Hi K. Frank,

Thanks for your explanation. I would like to validate my approach of getting the `counts`

in the sample code above and some of my concerns for volumetric CT data.

```
import torch
torch.manual_seed(3)
image = torch.randint(low=0, high=2, size=(3, 3), dtype=torch.float32)
labelA = torch.randint(low=0, high=2, size=(3, 3), dtype=torch.float32)
labelB = torch.randint(low=0, high=2, size=(3, 3), dtype=torch.float32)
```

Generating the background label from the annotated label A & B i.e 0 in pixel value where either A or B is 1 and 1 elsewhere

```
background = torch.zeros((labelB.shape), dtype=torch.long)
for label in [labelA, labelB]:
background |= background.long()
background = background^1
outputs = f"Image: {image},\n background: {background}, \n labelA: {labelA}, \n labelB: {labelB}"
print(outputs)
```

```
>>> outputs
Image: tensor([[0.0043, 0.1056, 0.2858],
[0.0270, 0.4716, 0.0601],
[0.7719, 0.7437, 0.5944]]),
background: tensor([[0, 1, 0],
[0, 0, 1],
[0, 0, 0]]),
labelA: tensor([[1., 0., 1.],
[1., 1., 0.],
[1., 1., 0.]]),
labelB: tensor([[0., 0., 0.],
[1., 1., 0.],
[0., 0., 1.]])
```

```
counts = torch.tensor([torch.sum(background), torch.sum(labelA), torch.sum(labelB)])
weights = 1.0 / counts
weights_normalized = (1.0 / counts) / (1.0 / counts).sum()
```

```
>>> counts
tensor([4., 3., 4.])
>>> weights
tensor([0.2500, 0.3333, 0.2500])
>>>weights_normalized
tensor([0.3000, 0.4000, 0.3000])
```

These weights can now be passed into the loss function. My concerns are:

- I believe my approach of creating the background is not well optimized, is there an inbuilt PyTorch function that can be used or another way around it?
- Is it computationally efficient to create the background label class (for each corresponding image and label A/B) in the data loader or separately create it out the data loader, save it (.npy), and then reference it just like the label class A & B?

Thanks for your enlightenment