# Source code for monai.metrics.hausdorff_distance

```# Copyright (c) MONAI Consortium
# you may not use this file except in compliance with the License.
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# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

import warnings
from typing import Optional, Union

import numpy as np
import torch

from monai.metrics.utils import (
do_metric_reduction,
get_surface_distance,
ignore_background,
is_binary_tensor,
)
from monai.utils import MetricReduction

from .metric import CumulativeIterationMetric

__all__ = ["HausdorffDistanceMetric", "compute_hausdorff_distance", "compute_percent_hausdorff_distance"]

[docs]class HausdorffDistanceMetric(CumulativeIterationMetric):
"""
Compute Hausdorff Distance between two tensors. It can support both multi-classes and multi-labels tasks.
It supports both directed and non-directed Hausdorff distance calculation. In addition, specify the `percentile`
parameter can get the percentile of the distance. Input `y_pred` is compared with ground truth `y`.
`y_preds` is expected to have binarized predictions and `y` should be in one-hot format.
You can use suitable transforms in ``monai.transforms.post`` first to achieve binarized values.
`y_preds` and `y` can be a list of channel-first Tensor (CHW[D]) or a batch-first Tensor (BCHW[D]).
The implementation refers to `DeepMind's implementation <https://github.com/deepmind/surface-distance>`_.

Example of the typical execution steps of this metric class follows :py:class:`monai.metrics.metric.Cumulative`.

Args:
include_background: whether to include distance computation on the first channel of
the predicted output. Defaults to ``False``.
distance_metric: : [``"euclidean"``, ``"chessboard"``, ``"taxicab"``]
the metric used to compute surface distance. Defaults to ``"euclidean"``.
percentile: an optional float number between 0 and 100. If specified, the corresponding
percentile of the Hausdorff Distance rather than the maximum result will be achieved.
Defaults to ``None``.
directed: whether to calculate directed Hausdorff distance. Defaults to ``False``.
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, if True, aggregate() returns (metric, not_nans).
Here `not_nans` count the number of not nans for the metric, thus its shape equals to the shape of the metric.

"""

def __init__(
self,
include_background: bool = False,
distance_metric: str = "euclidean",
percentile: Optional[float] = None,
directed: bool = False,
reduction: Union[MetricReduction, str] = MetricReduction.MEAN,
get_not_nans: bool = False,
) -> None:
super().__init__()
self.include_background = include_background
self.distance_metric = distance_metric
self.percentile = percentile
self.directed = directed
self.reduction = reduction
self.get_not_nans = get_not_nans

def _compute_tensor(self, y_pred: torch.Tensor, y: torch.Tensor):  # type: ignore
"""
Args:
y_pred: input data to compute, typical segmentation model output.
It must be one-hot format and first dim is batch, example shape: [16, 3, 32, 32]. The values
should be binarized.
y: ground truth to compute the distance. It must be one-hot format and first dim is batch.
The values should be binarized.

Raises:
ValueError: when `y` is not a binarized tensor.
ValueError: when `y_pred` has less than three dimensions.
"""
is_binary_tensor(y_pred, "y_pred")
is_binary_tensor(y, "y")

dims = y_pred.ndimension()
if dims < 3:
raise ValueError("y_pred should have at least three dimensions.")
# compute (BxC) for each channel for each batch
return compute_hausdorff_distance(
y_pred=y_pred,
y=y,
include_background=self.include_background,
distance_metric=self.distance_metric,
percentile=self.percentile,
directed=self.directed,
)

[docs]    def aggregate(self, reduction: Union[MetricReduction, str, None] = None):
"""
Execute reduction logic for the output of `compute_hausdorff_distance`.

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.

"""
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_hausdorff_distance(
y_pred: Union[np.ndarray, torch.Tensor],
y: Union[np.ndarray, torch.Tensor],
include_background: bool = False,
distance_metric: str = "euclidean",
percentile: Optional[float] = None,
directed: bool = False,
):
"""
Compute the Hausdorff distance.

Args:
y_pred: input data to compute, typical segmentation model output.
It must be one-hot format and first dim is batch, example shape: [16, 3, 32, 32]. The values
should be binarized.
y: ground truth to compute mean the distance. It must be one-hot format and first dim is batch.
The values should be binarized.
include_background: whether to skip distance computation on the first channel of
the predicted output. Defaults to ``False``.
distance_metric: : [``"euclidean"``, ``"chessboard"``, ``"taxicab"``]
the metric used to compute surface distance. Defaults to ``"euclidean"``.
percentile: an optional float number between 0 and 100. If specified, the corresponding
percentile of the Hausdorff Distance rather than the maximum result will be achieved.
Defaults to ``None``.
directed: whether to calculate directed Hausdorff distance. Defaults to ``False``.
"""

if not include_background:
y_pred, y = ignore_background(y_pred=y_pred, y=y)
if isinstance(y, torch.Tensor):
y = y.float()
if isinstance(y_pred, torch.Tensor):
y_pred = y_pred.float()

if y.shape != y_pred.shape:
raise ValueError(f"y_pred and y should have same shapes, got {y_pred.shape} and {y.shape}.")

batch_size, n_class = y_pred.shape[:2]
hd = np.empty((batch_size, n_class))
for b, c in np.ndindex(batch_size, n_class):
(edges_pred, edges_gt) = get_mask_edges(y_pred[b, c], y[b, c])
if not np.any(edges_gt):
warnings.warn(f"the ground truth of class {c} is all 0, this may result in nan/inf distance.")
if not np.any(edges_pred):
warnings.warn(f"the prediction of class {c} is all 0, this may result in nan/inf distance.")

distance_1 = compute_percent_hausdorff_distance(edges_pred, edges_gt, distance_metric, percentile)
if directed:
hd[b, c] = distance_1
else:
distance_2 = compute_percent_hausdorff_distance(edges_gt, edges_pred, distance_metric, percentile)
hd[b, c] = max(distance_1, distance_2)

[docs]def compute_percent_hausdorff_distance(
edges_pred: np.ndarray, edges_gt: np.ndarray, distance_metric: str = "euclidean", percentile: Optional[float] = None
):
"""
This function is used to compute the directed Hausdorff distance.
"""

surface_distance = get_surface_distance(edges_pred, edges_gt, distance_metric=distance_metric)

# for both pred and gt do not have foreground
if surface_distance.shape == (0,):
return np.nan

if not percentile:
return surface_distance.max()

if 0 <= percentile <= 100:
return np.percentile(surface_distance, percentile)
raise ValueError(f"percentile should be a value between 0 and 100, get {percentile}.")
```