3D Registration of Curves and Surfaces using Local Differential Information

TL;DR

This paper introduces a novel global method for registering 3D curves with surfaces using local differential information, achieving fast and accurate alignment without initialization, even with small overlaps and many outliers.

Contribution

It presents the first effective global registration algorithm for 3D curves and surfaces using point+vector pairs, with a closed-form solution and a fast correspondence search.

Findings

Accurate registration achieved in seconds.

Effective handling of small overlaps and outliers.

Extension to curve-curve and surface-surface registration.

Abstract

This article presents for the first time a global method for registering 3D curves with 3D surfaces without requiring an initialization. The algorithm works with 2-tuples point+vector that consist in pairs of points augmented with the information of their tangents or normals. A closed-form solution for determining the alignment transformation from a pair of matching 2-tuples is proposed. In addition, the set of necessary conditions for two 2-tuples to match is derived. This allows fast search of correspondences that are used in an hypothesise-and-test framework for accomplishing global registration. Comparative experiments demonstrate that the proposed algorithm is the first effective solution for curve vs surface registration, with the method achieving accurate alignment in situations of small overlap and large percentage of outliers in a fraction of a second. The proposed framework is extended to the cases of curve vs curve and surface vs surface registration, with the former being particularly relevant since it is also a largely unsolved problem.