<title>Method for registration of 3-D shapes</title>

TLDR

The ICP algorithm converges monotonically to a local minimum of a mean‑square distance metric, typically reaching rapid convergence in early iterations, and is useful for registering sensed data from unfixated rigid objects against ideal geometric models. This paper presents a general, representation‑independent method for accurately and efficiently registering 3‑D shapes, including free‑form curves and surfaces. The method employs an iterative closest point framework that handles all six degrees of freedom, requires only a closest‑point routine, and achieves global minimization by testing multiple initial rotations and translations, while also enabling shape congruence checks and motion estimation between point sets. Experiments demonstrate that the algorithm can register a model and sensed data in minutes using a single initial translation and a limited set of rotations, and it performs effectively on point sets, curves, and surfaces.

Abstract

This paper describes a general purpose, representation independent method for the accurate and computationally efficient registration of 3-D shapes including free-form curves and surfaces. The method handles the full six-degrees of freedom and is based on the iterative closest point (ICP) algorithm, which requires only a procedure to find the closest point on a geometric entity to a given point. The ICP algorithm always converges monotonically to the nearest local minimum of a mean-square distance metric, and experience shows that the rate of convergence is rapid during the first few iterations. Therefore, given an adequate set of initial rotations and translations for a particular class of objects with a certain level of 'shape complexity', one can globally minimize the mean-square distance metric over all six degrees of freedom by testing each initial registration. For examples, a given 'model' shape and a sensed 'data' shape that represents a major portion of the model shape can be registered in minutes by testing one initial translation and a relatively small set of rotations to allow for the given level of model complexity. One important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection. The described method is also useful for deciding fundamental issues such as the congruence (shape equivalence) of different geometric representations as well as for estimating the motion between point sets where the correspondences are not known. Experimental results show the capabilities of the registration algorithm on point sets, curves, and surfaces.