Morphology#

class kornia.losses.HausdorffERLoss(alpha=2.0, k=10, reduction='mean')[source]#

Hausdorff loss based on morphological erosion, one binary map per class channel.

Hausdorff Distance loss measures the maximum distance of a predicted segmentation boundary to the nearest ground-truth edge pixel. For two segmentation point sets X and Y , the one-sided HD from X to Y is defined as:

\[hd(X,Y) = \max_{x \in X} \min_{y \in Y}||x - y||_2\]

Furthermore, the bidirectional HD is:

\[HD(X,Y) = max(hd(X, Y), hd(Y, X))\]

This is an Hausdorff Distance (HD) Loss that based on morphological erosion, which provided a differentiable approximation of Hausdorff distance as stated in [KS19]. The code is refactored on top of here.

Convention:

pred holds per-class probabilities (B, C, H, W) and nothing is applied to it, unlike the logits of focal_loss(): pass a softmax. target holds int64 labels (B, 1, H, W) in [0, C). Channel c is compared with target == c, class 0 included.
The [0, C) check reads the data, so it is skipped wherever the call captures a graph (torch.compile or torch.export). A captured call whose target holds an out-of-range label scores those voxels in no class and returns a finite loss instead of raising; an eager call still raises.
reduction='none' returns (C, B, 1, H, W), class axis first; the default 'mean' is the plain mean of that tensor.
Each of the k erosions is min-max normalised per image and class and weighted by \((i + 1)^\alpha\) for \(i = 0, \dots, k - 1\): the value is a unitless surrogate, not a distance in pixels.

Parameters:

alpha (float, optional) – the exponent of the weight \((i + 1)^\alpha\) of erosion \(i = 0, \dots, k - 1\). Default: 2.0
k (int, optional) – the number of iterations of erosion. Default: 10
reduction (str, optional) – Specifies the reduction to apply to the output: ‘none’ | ‘mean’ | ‘sum’. ‘none’: no reduction will be applied, ‘mean’: the mean of the output is taken, ‘sum’: the output will be summed. Default: "mean"

Examples

>>> hdloss = HausdorffERLoss()
>>> input = torch.randn(5, 3, 20, 20).softmax(1)
>>> target = (torch.rand(5, 1, 20, 20) * 2).long()
>>> res = hdloss(input, target)

class kornia.losses.HausdorffERLoss3D(alpha=2.0, k=10, reduction='mean')[source]#

3D Hausdorff loss based on morphological erosion, one binary map per class channel.