Scale-Invariant Fast Functional Registration

TL;DR

This paper introduces FLS, a fast, scale-invariant functional registration algorithm that operates in linear time, effectively aligning point clouds with unknown scale, noise, and partial overlaps, outperforming existing methods in speed and accuracy.

Contribution

The paper presents a novel scale-invariant, linear time complexity functional registration method using orthonormal basis functions and least-squares formulation, enabling efficient and robust 3D point cloud registration.

Findings

FLS is an order of magnitude faster than existing functional registration algorithms.

FLS outperforms state-of-the-art methods in accuracy and robustness, even with unknown scale.

FLS effectively handles noisy, partial, and varying density point clouds from real-world data.

Abstract

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.