一种基于自监督学习的矢量球面卷积网络

陈康鑫; 赵杰煜; 陈豪

doi:10.16383/j.aas.c220694

一种基于自监督学习的矢量球面卷积网络

doi: 10.16383/j.aas.c220694

陈康鑫^1,,
赵杰煜^{1, 2,},
陈豪^1,

1.
宁波大学信息科学与工程学院宁波 315211
2.
浙江省移动网应用技术重点实验室宁波 315211

基金项目: 国家自然科学基金(62071260, 62006131), 浙江省自然科学基金(LZ22F020001, LQ21F020009)资助

详细信息

作者简介:
陈康鑫：宁波大学信息科学与工程学院硕士研究生. 主要研究方向为深度学习和计算机视觉. E-mail: kxchenxy@outlook.com

赵杰煜：宁波大学信息科学与工程学院教授. 1985年和1988年获浙江大学学士和硕士学位、1995年伦敦大学博士学位. 主要研究方向为深度学习和计算机视觉. 本文通信作者. E-mail: zhao_jieyu@nbu.edu.cn

陈豪：宁波大学信息科学与工程学院博士研究生. 主要研究方向为三维重建, 模式识别和机器学习. E-mail: 1901100014@nbu.edu.cn

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出版历程
- 收稿日期: 2022-09-02
- 录用日期: 2022-12-27
- 网络出版日期: 2023-05-05
- 刊出日期: 2023-06-20

A Vector Spherical Convolutional Network Based on Self-supervised Learning

CHEN Kang-Xin^1
,,
ZHAO Jie-Yu^{1, 2
,},
CHEN Hao^1
,

1.
Faculty of Electrical Engineering and Computer Science, Ningbo University, Ningbo 315211
2.
Mobile Network Application Technology Key Laboratory of Zhejiang Province, Ningbo 315211

Funds: Supported by National Natural Science Foundation of China (62071260, 62006131) and Natural Science Foundation of Zhejiang Province (LZ22F020001, LQ21F020009)

More Information

Author Bio:
CHEN Kang-Xin　Master student at the Faculty of Electrical Engineering and Computer Science, Ningbo University. His research interest covers deep learning and computer vision

ZHAO Jie-Yu　Professor at the Faculty of Electrical Engineering and Computer Science, Ningbo University. He received his bachelor and master degrees from Zhejiang University in 1985 and 1988, and his Ph.D. degree from Royal Holloway University of London in 1995. His research interest covers deep learning and computer vision. Corresponding author of this paper

CHEN Hao　Ph.D. candidate at the Faculty of Electrical Engineering and Computer Science, Ningbo University. His research interest covers 3D reconstruction, pattern recognition, and machine learning

摘要

摘要: 在三维视觉任务中, 三维目标的未知旋转会给任务带来挑战, 现有的部分神经网络框架对经过未知旋转后的三维目标进行识别或分割较为困难. 针对上述问题, 提出一种基于自监督学习方式的矢量型球面卷积网络, 用于学习三维目标的旋转信息, 以此来提升分类和分割任务的表现. 首先, 对三维点云信号进行球面采样, 映射到单位球上; 然后, 使用矢量球面卷积网络提取旋转特征, 同时将随机旋转后的三维点云信号输入相同结构的矢量球面卷积网络提取旋转特征, 利用自监督网络训练学习旋转信息; 最后, 对随机旋转的三维目标进行目标分类实验和部分分割实验. 实验表明, 所设计的网络在测试数据随机旋转的情况下, 在ModelNet40数据集上分类准确率提升75.75%, 在ShapeNet数据集上分割效果显著, 交并比(Intersection over union, IoU)提升51.48%.
- 矢量球面卷积网络 /
- 自监督学习 /
- 三维目标分类 /
- 三维目标部分分割
Abstract: The unknown rotation of 3D objects can bring challenges to the 3D vision tasks. It is difficult for some existing neural networks to classify or segment the 3D model after the unknown rotation. Aiming at the above problems, this paper proposes a vector spherical convolutional network based on self-supervised for learning the rotation information of 3D objects. First, the 3D point cloud signal is spherically sampled and mapped to the unit sphere; then, the rotational features are extracted by the vector spherical convolution network, while the randomly rotated 3D point cloud is input into the vector spherical convolution network of the same structure to extract rotation features, and the self-supervised network is used to train and learn the rotation information; finally, target classification experiments and part segmentation experiments are performed on randomly rotated 3D objects. Experimental results show that the network designed in this paper has a 75.75% improvement in classification accuracy on the ModelNet40 dataset and a significant segmentation effect on the ShapeNet dataset with a 51.48% improvement in the intersection over union (IoU) under random rotation of the test data.
- Vector spherical convolutional network /
- self-supervised learning /
- 3D object classification /
- 3D object part segmentation

HTML全文

图 1 自监督矢量球面卷积网络训练流程图

Fig. 1 Self-supervised vector spherical convolutional network

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图 2 矢量球面卷积层间计算方法流程图

Fig. 2 Vector spherical convolution interlayer calculation method

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图 3 规范方向实验框架图

Fig. 3 Canonical orientation experiment framework diagram

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图 4 点云网络结构图

Fig. 4 PointNet architecture

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图 5 分类分割实验框架图

Fig. 5 Classification and segmentation experiment framework diagram

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图 6 ModelNet40规范方向实验可视化结果

Fig. 6 ModelNet40 canonical orientation experiment visualization results

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图 7 ShapeNet规范方向实验可视化结果

Fig. 7 ShapeNet canonical orientation experiment visualization results

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图 8 部分分割实验可视化结果

Fig. 8 Part segmentation experiment visualization results

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表 1 常用符号表

Table 1 Table of common symbols

序号	符号	说明
1	$\left(a_i, b_j, c_k\right)$	球面网格坐标
2	$\left(\alpha_n, \beta_n, h_n\right)$	点云用球面坐标表示
3	$S^2$	单位球面
4	$SO(3)$	三维旋转群
5	$g$	表示$\mathrm{CON}$网络运算过程
6	$f$	指$S^2$或$SO(3)$信号
7	$L_R$	旋转操作符
8	$\psi$	卷积核
9	${\boldsymbol{h}}$	矢量神经元

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表 2 分类准确度 (%)

Table 2 Classification accuracy (%)

	PointNet^[43]	PointNet ++^[46]	Spherical CNN^[11]	LDGCNN^[47]	SO-Net^[48]	PRIN^[49]	SPRIN^[14]	CON+PointNet
NR/NR	$88.45$	$89.82$	$81.73$	$92.91$	94.44	$80.13$	$86.01$	$86.79$
NR/AR	$12.47$	$21.35$	$55.62$	$17.82$	$9.64$	$70.35$	$86.13$	88.22
AR/AR	$21.92$	$31.72$	—	—	—	$73.32$	$86.21$	88.27

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表 3 部分分割实验结果IoUs (%)

Table 3 Part segmentation experimental results IoUs (%)

	随机旋转																		不旋转
	avg. inst.	avg. cls.	飞机	包	帽子	汽车	椅子	耳机	吉他	刀	灯	笔记本电脑	摩托车	马克杯	手枪	火箭	滑板	桌子	avg. inst.	avg. cls.
PointNet^[43]	31.30	29.38	19.90	46.25	43.27	20.81	27.04	15.63	34.72	34.64	42.10	36.40	19.25	49.88	33.30	22.07	25.71	29.74	83.15	78.95
PointNet++^[46]	36.66	35.00	21.90	51.70	40.06	23.13	43.03	9.65	38.51	40.91	45.56	41.75	18.18	53.42	42.19	28.51	38.92	36.57	84.63	81.52
RS-Net^[50]	50.38	32.99	38.29	15.45	53.78	33.49	60.83	31.27	9.50	43.48	57.37	9.86	20.37	25.74	20.63	11.51	30.14	66.11	84.92	81.41
PCNN^[51]	28.80	31.72	23.46	46.55	35.25	22.62	24.27	16.67	32.89	39.80	52.18	38.60	18.54	48.90	27.83	27.46	27.60	24.88	85.13	81.80
SPLATNet^[52]	32.21	38.25	34.58	68.10	46.96	19.36	16.25	24.72	88.39	52.99	49.21	31.83	17.06	48.56	21.20	34.98	28.99	28.86	84.97	82.34
DGCNN^[53]	43.79	30.87	24.84	51.29	36.69	20.33	30.07	27.86	38.00	45.50	42.29	34.84	20.51	48.74	26.25	26.88	26.95	28.85	85.15	82.33
SO-Net^[48]	26.21	14.37	21.08	8.46	1.87	11.78	27.81	11.99	8.34	15.01	43.98	1.81	7.05	8.78	4.41	6.38	16.10	34.98	84.83	81.16
SpiderCNN^[54]	31.81	35.46	22.28	53.07	54.2	22.57	28.86	23.17	35.85	42.72	44.09	55.44	19.23	48.93	28.65	25.61	31.36	31.32	85.33	82.40
SHOT+PointNet^[55]	32.88	31.46	37.42	47.30	49.53	27.71	28.09	16.34	9.79	27.66	37.33	25.22	16.31	50.91	25.07	21.29	43.10	40.27	32.75	31.25
CGF+PointNet^[56]	50.13	46.26	50.97	70.34	60.44	25.51	59.08	33.29	50.92	71.64	40.77	31.91	23.93	63.17	27.73	30.99	47.25	52.06	50.13	46.31
RIConv^[57]	79.31	74.60	78.64	78.70	73.19	68.03	86.82	71.87	89.36	82.95	74.70	76.42	56.58	88.44	72.16	51.63	66.65	77.47	79.55	74.43
Kim 等^[58]	79.56	74.41	77.53	73.43	76.95	66.13	87.22	75.44	87.42	80.71	78.44	71.21	51.09	90.76	73.69	53.86	68.10	78.62	79.92	74.69
Li 等^[59]	82.17	78.78	81.49	80.07	85.55	74.83	88.62	71.34	90.38	82.82	80.34	81.64	68.87	92.23	74.51	54.08	74.59	79.11	82.47	79.40
PRIN^[49]	71.20	66.75	69.29	55.90	71.49	56.31	78.44	65.92	86.01	73.58	66.97	59.29	47.56	81.47	71.99	49.02	64.70	70.12	72.04	68.39
SPRIN^[14]	82.67	79.50	82.07	82.01	76.48	75.53	88.17	71.45	90.51	83.95	79.22	83.83	72.59	93.24	78.99	58.85	74.77	80.31	82.59	79.31
CON+PointNet	84.39	80.86	82.27	79.14	85.88	76.44	90.42	73.24	90.96	82.81	82.99	95.64	69.51	91.93	79.74	55.60	75.33	81.81	84.06	81.22

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表 4 与主流网络结合的分类准确度(%)

Table 4 Classification accuracy in combination with mainstream networks (%)

	PointNet^[43]	PointNet++^[46]	DGCNN^[53]	CON+DGCNN	CON+PointNet++	CON+PointNet
NR/NR	88.45	89.82	90.20	88.32	87.27	86.79
NR/AR	12.47	21.35	16.36	89.86	89.21	88.22
AR/AR	21.92	31.72	29.73	89.93	89.30	88.27

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表 5 与主流网络结合的部分分割实验结果IoUs (%)

Table 5 Experimental results of part segmentation combined with mainstream networks IoUs (%)

	随机旋转																		不旋转
	avg. inst.	avg. cls.	飞机	包	帽子	汽车	椅子	耳机	吉他	刀	灯	笔记本电脑	摩托车	马克杯	手枪	火箭	滑板	桌子	avg. inst.	avg. cls.
PointNet^[43]	31.30	29.38	19.90	46.25	43.27	20.81	27.04	15.63	34.72	34.64	42.10	36.40	19.25	49.88	33.30	22.07	25.71	29.74	83.15	78.95
PointNet++^[46]	36.66	35.00	21.90	51.70	40.06	23.13	43.03	9.65	38.51	40.91	45.56	41.75	18.18	53.42	42.19	28.51	38.92	36.57	84.63	81.52
DGCNN^[53]	43.79	30.87	24.84	51.29	36.69	20.33	30.07	27.86	38.00	45.50	42.29	34.84	20.51	48.74	26.25	26.88	26.95	28.85	85.15	82.33
CON+PointNet	84.39	80.86	82.27	79.14	85.88	76.44	90.42	73.24	90.96	82.81	82.99	95.64	69.51	91.93	79.74	55.60	75.33	81.81	84.06	81.22
CON+PointNet++	85.77	82.30	84.12	80.66	88.90	76.51	90.37	78.65	90.15	83.01	83.62	95.45	71.26	91.67	80.77	60.36	77.23	84.01	86.02	83.41
CON+DGCNN	85.21	81.36	83.71	79.02	86.91	74.21	93.22	74.43	91.90	82.31	84.24	96.53	70.22	90.86	81.37	58.28	76.96	83.27	85.73	82.62

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