Review for NeurIPS paper: LoopReg: Self-supervised Learning of Implicit Surface Correspondences, Pose and Shape for 3D Human Mesh Registration

Weaknesses: This is not a weakness per-say, but a suggestion to make the paper stronger. In juxtaposition to the existing work the authors present the argument several times that using a UV parameterization is inherently inferior to 3D representations, as it requires seam-cuts and results in distortion of highly curved regions, etc. While this is conceptually correct and true, it would have made the paper stronger if the authors had somehow demonstrated this to be true empirically as well for their problem. For example, perhaps via a simpler problem -- maybe for the fully-supervised case or for the case when the entire pipeline is not necessarily end-to-end differentiable, but a combination of a landmarks/correspondence estimation a traditional optimization approach. It would be interesting to see if the signed distance representation to predict correspondences with a CNN along with its Lagrangian loss formulation to encourage points to lie on the surface improves the accuracy of correspond prediction by itself and if so by how much versus an approach that learns to map scan points to the UV space instead.