Bayesian perspective for the registration of multiple 3D views

https://doi.org/10.1016/j.cviu.2013.09.003Get rights and content

Highlights

  • Use of a Bayesian framework allows tolerance to incorrect pairwise registrations.

  • Correspondence weights vary depending on their reliability, until a specific criteria is achieved.

  • Results show that an important improvement is achieved in objects with degraded correspondences.

  • Also in cases without degraded correspondences, the proposed method improves the accuracy in comparison to other methods.

Abstract

The registration of multiple 3D structures in order to obtain a full-side representation of a scene is a long-time studied subject. Even if the multiple pairwise registrations are almost correct, usually the concatenation of them along a cycle produces a non-satisfactory result at the end of the process due to the accumulation of the small errors. Obviously, the situation can still be worse if, in addition, we have incorrect pairwise correspondences between the views. In this paper, we embed the problem of global multiple views registration into a Bayesian framework, by means of an Expectation–Maximization (EM) algorithm, where pairwise correspondences are treated as missing data and, therefore, inferred through a maximum a posteriori (MAP) process. The presented formulation simultaneously considers uncertainty on pairwise correspondences and noise, allowing a final result which outperforms, in terms of accuracy and robustness, other state-of-the-art algorithms. Experimental results show a reliability analysis of the presented algorithm with respect to the percentage of a priori incorrect correspondences and their consequent effect on the global registration estimation. This analysis compares current state-of-the-art global registration methods with our formulation revealing that the introduction of a Bayesian formulation allows reaching configurations with a lower minimum of the global cost function.

Introduction

Current technology allows to obtain 3D representations of real objects or scenarios by using different methods. From usual methods like stereoscopy to complex devices like LADAR or time-of-flight cameras, the possibilities are growing continuously. However, acquisition techniques usually have problems with occluded surfaces or the limited field of view, so it is usually necessary to combine different views of the same object or scenario in order to obtain a full representation. Using this process another problem then arises: the registration of these individual 3D views which will enable, at the end of the process, to a whole 3D reconstruction of the desired object or scene.

First step for this objective is the so-called pairwise registration, where the 3D representations are registered pair to pair. Depending if the two structures have overlap, pairwise registration methods will give as a result a transformation which registers the first 3D view to the second one.

Multiview registration is the second step of this process, and is usually a more complex situation. Assuming that pairwise registrations are correct, their concatenation along a cycle will probably result in a non-satisfactory multiview registration because of the accumulation of the different pairwise errors. An example of this effect can be seen in Fig. 1.

In addition, there could exist another situation which produces more problems. Even if two structures register perfectly in the pairwise registration process, their transformation could be incorrect in a global environment. This could happen specially if we are working with objects with symmetries, planes or repetitive patterns. In these cases, most of the current multiview registration algorithms will fail because they are not ready to deal with this kind of error.

The main contribution of this paper, in opposition to other state-of-the-art papers, is the possibility of detecting these incorrect registrations between different views and therefore minimize their impact in the global registration process. This feature is achieved thanks to the use of different weights which encode the reliability we have in the correspondences between the views.

The structure of the document is as follows: a review of different registration algorithms is presented in Section 2, followed by an introduction to the main problematic of multiview registration in Section 3. The proposed algorithm is explained in detail in Section 4, and the obtained experimental results are shown in Section 5. Finally, conclusions and possible future improvements are explained at the end of the paper in Section 6.

Section snippets

State of the art

As previously stated the first step in order to achieve the registration of multiple 3D representations is the computation of the pairwise registrations. The most usual method consists in the establishment of correspondences between points of the two views, which can be found by using descriptors like the Spin-Images of Johnson and Hebert [1] or covariance descriptors like the one presented by Fehr et al. in [2]. The combination of correspondences between the two views determines an

Problematic issues in the multiview registration process

The most usual problem related with the multiview registration process is the minimization of the global error which is produced due to the small errors in every pairwise registration. These errors could be produced by different factors, like a noisy acquisition process, differences in the 3D structure of two overlapping views due to the different date of acquisition, or, in most of the cases, by an inaccurate selection of correspondences. Having a look at the example already shown in the left

Bayesian-based multiview registration method

In this section our developed method for the 3D registration of multiple views is explained, which will be called Bayesian-Based Multiview Registration (BBMR) method in the following. As previously stated, this method is based on the previous work presented by Krishnan et al. in [13]. In our work we apply an additional layer over this method, adding an uncertainty which is solved thanks to the use of the Expectation Maximization algorithm.

As an introduction to the problem, we first describe the

Experimental results

In this paper we focus on two main issues: the uncertainty on pairwise correspondences and the combination of global and local information in the registration process of multiple views.

Our technique needs, as a starting point, setting up correspondences between pairs of points belonging to two different overlapping views. These pairwise correspondences may contain some errors due to the fact that they are established by using only the information from the corresponding pair of views, which in

Conclusions and future work

This paper presents our Bayesian-Based Multiview Registration (BBMR) method for the registration of multiple 3D scans. The main property of our BBMR method consists in the property of being tolerant to a certain number of incorrect correspondences which could be caused by different factors like an incorrect manual selection, symmetries on the scanned 3D object or repetitive patterns. This tolerance is achieved thanks to the use of an additional layer placed over an existing multiview

Acknowledgment

This work was partially funded by the research project TIN2012-39203.

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