`apply_affine_to_boxes` does not handle flipping properly, due to the left-closed and right-open nature of the boxes

[function2-llx]

Describe the bug apply_affine_to_boxes does not handle flipping properly, due to the left-closed and right-open nature of the boxes. That is to say, when a box is flipped, the left-closed and right-open coordinates become left-open and right closed, which should be maintained.

To be clarified, I understand that there's a flip_boxes function available, but I want to use this example for simplicity. Same issue exists for more complicated affine matrix, as long as containing flipping.

To Reproduce

import torch

from monai.apps.detection.transforms.box_ops import apply_affine_to_boxes
from monai.data import MetaTensor
import monai.transforms as mt

def main():
    for flip_axis in range(3):
        flip = mt.Flip(spatial_axis=flip_axis)
        x = torch.zeros(1, 1, 1, 1)
        flipped: MetaTensor = flip(x)
        box = torch.tensor([[0, 0, 0, 1, 1, 1]])
        box_flipped = apply_affine_to_boxes(box, flipped.affine.inverse())
        print(box_flipped)

if __name__ == '__main__':
    main()

Expected behavior Produce the same results as flip_boxes.

Actual Results

tensor([[-1,  0,  0,  0,  1,  1]])
tensor([[ 0, -1,  0,  1,  0,  1]])
tensor([[ 0,  0, -1,  1,  1,  0]])

Suggestion My suggestion for the fix is to convert the box coordinates to be closed on the both sides before applying the affine matrix, and convert them back to the desired format after applying the affine.

Additional Context

If I understand correctly, the left-closed and right open nature is suggested here: https://github.com/Project-MONAI/MONAI/blob/e1a69b03c86ce065db2816b696ea4a6b57d46435/monai/data/box_utils.py#L40-L45

Feature Request

This is not about the major topic of this issue, but by the way, I would like to mention that in the code above I calculate the inverse of the affine matrix. Currently, I only find this way works to apply arbitrary affine transform to boxes. It would be nice if apply_affine_to_boxes could do it for be internally by solving a linear equation for numerical stability.