Point sets non-rigid registration using T-distribution mixture model

ZHOU Zhi-yong1; 2; 3; XUE Wei-qin1; ZHENG Jian3; KUAI Duo-jie3; ZHANG Tao3; HU Su4

doi:10.3788/OPE.20132109.2405

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Point sets non-rigid registration using T-distribution mixture model

更新时间：2020-08-12

- Point sets non-rigid registration using T-distribution mixture model
- Optics and Precision Engineering Vol. 21, Issue 9, Pages: 2405-2420(2013)
- 作者机构：
  
  1. 中国科学院大学北京,中国,100049
  2. 中国科学院长春光学精密机械与物理研究所，吉林长春 130033
  3. 中国科学院苏州生物医学工程技术研究所，江苏苏州 215163
  4. 苏州大学附属第一医院,江苏苏州,215006
- 作者简介：
- 基金信息：
- DOI：10.3788/OPE.20132109.2405
  CLC： TP391
- Received：09 April 2012，
  
  Revised：06 July 2012，
  
  Published Online：30 September 2013，
  
  Published：15 September 2013
- 稿件说明：
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周志勇薛维琴郑健蒯多杰张涛胡粟. 基于T分布混合模型的点集非刚性配准算法[J]. 光学精密工程, 2013,21(9): 2405-2420

ZHOU Zhi-yong XUE Wei-qin ZHENG Jian KUAI Duo-jie ZHANG Tao H U Su. Point sets non-rigid registration using T-distribution mixture model[J]. Editorial Office of Optics and Precision Engineering, 2013,21(9): 2405-2420
周志勇薛维琴郑健蒯多杰张涛胡粟. 基于T分布混合模型的点集非刚性配准算法[J]. 光学精密工程, 2013,21(9): 2405-2420 DOI： 10.3788/OPE.20132109.2405.

ZHOU Zhi-yong XUE Wei-qin ZHENG Jian KUAI Duo-jie ZHANG Tao H U Su. Point sets non-rigid registration using T-distribution mixture model[J]. Editorial Office of Optics and Precision Engineering, 2013,21(9): 2405-2420 DOI： 10.3788/OPE.20132109.2405.

摘要

考虑高斯混合模型（TMM）的点集非刚性配准算法易受异常点和重尾点的影响，提出了基于t分布混合模型的运动一致性非刚性配准算法。通过期望最大化（EM）框架的完整数据定义将高斯混合模型推广为t分布混合模型，使用EM算法最小化参数的条件期望获得非刚性配准参数的闭合解。在EM算法中计算浮动点集各个点的先验权重，减小异常点和重尾点对配准结果的影响；计算浮动点集各个点的自由度，自适应地改变每个点的概率密度分布模型，提高算法的鲁棒性，并避免了异常点水平估计误差对配准结果的影响。在t分布混合模型的条件期望函数中加入点集位移的正则项，使邻近点具有运动一致性（CPD）。仿真数据表明，当噪声水平很高时，TMM-CPD仍可以精确配准点集，且误差仅为对比算法的1/10。真实图像的近似椭圆状分布、管状分布和三维点云状分布的点集配准结果表明，TMM-CPD的配准误差仅为对比算法的42.0%、80.1%和77.5%。实验表明，TMM-CPD配准含有重尾点和异常点的点集，具有精度高、鲁棒性好和受重尾点与异常点干扰小等优点。

Abstract

A robust non-rigid registration approach with a t-distribution Mixture Model(TMM) was proposed because point sets as Gaussian mixture model is vulnerable to the outliers and the data with longer than normal tails. The Gaussian mixture model was extended to the students-t Mixture Model by full data definition in the Expectation Maximazation(EM) frame

then the closed solutions of the parameter set of the t-distribution mixture model were solved by re-parameterization of the t-distribution mixture model in the EM algorithm. The priori-weight of each float point was calculated in EM framework to reduce the effects of outliers and the data with longer than normal tails on the matching results. The degree of freedom of each float point in the t-distribution mixture model was calculated to change the probability density distribution

improve the robustness of the algorithm and avoid the effect of estimating the outlier level of point sets that may bring additional errors. The conditional expectation function in t-distribution mixture model was added a regular item of point set

so that the points have a feature of Coherent Point Drift(CPD). The simulation data show that the error from the TMM-CPD is only one tenth of that from comparison algorithms. When the point sets are approximate ellipse shape

tubular and three dimensions

the registration errors of TMM-CPD are only 42.0%

80.1% and77.5% of those using comparison algorithms

respectively. The experiments show that this non-rigid registration approach using the t-distribution mixture model has features of high-accuracy

good robustness compared to other point set registration algorithms for point sets containing outliers and data with longer than normal tails.

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Keywords

references

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