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...
================================
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...
================================
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...
================================
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.