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("y_pred and y should have same shapes.")
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)
return torch.from_numpy(hd)
def compute_average_surface_distance(
y_pred: Union[np.ndarray, torch.Tensor],
y: Union[np.ndarray, torch.Tensor],
include_background: bool = False,
symmetric: bool = False,
distance_metric: str = "euclidean",
):
"""
This function is used to compute the Average Surface Distance from `y_pred` to `y`
under the default setting.
In addition, if sets ``symmetric = True``, the average symmetric surface distance between
these two inputs will be returned.
The implementation refers to `DeepMind's implementation <https://github.com/deepmind/surface-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``.
symmetric: whether to calculate the symmetric average surface distance between
`seg_pred` and `seg_gt`. Defaults to ``False``.
distance_metric: : [``"euclidean"``, ``"chessboard"``, ``"taxicab"``]
the metric used to compute surface distance. Defaults to ``"euclidean"``.
"""
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]
asd = 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."
)
surface_distance = get_surface_distance(
edges_pred, edges_gt, distance_metric=distance_metric)
if symmetric:
surface_distance_2 = get_surface_distance(
edges_gt, edges_pred, distance_metric=distance_metric)
surface_distance = np.concatenate(
[surface_distance, surface_distance_2])
asd[b, c] = np.nan if surface_distance.shape == (
0, ) else surface_distance.mean()
return convert_data_type(asd, torch.Tensor)[0]
def compute_average_surface_distance(
y_pred: Union[np.ndarray, torch.Tensor],
y: Union[np.ndarray, torch.Tensor],
include_background: bool = False,
symmetric: bool = False,
distance_metric: str = "euclidean",
):
"""
This function is used to compute the Average Surface Distance from `y_pred` to `y`
under the default setting.
In addition, if sets ``symmetric = True``, the average symmetric surface distance between
these two inputs will be returned.
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``.
symmetric: whether to calculate the symmetric average surface distance between
`seg_pred` and `seg_gt`. Defaults to ``False``.
distance_metric: : [``"euclidean"``, ``"chessboard"``, ``"taxicab"``]
the metric used to compute surface distance. Defaults to ``"euclidean"``.
"""
if not include_background:
y_pred, y = ignore_background(
y_pred=y_pred,
y=y,
)
y = y.float()
y_pred = y_pred.float()
if y.shape != y_pred.shape:
raise ValueError("y_pred and y should have same shapes.")
batch_size, n_class = y_pred.shape[:2]
asd = 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])
surface_distance = get_surface_distance(
edges_pred, edges_gt, distance_metric=distance_metric)
if surface_distance.shape == (0, ):
avg_surface_distance = np.nan
else:
avg_surface_distance = surface_distance.mean()
if not symmetric:
asd[b, c] = avg_surface_distance
else:
surface_distance_2 = get_surface_distance(
edges_gt, edges_pred, distance_metric=distance_metric)
if surface_distance_2.shape == (0, ):
avg_surface_distance_2 = np.nan
else:
avg_surface_distance_2 = surface_distance_2.mean()
asd[b, c] = np.mean((avg_surface_distance, avg_surface_distance_2))
return torch.from_numpy(asd)
def compute_surface_dice(
y_pred: torch.Tensor,
y: torch.Tensor,
class_thresholds: List[float],
include_background: bool = False,
distance_metric: str = "euclidean",
):
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 images.
Be aware that the computation of boundaries is different from DeepMind's implementation
https://github.com/deepmind/surface-distance. In this implementation, the length 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).
Args:
y_pred: Predicted segmentation, typically segmentation model output.
It must be a one-hot encoded, batch-first tensor [B,C,H,W].
y: Reference segmentation.
It must be a one-hot encoded, batch-first tensor [B,C,H,W].
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 skip 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"``.
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() != 4 or y.ndimension() != 4:
raise ValueError(
"y_pred and y should have four dimensions: [B,C,H,W].")
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)."
)
if not torch.all(y_pred.byte() == y_pred) or not torch.all(y.byte() == y):
raise ValueError(
"y_pred and y should be binarized tensors (e.g. torch.int64).")
if torch.any(y_pred > 1) or torch.any(y > 1):
raise ValueError("y_pred and y should be one-hot encoded.")
y = y.float()
y_pred = y_pred.float()
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 = 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],
crop=False)
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."
)
distances_pred_gt = get_surface_distance(
edges_pred, edges_gt, distance_metric=distance_metric)
distances_gt_pred = get_surface_distance(
edges_gt, edges_pred, distance_metric=distance_metric)
boundary_complete = len(distances_pred_gt) + len(distances_gt_pred)
boundary_correct = np.sum(
distances_pred_gt <= class_thresholds[c]) + np.sum(
distances_gt_pred <= class_thresholds[c])
if boundary_complete == 0:
# the class is neither present in the prediction, nor in the reference segmentation
nsd[b, c] = np.nan
else:
nsd[b, c] = boundary_correct / boundary_complete
return convert_data_type(nsd, torch.Tensor)[0]
