This submission received mixed ratings. The most positive reviewers has a non confident rating. R1 and R2 appreciate that the paper is well written and presents an interesting approach to image registration. R1 and R3 point out that the central contribution is not clearly stated in the text. Also overlap of text in sections 3.1-3.3 with previous work exists. In the discussion R3 argues that the paper combines previous work in 3.1/3.2 which limits the novelty and in addition that more clarification and extensive testing is required. R1 agrees that the theoretical section is rather confusing. The authors agree that there is overlap in Section 3.3 with DenseSDF and Occupancy Networks which they rate as not problematic as CVPR19 release was after the NeurIPS submission deadline. Most reviewers agree that there is value to the the combined method presented but exposition needs to be improved. With confidence in that the authors will do as promised in the rebuttal and revise the entire Section 3 and add references therein the agreement was to accept this submission. The novelty part of the submission are sufficient, but the presentation of the paper needs to be improved along the review remarks.