考虑法向离群的自适应双边滤波点云平滑及IMLS评价方法

doi:10.11996/JG.j.2095-302X.2023010131

图学学报 ›› 2023, Vol. 44 ›› Issue (1): 131-138.DOI: 10.11996/JG.j.2095-302X.2023010131

• 计算机图形学与虚拟现实 • 上一篇下一篇

考虑法向离群的自适应双边滤波点云平滑及IMLS评价方法

陈亚超¹^,²(), 樊彦国¹(), 禹定峰³, 樊博文⁴

1.中国石油大学(华东)海洋与空间信息学院，山东青岛 266580
2.中国民用航空总局第二研究所科研开发中心，四川成都 610041
3.齐鲁工业大学(山东省科学院)山东省科学院海洋仪器仪表研究所，山东青岛 266061
4.哈尔滨工程大学水声工程学院，黑龙江哈尔滨 150001

收稿日期:2022-03-20 修回日期:2022-07-31 出版日期:2023-10-31 发布日期:2023-02-16
通讯作者: 樊彦国
作者简介:陈亚超(1996-)，男，硕士研究生。主要研究方向为图形图像处理。E-mail：yachaochen1@163.com
基金资助:
山东省重点研发计划项目(2019GHY112017)

Adaptive bilateral filtering point cloud smoothing and IMLS evaluation method considering normal outliers

CHEN Ya-chao¹^,²(), FAN Yan-guo¹(), YU Ding-feng³, FAN Bo-wen⁴

1. College of Oceanography and Space Informatics, China University of Petroleum, Qingdao Shandong 266580, China
2. Research and Development Center, The Second Institute of Civil Aviation Administration of China, Chengdu Sichuan 610041, China
3. Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao Shandong 266061, China
4. College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin Heilongjiang 150001, China

Received:2022-03-20 Revised:2022-07-31 Online:2023-10-31 Published:2023-02-16
Contact: FAN Yan-guo
About author:CHEN Ya-chao (1996-), master student. His main research interest covers graphic image processing. E-mail：yachaochen1@163.com
Supported by:
Key Research and Development Project of Shandong Province(2019GHY112017)

摘要/Abstract

摘要：

针对目前在点云双边滤波平滑算法中，人工输入不合理参数导致的点云平滑效果不佳，且易导致体积收缩及现有去噪后点云质量评价方法存在表达局限性等问题，提出一种自适应参数的点云双边滤波算法和基于隐性移动最小二乘(IMLS)的质量评价方法。首先构建KD-tree数据结构用于点云拓扑，之后搜索各点邻域，利用奇异值分解法计算法向量信息，并在双边滤波公式中引入法向离群因子以剔除邻域内离群点，然后通过扩展高斯核函数的权值计算式，在点云邻域内自适应获取空间与法向特征参数，最后应用改进模型进行点云平滑并引入IMLS方法评价点云质量。实验结果表明，考虑法向离群的自适应双边滤波点云平滑算法具有良好的去噪效果，相比其他算法体积收缩更小，且IMLS评价方法客观有效。

关键词: 点云平滑, 双边滤波, 法向离群因子, 去噪质量评价

Abstract:

In order to address the problems that the unreasonable parameters of bilateral filtering lead to poor smoothing effect of point cloud, volume shrinkage, and the limitation of existing quality evaluation methods, a bilateral filtering algorithm with adaptive parameters and a quality evaluation method based on implicit moving least squares (IMLS) were proposed. Firstly, the KD-tree data structure was constructed for point cloud topology, then the neighborhood of each point was searched to calculate the normal of each point using the SVD decomposition method, and the normal outlier factor was introduced into bilateral filtering to remove outliers in the neighborhood. Additionally, the space and normal characteristic parameters were calculated according to the Gaussian kernel function extended by the neighborhood norm. Finally, the constructed bilateral filtering model was applied to the smoothing of the point cloud, and the implicit moving least squares method was introduced to evaluate the quality of smoothing. The experimental results of the point cloud with noise show that the adaptive bilateral filtering point cloud smoothing algorithm considering normal outliers could attain a good effect and result in smaller volume shrinkage compared with other algorithms, and that the IMLS evaluation method could be objective and effective.

Key words: point cloud smoothing, bilateral filtering, normal outlier, evaluation of denoising quality

中图分类号:

TP391

陈亚超, 樊彦国, 禹定峰, 樊博文. 考虑法向离群的自适应双边滤波点云平滑及IMLS评价方法[J]. 图学学报, 2023, 44(1): 131-138.

CHEN Ya-chao, FAN Yan-guo, YU Ding-feng, FAN Bo-wen. Adaptive bilateral filtering point cloud smoothing and IMLS evaluation method considering normal outliers[J]. Journal of Graphics, 2023, 44(1): 131-138.

图/表 10

图1 不同邻域的测点平滑移动

Fig. 1 Smooth movement of measuring point in different neighborhood

图2 包含浮动点的测点平滑移动

Fig. 2 Smooth movement of measuring point containing floating points

图3 法向离群因子判别

Fig. 3 Discrimination of normal outlier factor

图4 MLS构建隐性曲面

Fig. 4 Implicit surface of IMLS

图5 Elephant模型不同算法效果比较((A)不同算法过平滑效果比较；(B)不同算法细节效果比较)

Fig. 5 Comparison of effect between different algorithms for elephant model ((A) Comparison of over smoothing effect of different algorithms; (B) Comparison of detail effect of different algorithms)

图6 Gargo模型不同算法效果比较((A)不同算法过平滑效果比较；(B)不同算法细节效果比较)

Fig. 6 Comparison of effect between different algorithms for gargo model ((A) Comparison of over smoothing effect of different algorithms; (B) Comparison of detail effect of different algorithms)

表1 Elephant模型不同去噪算法定量评价表

Table 1 Quantitative evaluation table of different denoising algorithms for elephant model

方法	空间超参数	法向超参数	拟高斯噪声(%)	运行时间(s)	P-Point ^[18]评分	IMLS评分
核函数 MeanShift	10	0.1	0	0.121	1.323	0.325
	50	0.1	0	0.121	2.412	0.314
	10	0.1	10	0.124	3.377	0.522
	50	0.1	10	0.123	4.327	0.386
文献[9]	10	0.1	0	0.239	2.075	0.453
	50	0.1	0	0.233	2.287	0.466
	10	0.1	10	0.239	8.103	1.103
	50	0.1	10	0.237	8.348	1.103
文献[11]	10	0.1	0	0.252	0.861	0.370
	50	0.1	0	0.246	1.343	0.377
	10	0.1	10	0.250	2.443	0.699
	50	0.1	10	0.250	3.090	0.675
本文算法	-	-	0	0.395	0.462	0.319
本文算法	-	-	10	0.390	1.717	0.579

表2 Gargo模型的不同去噪算法定量评价表

Table 2 Quantitative evaluation table of different denoising algorithms for gargo model

方法	空间超参数	法向超参数	拟高斯噪声(%)	运行时间(s)	P-Point ^[18]评分	IMLS评分
核函数 MeanShift	10	0.1	0	0.122	8.846	0.979
	50	0.1	0	0.120	15.677	0.866
	10	0.1	10	0.125	8.603	1.228
	50	0.1	10	0.123	17.238	0.912
文献[9]	10	0.1	0	0.234	20.852	1.440
	50	0.1	0	0.235	23.995	1.429
	10	0.1	10	0.242	32.969	1.962
	50	0.1	10	0.236	36.104	1.913
文献[11]	10	0.1	0	0.247	2.801	1.134
	50	0.1	0	0.251	6.373	1.074
	10	0.1	10	0.248	6.529	1.388
	50	0.1	10	0.246	9.984	1.281
本文算法	-	-	0	0.391	3.548	0.887
本文算法	-	-	10	0.391	6.407	1.036

图7 Elephant模型双边滤波类算法迭代结果((a)拟高斯噪声0%；(b)拟高斯噪声10%)

Fig. 7 Iteration result of bilateral filtering class algorithm for elephant model ((a) Quasi Gaussian noise 0%; (b) Quasi Gaussian noise 10%)

图8 Gargo模型双边滤波类算法迭代结果((a)拟高斯噪声0%；(b)拟高斯噪声10%)

Fig. 8 Iteration result of bilateral filtering class algorithm for Gargo model ((a) Quasi Gaussian noise 0%; (b) Quasi Gaussian noise 10%)

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考虑法向离群的自适应双边滤波点云平滑及IMLS评价方法

Adaptive bilateral filtering point cloud smoothing and IMLS evaluation method considering normal outliers

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