Robust and precise isotropic scaling registration algorithm using bi-directional distance and correntropy

Highlights

• The scale factor is introduced to deal with the oral cavity registration of multi-source data sets.

• Correntropy is introduced into the scaling registration algorithm to suppress noise and outliers interference.

• Bi-directional distance is used to ensure the robustness of the proposed algorithm.

Abstract

In orthodontics, a patient is collected a lot of 3D oral cavity data, including oral cavity gypsum and scan data sets. To accurately measure the patient's tooth movement, this paper proposes a robust and precise isotropic scaling registration algorithm using bi-directional distance and correntropy. Firstly, because the oral cavity gypsum data sets have a lot of gypsum tumors and bubbles, which can cause the accuracy of registration results to decrease. Then, we introduce the correntropy into the traditional scaling registration model. Secondly, since unconstrained scaling registration is an ill-posed problem, bi-directional distance is used to enhance the robustness. In this way, a registration model using bi-directional distance and correntropy is established. In order to solve this problem, this paper proposes a new registration algorithm with iterative closest point. Moreover, the convergence of the algorithm is proved theoretically. Finally, the proposed algorithm is tested on the orthodontic database, and our experimental results demonstrate that our algorithm performs robust and high accuracy.

Introduction

With the rapid development of 3D data acquisition technology in various fields such as image processing [1], [2], [3], machine vision [4], [5], [6] and pattern recognition [7], [8], [9], the multi-source data fusion has become increasingly significant. In practical applications, multi-source data obtained from multiple sensors often need to be aligned. To solve this problem, we can use the point set registration method. The purpose of point set registration is to match the point sets of two or more model data obtained from different times, different sensors and different environments, which makes the matched point sets have a consistent spatial expression. Therefore, many scholars have devoted themselves to the research of point set registration.

One of the most classic registration algorithms is the iterative closest point (ICP) algorithm proposed by Besl and McKay [10]. Different from other registration methods, it can achieve fast speed between two point sets while saving the feature extraction and pre-processing steps. In a real scene, point sets to be registered usually have some deformation, and the rigid registration problem can no longer meet the actual needs. Therefore, how to effectively solve the non-rigid registration problems have gradually become another significant problem studied by a large number of scholars.

To deal with scaling deformation problems, Zha et al. [11] put forward a registration algorithm that used the extended signal image to estimate the similarity transformation of the corresponding point set, but the calculation speed is slow. To increase calculation speed, Timo et al. [12] came up with a similar registration algorithm based on the ICP registration algorithm. High speed as the algorithm is, it is short of stability. Du et al. [13] introduced constrained scaling into the traditional ICP registration algorithm, which can solve the problem of shape scaling registration. Moreover, some scholars have extended these methods to affine registration [14], [15], [16] or non-linear registration [17].

In addition, point sets always have noise and outliers, which may decrease the precision or even lead the registration failure. Therefore, the point-to-point correspondence approaches, such as ICP, have been improved. Chetverikov et al. [18] advanced a trimmed-ICP registration algorithm to accomplish registration with an overlap rate. Phillip et al. [19] made the trimmed-ICP registration algorithm better, which further improved the accuracy of registration. Furthermore, full correspondence methods have been presented. Chui and Rangarajan [20] propounded a Thin Plate Spline-Robust Point Match (TPS-RPM) registration algorithm, which makes the registration accuracy increase. Myronenko et al. [21] proposed a Coherent Point Drift (CPD) based on probability algorithm. This algorithm fits the Gaussian mixture model centroid into data through maximum likelihood estimation, which overcomes noise and outlies. The accuracy of these registration methods as it improves, it is slower to calculate.

These point set registration methods could be applied to register 3D oral cavity data, including oral cavity gypsum and scan data sets, to measure a patient's tooth movement in orthodontics. However, the oral cavity may have slight scaling deformation, and the gypsum data sets of the oral cavity contain a lot of gypsum tumors and bubbles, which lead the traditional scaling ICP algorithm based on Euclidean distance to a reduction in registration accuracy. As correntropy could overcome the noise and outliers, a scaling registration method based on correntropy can be considered. However, in the unconstrained scaling registration algorithm, the changes in scaling transformation may cause the registration to fall into a local optimum, which reduces the registration accuracy. Therefore, the bi-directional distance is introduced to the traditional scaling registration algorithm based on correntropy, thereby improving the robustness and accuracy of our algorithm. Moreover, experimental results on the oral cavity data set demonstrate the robustness and precision of our algorithm.

This paper is organized as follows. Among them, we mainly introduce the scaling registration in Section 2. In Section 3, the scaling registration algorithm with bi-directional distance and correntropy algorithm is proposed. Moreover, we analyze the experimental results in Section 4. At last, the conclusion is summarized in the last section.