Computing chamfer loss with mahalanobis distance

[HarshitGupta29]

Hi,

I have a gaussian point cloud and a point cloud. I want to compute chamfer loss between them, but using normal chamfer loss is not accurate. I want to replace euclidean distance with mahalanobis distance. Both point clouds are pretty large so I am hesistant to write my own function.

I can find whitening matrices for gaussian point cloud and then multiply it with the difference ||W(x-p)||. Any tricks I could use to compute this ?

Any ideas or help is appreciated!