# Source code for monai.metrics.surface_dice

```
# 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
from collections.abc import Sequence
from typing import Any
import numpy as np
import torch
from monai.metrics.utils import do_metric_reduction, get_edge_surface_distance, ignore_background, prepare_spacing
from monai.utils import MetricReduction
from .metric import CumulativeIterationMetric
[docs]
class SurfaceDiceMetric(CumulativeIterationMetric):
"""
Computes the Normalized Surface Dice (NSD) for each batch sample and class of
predicted segmentations `y_pred` and corresponding reference segmentations `y` according to equation :eq:`nsd`.
This implementation is based on https://arxiv.org/abs/2111.05408 and supports 2D and 3D images.
Be aware that by default (`use_subvoxels=False`), the computation of boundaries is different from DeepMind's
implementation https://github.com/deepmind/surface-distance.
In this implementation, the length/area of a segmentation boundary is
interpreted as the number of its edge pixels. In DeepMind's implementation, the length of a segmentation boundary
depends on the local neighborhood (cf. https://arxiv.org/abs/1809.04430).
This issue is discussed here: https://github.com/Project-MONAI/MONAI/issues/4103.
The class- and batch sample-wise NSD values can be aggregated with the function `aggregate`.
Example of the typical execution steps of this metric class follows :py:class:`monai.metrics.metric.Cumulative`.
Args:
class_thresholds: List of class-specific thresholds.
The thresholds relate to the acceptable amount of deviation in the segmentation boundary in pixels.
Each threshold needs to be a finite, non-negative number.
include_background: Whether to include NSD computation on the first channel of the predicted output.
Defaults to ``False``.
distance_metric: The metric used to compute surface distances.
One of [``"euclidean"``, ``"chessboard"``, ``"taxicab"``].
Defaults to ``"euclidean"``.
reduction: define mode of reduction to the metrics, will only apply reduction on `not-nan` values,
available reduction modes: {``"none"``, ``"mean"``, ``"sum"``, ``"mean_batch"``, ``"sum_batch"``,
``"mean_channel"``, ``"sum_channel"``}, default to ``"mean"``. if "none", will not do reduction.
get_not_nans: whether to return the `not_nans` count.
Defaults to ``False``.
`not_nans` is the number of batch samples for which not all class-specific NSD values were nan values.
If set to ``True``, the function `aggregate` will return both the aggregated NSD and the `not_nans` count.
If set to ``False``, `aggregate` will only return the aggregated NSD.
use_subvoxels: Whether to use subvoxel distances. Defaults to ``False``.
"""
def __init__(
self,
class_thresholds: list[float],
include_background: bool = False,
distance_metric: str = "euclidean",
reduction: MetricReduction | str = MetricReduction.MEAN,
get_not_nans: bool = False,
use_subvoxels: bool = False,
) -> None:
super().__init__()
self.class_thresholds = class_thresholds
self.include_background = include_background
self.distance_metric = distance_metric
self.reduction = reduction
self.get_not_nans = get_not_nans
self.use_subvoxels = use_subvoxels
def _compute_tensor(self, y_pred: torch.Tensor, y: torch.Tensor, **kwargs: Any) -> torch.Tensor: # type: ignore[override]
r"""
Args:
y_pred: Predicted segmentation, typically segmentation model output.
It must be a one-hot encoded, batch-first tensor [B,C,H,W] or [B,C,H,W,D].
y: Reference segmentation.
It must be a one-hot encoded, batch-first tensor [B,C,H,W] or [B,C,H,W,D].
kwargs: additional parameters: ``spacing`` should be passed to correctly compute the metric.
``spacing``: spacing of pixel (or voxel). This parameter is relevant only
if ``distance_metric`` is set to ``"euclidean"``.
If a single number, isotropic spacing with that value is used for all images in the batch. If a sequence of numbers,
the length of the sequence must be equal to the image dimensions.
This spacing will be used for all images in the batch.
If a sequence of sequences, the length of the outer sequence must be equal to the batch size.
If inner sequence has length 1, isotropic spacing with that value is used for all images in the batch,
else the inner sequence length must be equal to the image dimensions. If ``None``, spacing of unity is used
for all images in batch. Defaults to ``None``.
use_subvoxels: Whether to use subvoxel distances. Defaults to ``False``.
Returns:
Pytorch Tensor of shape [B,C], containing the NSD values :math:`\operatorname {NSD}_{b,c}` for each batch
index :math:`b` and class :math:`c`.
"""
return compute_surface_dice(
y_pred=y_pred,
y=y,
class_thresholds=self.class_thresholds,
include_background=self.include_background,
distance_metric=self.distance_metric,
spacing=kwargs.get("spacing"),
use_subvoxels=self.use_subvoxels,
)
[docs]
def aggregate(
self, reduction: MetricReduction | str | None = None
) -> torch.Tensor | tuple[torch.Tensor, torch.Tensor]:
r"""
Aggregates the output of `_compute_tensor`.
Args:
reduction: define mode of reduction to the metrics, will only apply reduction on `not-nan` values,
available reduction modes: {``"none"``, ``"mean"``, ``"sum"``, ``"mean_batch"``, ``"sum_batch"``,
``"mean_channel"``, ``"sum_channel"``}, default to `self.reduction`. if "none", will not do reduction.
Returns:
If `get_not_nans` is set to ``True``, this function returns the aggregated NSD and the `not_nans` count.
If `get_not_nans` is set to ``False``, this function returns only the aggregated NSD.
"""
data = self.get_buffer()
if not isinstance(data, torch.Tensor):
raise ValueError("the data to aggregate must be PyTorch Tensor.")
# do metric reduction
f, not_nans = do_metric_reduction(data, reduction or self.reduction)
return (f, not_nans) if self.get_not_nans else f
[docs]
def compute_surface_dice(
y_pred: torch.Tensor,
y: torch.Tensor,
class_thresholds: list[float],
include_background: bool = False,
distance_metric: str = "euclidean",
spacing: int | float | np.ndarray | Sequence[int | float | np.ndarray | Sequence[int | float]] | None = None,
use_subvoxels: bool = False,
) -> torch.Tensor:
r"""
This function computes the (Normalized) Surface Dice (NSD) between the two tensors `y_pred` (referred to as
:math:`\hat{Y}`) and `y` (referred to as :math:`Y`). This metric determines which fraction of a segmentation
boundary is correctly predicted. A boundary element is considered correctly predicted if the closest distance to the
reference boundary is smaller than or equal to the specified threshold related to the acceptable amount of deviation
in pixels. The NSD is bounded between 0 and 1.
This implementation supports multi-class tasks with an individual threshold :math:`\tau_c` for each class :math:`c`.
The class-specific NSD for batch index :math:`b`, :math:`\operatorname {NSD}_{b,c}`, is computed using the function:
.. math::
\operatorname {NSD}_{b,c} \left(Y_{b,c}, \hat{Y}_{b,c}\right) = \frac{\left|\mathcal{D}_{Y_{b,c}}^{'}\right| +
\left| \mathcal{D}_{\hat{Y}_{b,c}}^{'} \right|}{\left|\mathcal{D}_{Y_{b,c}}\right| +
\left|\mathcal{D}_{\hat{Y}_{b,c}}\right|}
:label: nsd
with :math:`\mathcal{D}_{Y_{b,c}}` and :math:`\mathcal{D}_{\hat{Y}_{b,c}}` being two sets of nearest-neighbor
distances. :math:`\mathcal{D}_{Y_{b,c}}` is computed from the predicted segmentation boundary towards the reference
segmentation boundary and vice-versa for :math:`\mathcal{D}_{\hat{Y}_{b,c}}`. :math:`\mathcal{D}_{Y_{b,c}}^{'}` and
:math:`\mathcal{D}_{\hat{Y}_{b,c}}^{'}` refer to the subsets of distances that are smaller or equal to the
acceptable distance :math:`\tau_c`:
.. math::
\mathcal{D}_{Y_{b,c}}^{'} = \{ d \in \mathcal{D}_{Y_{b,c}} \, | \, d \leq \tau_c \}.
In the case of a class neither being present in the predicted segmentation, nor in the reference segmentation,
a nan value will be returned for this class. In the case of a class being present in only one of predicted
segmentation or reference segmentation, the class NSD will be 0.
This implementation is based on https://arxiv.org/abs/2111.05408 and supports 2D and 3D images.
The computation of boundaries follows DeepMind's implementation
https://github.com/deepmind/surface-distance when `use_subvoxels=True`; Otherwise the length of a segmentation
boundary is interpreted as the number of its edge pixels.
Args:
y_pred: Predicted segmentation, typically segmentation model output.
It must be a one-hot encoded, batch-first tensor [B,C,H,W] or [B,C,H,W,D].
y: Reference segmentation.
It must be a one-hot encoded, batch-first tensor [B,C,H,W] or [B,C,H,W,D].
class_thresholds: List of class-specific thresholds.
The thresholds relate to the acceptable amount of deviation in the segmentation boundary in pixels.
Each threshold needs to be a finite, non-negative number.
include_background: Whether to include the surface dice computation on the first channel of
the predicted output. Defaults to ``False``.
distance_metric: The metric used to compute surface distances.
One of [``"euclidean"``, ``"chessboard"``, ``"taxicab"``].
Defaults to ``"euclidean"``.
spacing: spacing of pixel (or voxel). This parameter is relevant only if ``distance_metric`` is set to ``"euclidean"``.
If a single number, isotropic spacing with that value is used for all images in the batch. If a sequence of numbers,
the length of the sequence must be equal to the image dimensions. This spacing will be used for all images in the batch.
If a sequence of sequences, the length of the outer sequence must be equal to the batch size.
If inner sequence has length 1, isotropic spacing with that value is used for all images in the batch,
else the inner sequence length must be equal to the image dimensions. If ``None``, spacing of unity is used
for all images in batch. Defaults to ``None``.
use_subvoxels: Whether to use subvoxel distances. Defaults to ``False``.
Raises:
ValueError: If `y_pred` and/or `y` are not PyTorch tensors.
ValueError: If `y_pred` and/or `y` do not have four dimensions.
ValueError: If `y_pred` and/or `y` have different shapes.
ValueError: If `y_pred` and/or `y` are not one-hot encoded
ValueError: If the number of channels of `y_pred` and/or `y` is different from the number of class thresholds.
ValueError: If any class threshold is not finite.
ValueError: If any class threshold is negative.
Returns:
Pytorch Tensor of shape [B,C], containing the NSD values :math:`\operatorname {NSD}_{b,c}` for each batch index
:math:`b` and class :math:`c`.
"""
if not include_background:
y_pred, y = ignore_background(y_pred=y_pred, y=y)
if not isinstance(y_pred, torch.Tensor) or not isinstance(y, torch.Tensor):
raise ValueError("y_pred and y must be PyTorch Tensor.")
if y_pred.ndimension() not in (4, 5) or y.ndimension() not in (4, 5):
raise ValueError("y_pred and y should be one-hot encoded: [B,C,H,W] or [B,C,H,W,D].")
if y_pred.shape != y.shape:
raise ValueError(
f"y_pred and y should have same shape, but instead, shapes are {y_pred.shape} (y_pred) and {y.shape} (y)."
)
batch_size, n_class = y_pred.shape[:2]
if n_class != len(class_thresholds):
raise ValueError(
f"number of classes ({n_class}) does not match number of class thresholds ({len(class_thresholds)})."
)
if any(~np.isfinite(class_thresholds)):
raise ValueError("All class thresholds need to be finite.")
if any(np.array(class_thresholds) < 0):
raise ValueError("All class thresholds need to be >= 0.")
nsd = torch.empty((batch_size, n_class), device=y_pred.device, dtype=torch.float)
img_dim = y_pred.ndim - 2
spacing_list = prepare_spacing(spacing=spacing, batch_size=batch_size, img_dim=img_dim)
for b, c in np.ndindex(batch_size, n_class):
(edges_pred, edges_gt), (distances_pred_gt, distances_gt_pred), areas = get_edge_surface_distance( # type: ignore
y_pred[b, c],
y[b, c],
distance_metric=distance_metric,
spacing=spacing_list[b],
use_subvoxels=use_subvoxels,
symmetric=True,
class_index=c,
)
boundary_correct: int | torch.Tensor | float
boundary_complete: int | torch.Tensor | float
if not use_subvoxels:
boundary_complete = len(distances_pred_gt) + len(distances_gt_pred)
boundary_correct = torch.sum(distances_pred_gt <= class_thresholds[c]) + torch.sum(
distances_gt_pred <= class_thresholds[c]
)
else:
areas_pred, areas_gt = areas # type: ignore
areas_gt, areas_pred = areas_gt[edges_gt], areas_pred[edges_pred]
boundary_complete = areas_gt.sum() + areas_pred.sum()
gt_true = areas_gt[distances_gt_pred <= class_thresholds[c]].sum() if len(areas_gt) > 0 else 0.0
pred_true = areas_pred[distances_pred_gt <= class_thresholds[c]].sum() if len(areas_pred) > 0 else 0.0
boundary_correct = gt_true + pred_true
if boundary_complete == 0:
# the class is neither present in the prediction, nor in the reference segmentation
nsd[b, c] = torch.tensor(np.nan)
else:
nsd[b, c] = boundary_correct / boundary_complete
return nsd
```