Point registration via efficient convex relaxation

Journal Article

Point cloud registration is a fundamental task in computer graphics, and more specifically, in rigid and non-rigid shape matching. The rigid shape matching problem can be formulated as the problem of simultaneously aligning and labelling two point clouds in 3D so that they are as similar as possible. We name this problem the Procrustes matching (PM) problem. The non-rigid shape matching problem can be formulated as a higher dimensional PM problem using the functional maps method. High dimensional PM problems are difficult non-convex problems which currently can only be solved locally using iterative closest point (ICP) algorithms or similar methods. Good initialization is crucial for obtaining a good solution. We introduce a novel and efficient convex SDP (semidefinite programming) relaxation for the PM problem. The algorithm is guaranteed to return a correct global solution of the problem when matching two isometric shapes which are either asymmetric or bilaterally symmetric. We show our algorithm gives state of the art results on popular shape matching datasets. We also show that our algorithm gives state of the art results for anatomical classification of shapes. Finally we demonstrate the power of our method in aligning shape collections.

Full Text

Duke Authors

Cited Authors

  • Maron, H; Dym, N; Kezurer, I; Kovalsky, S; Lipman, Y

Published Date

  • July 11, 2016

Published In

Volume / Issue

  • 35 / 4

Electronic International Standard Serial Number (EISSN)

  • 1557-7368

International Standard Serial Number (ISSN)

  • 0730-0301

Digital Object Identifier (DOI)

  • 10.1145/2897824.2925913

Citation Source

  • Scopus