REFORM: Rotor Estimation From Object Resampling and Matching

Abstract

In this paper we tackle the problem of correspondence and rotor estimation between models composed of geometric primitives of different types. We frame this problem as searching for the rotor that takes a query model to a reference model. The situations that we consider are those in which our query model: contains additional primitives not present in the reference; is missing primitives that are present in the reference. We will also look at cases in which there are a large number of primitives per model. These are all common issues facing any SLAM-type (simultaneous localisation and mapping) systems. To overcome these problems we introduce an inter-object rotor magnitude-based matching function and a subsampled iterative rotor estimation and matching algorithm. We title the finished algorithm: Rotor Estimation From Object Resampling and Matching—REFORM. REFORM builds on ideas from the RANSAC (RAndom SAmple Consensus) [7] and ICP (Iterative Closest Point) [3, 11] algorithms and extends these to multivector correspondence. It is easily parallelisable and designed for good convergence performance with models of real objects.