Understanding LocalNormalizedCrossCorrelationLoss

[ArjunNarayanan]

Hello,

I'm trying to understand how to use monai.losses.LocalNormalizedCrossCorrelationLoss for image registration. I'm finding it a little difficult to understand how to interpret this loss. For example, if I take two images and compute the LNCC loss,

from monai.losses import LocalNormalizedCrossCorrelationLoss
lncc_loss = LocalNormalizedCrossCorrelationLoss(kernel_size=3)
example_image # input image of size [B,C,128,128,128] 

self_loss = lncc_loss(example_image, example_image) # result is tensor(-0.1860) for my image

I would expect the cross-correlation of an image with itself to be $-1$ but this is not the case. When I make the kernel_size=127 (which corresponds to NCC instead of LNCC if my understanding is correct), the loss value is indeed $-1$. Can someone explain this to me?

[wyli]

thanks, I've tested this example will return -1...

import torch

from monai.losses import LocalNormalizedCrossCorrelationLoss

lncc_loss = LocalNormalizedCrossCorrelationLoss(kernel_size=3)
example_image = torch.randn(3, 2, 128, 128, 128, dtype=float)

self_loss = lncc_loss(example_image, example_image)
print(self_loss)

but example_image = torch.ones(3, 2, 128, 128, 128, dtype=float) doesn't return -1 because the small constant added

MONAI/monai/losses/image_dissimilarity.py

Lines 70 to 71 in 6de86a4

	smooth_nr: float = 0.0,
	smooth_dr: float = 1e-5,

[ArjunNarayanan]

Okay that makes sense. Since an image with all constants will have a zero variance, the LNCC will be undefined so we have to add a small smoothing constant. In my case, the image had a lot of background pixels that were constant and so this was ending up affecting the LNCC. If I compute the loss with reduction="none" and mask out the background pixels, the LNCC is indeed $-1$. Thanks for your help in understanding this :)