Scale-Invariant Fast Functional Registration

Muchen Sun*, Allison Pinosky, Ian Abraham, Todd Murphey

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Functional registration algorithms represent point clouds as functions (e.g. spacial occupancy field) avoiding unreliable correspondence estimation in conventional least-squares registration algorithms. However, existing functional registration algorithms are computationally expensive. Furthermore, the capability of registration with unknown scale is necessary in tasks such as CAD model-based object localization, yet no such support exists in functional registration. In this work, we propose a scale-invariant, linear time complexity functional registration algorithm. We achieve linear time complexity through an efficient approximation of L2 -distance between functions using orthonormal basis functions. The use of orthonormal basis functions leads to a formulation that is compatible with least-squares registration. Benefited from the least-square formulation, we use the theory of translation-rotation-invariant measurement to decouple scale estimation and therefore achieve scale-invariant registration. We evaluate the proposed algorithm, named FLS (functional least-squares), on standard 3D registration benchmarks, showing FLS is an order of magnitude faster than state-of-the-art functional registration algorithm without compromising accuracy and robustness. FLS also outperforms state-of-the-art correspondence-based least-squares registration algorithm on accuracy and robustness, with known and unknown scale. Finally, we demonstrate applying FLS to register point clouds with varying densities and partial overlaps, point clouds from different objects within the same category, and point clouds from real world objects with noisy RGB-D measurements.

Original languageEnglish (US)
Title of host publicationRobotics Research
EditorsAude Billard, Tamim Asfour, Oussama Khatib
PublisherSpringer Nature
Number of pages17
ISBN (Print)9783031255540
StatePublished - 2023
Event18th International Symposium of Robotics Research, ISRR 2022 - Geneva, Switzerland
Duration: Sep 25 2022Sep 30 2022

Publication series

NameSpringer Proceedings in Advanced Robotics
Volume27 SPAR
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264


Conference18th International Symposium of Robotics Research, ISRR 2022

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Mechanical Engineering
  • Engineering (miscellaneous)
  • Artificial Intelligence
  • Computer Science Applications
  • Applied Mathematics


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