Robust Point Set Registration Using Gaussian Mixture Models

TLDR

The paper proposes a unified framework for rigid and nonrigid point set registration that handles significant noise and outliers. The framework models point sets as Gaussian mixture models and aligns them by minimizing a closed‑form L2 discrepancy, yielding a computationally efficient algorithm that is compared theoretically and experimentally to other robust methods. The algorithm is shown to be statistically robust, intuitively interpretable, easy to implement, and performs comparably to or better than existing methods such as ICP, as demonstrated by theoretical analysis and experiments.

Abstract

In this paper, we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers. The key idea of this registration framework is to represent the input point sets using Gaussian mixture models. Then, the problem of point set registration is reformulated as the problem of aligning two Gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized. We show that the popular iterative closest point (ICP) method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework. Our instantiation of this general framework is based on the the L2 distance between two Gaussian mixtures, which has the closed-form expression and in turn leads to a computationally efficient registration algorithm. The resulting registration algorithm exhibits inherent statistical robustness, has an intuitive interpretation, and is simple to implement. We also provide theoretical and experimental comparisons with other robust methods for point set registration.