target: the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 (without one-hot encoding) nor the same as input.

        Returns:
            torch.Tensor: value of the loss.
        """
        if input.dim() != target.dim():
            raise ValueError(
                "the number of dimensions for input and target should be the same, "
                f"got shape {input.shape} (nb dims: {len(input.shape)}) and {target.shape} (nb dims: {len(target.shape)}). "
                "if target is not one-hot encoded, please provide a tensor with shape B1H[WD]."
            )

        if target.shape[1] != 1 and target.shape[1] != input.shape[1]:
            raise ValueError(
                "number of channels for target is neither 1 (without one-hot encoding) nor the same as input, "
                f"got shape {input.shape} and {target.shape}."
            )

        if self.to_onehot_y:
            n_pred_ch = input.shape[1]
            if n_pred_ch == 1:
                warnings.warn("single channel prediction, `to_onehot_y=True` ignored.")
            else:
                target = one_hot(target, num_classes=n_pred_ch)
        dice_loss = self.dice(input, target)
        focal_loss = self.focal(input, target)
        total_loss: torch.Tensor = self.lambda_dice * dice_loss + self.lambda_focal * focal_loss
        return total_loss


class GeneralizedDiceFocalLoss(_Loss):
    """Compute both Generalized Dice Loss and Focal Loss, and return their weighted average. The details of Generalized Dice Loss
    and Focal Loss are available at ``monai.losses.GeneralizedDiceLoss`` and ``monai.losses.FocalLoss``.

    Args:
        include_background (bool, optional): if False channel index 0 (background category) is excluded from the calculation.
            Defaults to True.
        to_onehot_y: whether to convert the ``target`` into the one-hot format,
            using the number of classes inferred from `input` (``input.shape[1]``). Defaults to False.
        sigmoid (bool, optional): if True, apply a sigmoid function to the prediction. Defaults to False.
        softmax (bool, optional): if True, apply a softmax function to the prediction. Defaults to False.
        other_act (Optional[Callable], optional): callable function to execute other activation layers,
            Defaults to ``None``. for example: `other_act = torch.tanh`.
            only used by the `GeneralizedDiceLoss`, not for the `FocalLoss`.
        w_type (Union[Weight, str], optional): {``"square"``, ``"simple"``, ``"uniform"``}. Type of function to transform
            ground-truth volume to a weight factor. Defaults to ``"square"``.
        reduction (Union[LossReduction, str], optional): {``"none"``, ``"mean"``, ``"sum"``}. Specified the reduction to
            apply to the output. Defaults to ``"mean"``.
            - ``"none"``: no reduction will be applied.
            - ``"mean"``: the sum of the output will be divided by the number of elements in the output.
            - ``"sum"``: the output will be summed.
        smooth_nr (float, optional): a small constant added to the numerator to avoid zero. Defaults to 1e-5.
        smooth_dr (float, optional): a small constant added to the denominator to avoid nan. Defaults to 1e-5.
        batch (bool, optional): whether to sum the intersection and union areas over the batch dimension before the dividing.
            Defaults to False, i.e., the areas are computed for each item in the batch.
        gamma (float, optional): value of the exponent gamma in the definition of the Focal loss. Defaults to 2.0.
        weight (Optional[Union[Sequence[float], float, int, torch.Tensor]], optional): weights to apply to
            the voxels of each class. If None no weights are applied. The input can be a single value
            (same weight for all classes), a sequence of values (the length of the sequence hould be the same as
            the number of classes). Defaults to None.
        lambda_gdl (float, optional): the trade-off weight value for Generalized Dice Loss. The value should be
            no less than 0.0. Defaults to 1.0.
        lambda_focal (float, optional): the trade-off weight value for Focal Loss. The value should be no less
            than 0.0. Defaults to 1.0.

    Raises:
        ValueError: if either `lambda_gdl` or `lambda_focal` is less than 0.
    """

    def __init__(
        self,
        include_background: bool = True,
        to_onehot_y: bool = False,
        sigmoid: bool = False,
        softmax: bool = False,
        other_act: Callable | None = None,
        w_type: Weight | str = Weight.SQUARE,
        reduction: LossReduction | str = LossReduction.MEAN,
        smooth_nr: float = 1e-5,
        smooth_dr: float = 1e-5,
        batch: bool = False,
        gamma: float = 2.0,
        weight: Sequence[float] | float | int | torch.Tensor | None = None,
        lambda_gdl: float = 1.0,
        lambda_focal: float = 1.0,
    ) -> None:
        super().__init__()
        self.generalized_dice = GeneralizedDiceLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            sigmoid=sigmoid,
            softmax=softmax,
            other_act=other_act,
            w_type=w_type,
            reduction=reduction,
            smooth_nr=smooth_nr,
            smooth_dr=smooth_dr,
            batch=batch,
        )
        self.focal = FocalLoss(
            include_background=include_background,
            to_onehot_y=to_onehot_y,
            gamma=gamma,
            weight=weight,
            reduction=reduction,
        )
        if lambda_gdl < 0.0:
            raise ValueError("lambda_gdl should be no less than 0.0.")
        if lambda_focal < 0.0:
            raise ValueError("lambda_focal should be no less than 0.0.")
        self.lambda_gdl = lambda_gdl
        self.lambda_focal = lambda_focal

    def forward(self, input: torch.Tensor, target: torch.Tensor) -> torch.Tensor:
        """
        Args:
            input (torch.Tensor): the shape should be BNH[WD]. The input should be the original logits
                due to the restriction of ``monai.losses.FocalLoss``.
            target (torch.Tensor): the shape should be BNH[WD] or B1H[WD].

        Raises:
            ValueError: When number of dimensions for input and target are different.
            ValueError: When number of channels for target is neither 1 (without one-hot encoding) nor the same as input.

        Returns:
            torch.Tensor: value of the loss.
        """
        if input.dim() != target.dim():
            raise ValueError(
                "the number of dimensions for input and target should be the same, "
                f"got shape {input.shape} (nb dims: {len(input.shape)}) and {target.shape} (nb dims: {len(target.shape)}). "
                "if target is not one-hot encoded, please provide a tensor with shape B1H[WD]."
            )

        if target.shape[1] != 1 and target.shape[1] != input.shape[1]:
            raise ValueError(
                "number of channels for target is neither 1 (without one-hot encoding) nor the same as input, "
                f"got shape {input.shape} and {target.shape}."
            )

        gdl_loss = self.generalized_dice(input, target)
        focal_loss = self.focal(input, target)
        total_loss: torch.Tensor = self.lambda_gdl * gdl_loss + self.lambda_focal * focal_loss
        return total_loss


Dice = DiceLoss
dice_ce = DiceCELoss
dice_focal = DiceFocalLoss
generalized_dice = GeneralizedDiceLoss
generalized_dice_focal = GeneralizedDiceFocalLoss
generalized_wasserstein_dice = GeneralizedWassersteinDiceLoss