Jaccard, Dice and Tversky losses are incompatible with soft labels

[zifuwanggg]

Describe the bug
The Jaccard, Dice and Tversky losses are incompatible with soft labels [1, 2]. For example, with a ground truth value of 0.5 for a single pixel, the Dice loss is minimized when the predicted value is 1, which is clearly erroneous.

To Reproduce

import torch
from monai.losses.dice import DiceLoss
from monai.losses.tversky import TverskyLoss

torch.manual_seed(0)

B, C, H, W = 7, 5, 3, 2
input = torch.rand(B, C, H, W).softmax(1)
jaccard_loss = DiceLoss(jaccard=True, reduction='mean')
dice_loss = DiceLoss(reduction='mean')
tversky_loss = TverskyLoss(reduction='mean')

jaccard_loss_value = jaccard_loss(input, input)
dice_loss_value = dice_loss(input, input)
tversky_loss_value = tversky_loss(input, input)

print(jaccard_loss_value, dice_loss_value, tversky_loss_value)

# tensor(0.8817) tensor(0.7888) tensor(0.7888)

Expected behavior
When the input is equal to the target, the loss should be minimized and equals 0.

Environment

================================
Printing MONAI config...
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MONAI version: 0+unknown
Numpy version: 1.26.4
Pytorch version: 2.2.2
MONAI flags: HAS_EXT = False, USE_COMPILED = False, USE_META_DICT = False
MONAI rev id: 25589c377ac63d6be28ab9bb65dd8cb52f2bebdf
MONAI __file__: /Users/<username>/Desktop/loss/MONAI-dev/monai/__init__.py

Optional dependencies:
Pytorch Ignite version: 0.4.11
ITK version: 5.4.0
Nibabel version: 5.2.1
scikit-image version: 0.24.0
scipy version: 1.13.1
Pillow version: 10.4.0
Tensorboard version: 2.17.1
gdown version: 5.2.0
TorchVision version: 0.17.2
tqdm version: 4.66.5
lmdb version: 1.5.1
psutil version: 6.0.0
pandas version: 2.2.2
einops version: 0.8.0
transformers version: 4.40.2
mlflow version: 2.16.2
pynrrd version: 1.0.0
clearml version: 1.16.5rc0

For details about installing the optional dependencies, please visit:
    https://docs.monai.io/en/latest/installation.html#installing-the-recommended-dependencies


================================
Printing system config...
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System: Darwin
Mac version: 10.16
Platform: macOS-10.16-x86_64-i386-64bit
Processor: i386
Machine: x86_64
Python version: 3.9.19
Process name: python3.9
Command: ['python', '-c', 'import monai; monai.config.print_debug_info()']
Open files: []
Num physical CPUs: 8
Num logical CPUs: 8
Num usable CPUs: UNKNOWN for given OS
CPU usage (%): [55.2, 54.9, 31.8, 54.8, 12.8, 13.5, 7.7, 7.0]
CPU freq. (MHz): 2400
Load avg. in last 1, 5, 15 mins (%): [59.1, 62.0, 55.6]
Disk usage (%): 95.6
Avg. sensor temp. (Celsius): UNKNOWN for given OS
Total physical memory (GB): 16.0
Available memory (GB): 1.3
Used memory (GB): 1.9

================================
Printing GPU config...
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Num GPUs: 0
Has CUDA: False
cuDNN enabled: False
NVIDIA_TF32_OVERRIDE: None
TORCH_ALLOW_TF32_CUBLAS_OVERRIDE: None

References
[1] Dice Semimetric Losses: Optimizing the Dice Score with Soft Labels. Zifu Wang, Teodora Popordanoska, Jeroen Bertels, Robin Lemmens, Matthew B. Blaschko. MICCAI 2023.

[2] Jaccard Metric Losses: Optimizing the Jaccard Index with Soft Labels. Zifu Wang, Xuefei Ning, Matthew B. Blaschko. NeurIPS 2023.

[coolteemf]

Using squared_pred=True fixes this issue, though I don't know why it isn't True by default.

[zifuwanggg]

L1 and L2 norms will yield different versions of the loss functions. The issue exists for the L1 version, but not for the L2 version. However, the L1 version is more widely used and often leads to better results. [2, 3] provides a comparison of the two.

References
[2] Jaccard Metric Losses: Optimizing the Jaccard Index with Soft Labels. Zifu Wang, Xuefei Ning, Matthew B. Blaschko. NeurIPS 2023.

[3] Optimization for Medical Image Segmentation: Theory and Practice When Evaluating With Dice Score or Jaccard Index. Eelbode et al. TMI 2020.