Find the nearest neighbor and SVD to solve for the transformation

[BiaoBiaoLi]

Hi yewzijian: Thanks your work,I want ask two questions:

1. As for finding the nearest neighbor: group_idx[sqrdists > radius ** 2] = N group_idx = group_idx.sort(dim=-1)[0][:, :, :nsample] In the process, did you not use the 64 closest points? just took the 64 points that satisfy the distance requirement?
2. SVD to solve for the transformation: In this function below: transform = compute_rigid_transform(xyz_src, weighted_ref, weights=torch.sum(perm_matrix, dim=2)) cov = a_centered.transpose(-2, -1) @ (b_centered * weights_normalized) the cov should be cov = a_centered.transpose(-2, -1) @ b_centered ?

[yewzijian]

1. Yes, we select up to 64 points that within the desired radius as in the original PointNet++. This works better than using the closest points in practice.
2. The covariance is weighted so we scale the contribution of each correspondence by its weight.

[BiaoBiaoLi]

ok,thanks

[BiaoBiaoLi]

Thanks your answer,I also want to konw the the if the codes of RPM in your paper is open source.

[yewzijian]

I think you are referring to the license? The source code uses a MIT license, as seen in the license file in the repository.

[BiaoBiaoLi]

Sorry,I don't make myself clear. I want to konw if the codes of RPM(New algorithms for 2D and 3D point matching: pose estimation and correspondence) in your paper is open source. I can't find it in Internet.

[yewzijian]

Oh, you mean the codes of the original RPM? The author's codes can be found here. This version is written for non-rigid point cloud registration.

For the results in my paper, I used my own implementation.

[BiaoBiaoLi]

Yes,thank you so much, I find it for a long time.

[BiaoBiaoLi]

Hi yewzijian: Thanks your work,I also want to know why sinkhorn use logarithms to normalize the matrices? what i read the original RPM is showed below, it does not use logarithms.

Can you tell me what is the difference?

[yewzijian]

We perform the normalization in log space in the actual implementation for numerical stability. The operations are otherwise the same, e.g. the division in linear space is changed to subtraction in log space.

Zi Jian