On evaluating consensus in RANSAC surface registration

Abstract

Random Sample Consensus is a powerful paradigm that was successfully applied in various contexts, including Location Determination Problem, fundamental matrix estimation and global 3D surface registration, where many previously proposed algorithms can be interpreted as a particular implementation of this concept. In general, a set of candidate transformations is generated by some simple procedure, and an aligning transformation is chosen within this set, such that it aligns the largest portion of the input data. We observe that choosing the aligning transformation may also be interpreted as finding consensus among the candidates, which in turn involves measuring similarity of candidate rigid transformations. While it is not difficult to construct a metric that provides reasonable results, most approaches come with certain limitations and drawbacks. In this paper, we investigate possible means of measuring distances in SE(3) and compare their properties both theoretically and experimentally in a model RANSAC registration algorithm. We also propose modifications to existing measures and propose a novel method of locating the consensus transformation based on Vantage Point Tree data structure.

Plane Space Representation in Context of Mode-Based Symmetry Plane Detection

“…As pointed out in [8], distance between transformations cannot be well defined without the context (the object on which the transformations are applied), which is consistent with Sect. 2.2.…”

“…Other uses for symmetry plane detection are in [9,12]. Similar approach has recently been used by Hruda et al in rigid surface registration [8] which can be understood as symmetry detection between two objects. The candidate space contained rigid transformations and a mode was found by a density peak estimation algorithm.…”

“…The important aspect is to have distances between points in the space well corresponding to the actual similarity/dissimilarity of the planes in E 3 . The mode(s) can be found in an arbitrary non-Euclidean space only using distances between the points, their coordinates are not needed [8,18]. Proximity queries in non-Euclidean spaces can be accelerated using the Vantage Point Tree data structure [19] as done in [8].…”

“…The mode(s) can be found in an arbitrary non-Euclidean space only using distances between the points, their coordinates are not needed [8,18]. Proximity queries in non-Euclidean spaces can be accelerated using the Vantage Point Tree data structure [19] as done in [8]. In context of symmetry detection, planes can be understood as transformations reflecting points over the given plane.…”

“…In context of symmetry detection, planes can be understood as transformations reflecting points over the given plane. The problem of computing distances between rigid transformations has been analyzed in [8], however, the same problem does not seem to be sufficiently addressed in the literature for reflection transformations or planes, in spite of the popularity of the Mode-based approach.…”