基于迭代计算的透明液体剖面线重建算法优化

王明远; 冯诗愚; 付子祺; 王晨臣; 范菊莉

doi:10.13224/j.cnki.jasp.20240233

基于迭代计算的透明液体剖面线重建算法优化

doi: 10.13224/j.cnki.jasp.20240233

1.
南京航空航天大学航空学院飞行器环境控制与生命保障工业和信息化部重点实验室，南京 210016
2.
中国航空工业集团有限公司金城南京机电液压工程研究中心航空机电系统综合航空科技重点实验室，南京 211106

基金项目: 国家自然科学基金（52372331）

详细信息

作者简介:
王明远（2000-），男，硕士生，主要研究方向为透明液体液面重建。E-mail：18851892516@163.com

通讯作者:
范菊莉（1982-），女，副教授，博士，主要研究方向为人机与环境系统工程。E-mail：fjl@nuaa.edu.cn

中图分类号: V228.1；TP391
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出版历程
- 收稿日期: 2024-04-17
- 网络出版日期: 2024-12-04

Optimization of transparent liquid profile line reconstruction algorithm based on iterative calculation

1.
Key Laboratory of Aircraft Environmental Control and Life Support Industry and Information Technology，College of Aerospace Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China
2.
Aviation Key Laboratory of Science and Technology on Aero Electromechanical System Integration， Jincheng Nanjing Engineering Institute of Aircraft System，Aviation Industry Corporation of China Limited，Nanjing 211106，China

摘要

摘要:
对单视角下透明液体剖面线的重建算法进行了研究，通过在迭代计算误差产生的计算步骤引入修正因子来对重建过程进行修正。对修正因子的影响因素进行探究，给出了修正因子确定方法。对算法有效性进行了验证，并应用优化后的算法对多个的液面剖面线及三维液面进行重建分析。结果表明：修正因子的添加应根据曲线的曲率及重建过程底部特征点布置步长来分段确定，分段修正后整体精度提升30.88%，最大误差降低45.72%。优化后的算法提高了同步长特征点下的重建精度，对于所重建的标准液面剖面线和标准三维液面，在达到同样精度的前提下将特征点布置分别减少38.46%和20%；在累积误差控制方面具有良好的效果，且具有普遍适用性。
- 液面重建 /
- 修正因子 /
- 计算机视觉 /
- 折射定律 /
- 虚拟实验
Abstract:
The algorithm for reconstructing the profile of transparent liquids from a single viewpoint was investigated. A correction factor was introduced in the iterative error calculation steps to refine the reconstruction process. The influencing factors of the correction factor were explored, and a method for determining it was provided. The validity of the algorithm was verified, and the optimized algorithm was applied to analyze the reconstruction of multiple liquid surface profiles and 3D liquid surfaces. The results showed that the correction factor should be segmented based on the curvature of the curve and the step size of feature point placement during the reconstruction process. After applying segmented correction, the overall accuracy was improved by 30.88%, and the maximum error was reduced by 45.72%. The optimized algorithm enhanced the reconstruction accuracy for synchronized long feature points. For the standard liquid surface profile and the standard 3D liquid surface reconstructed, the number of feature points required to achieve the same accuracy was reduced by 38.46% and 20%, respectively. Additionally, the algorithm demonstrated effective control of cumulative errors and exhibited broad applicability.
- reconstruction of the liquid surface /
- modification factor /
- computer vision /
- Snell’s law /
- virtual experiment

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图 1 计算原理以及误差来源

Figure 1. Calculation principles and sources of errors

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图 2 算法优化思路

Figure 2. Algorithm optimization ideas

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图 3 5 mm步长下夹角差值与二阶导数关系

Figure 3. Relationship between the angle difference and the second derivative of 5 mm step length

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图 4 1 mm步长下夹角差值与二阶导数的关系

Figure 4. Relationship between the angle difference and the second derivative of 1 mm step length

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图 5 标准液面重建结果

Figure 5. Reconstruction results of standard liquid surface profile curve

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图 6 不同修正方式误差对比

Figure 6. Error comparison of different correction methods

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图 7 分段修正

Figure 7. Algorithmic approaches for segmentation correction

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图 8 优化后算法效果体现

Figure 8. Demonstration of the effect to the reconstruction results of the modified algorithm

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图 9 不同步长重建误差对比

Figure 9. Error comparison of reconstruction results with different step length

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图 10 长液面重建结果

Figure 10. Reconstruction results of long liquid surface profile curve

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图 11 长液面重建误差

Figure 11. Reconstruction error of long liquid surface profile curve

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图 12 复杂波动液面重建结果

Figure 12. Reconstruction results of complex fluctuating liquid surface profile curve

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图 13 复杂波动液面重建误差

Figure 13. Reconstruction error of complex fluctuating liquid surface profile curve

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图 14 修正后算法三维液面重建结果

Figure 14. Reconstruction result of 3D liquid surface by modified algorithm

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图 15 未修正算法三维液面重建结果

Figure 15. Reconstruction result of 3D liquid surface by unmodified algorithm

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图 16 三维液面重建误差对比

Figure 16. Error comparison of reconstruction results by different algorithms

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表 1 5 mm步长相关数据

Table 1. 5 mm step size related data

横坐标/mm	对应点纵坐标/mm	二阶导值	曲率	夹角差值/rad
0	11.000
5	10.672	−0.019	0.018	−0.057
10	9.904	0.003	0.003	−0.012
15	9.199	0.022	0.022	0.041
20	9.018	0.027	0.027	0.068
25	9.481	0.014	0.014	0.049
30	10.284	−0.008	0.008	−0.001
35	10.901	−0.025	0.025	−0.050
40	10.927	−0.026	0.026	−0.068
45	10.347	−0.010	0.009	−0.039

下载: 导出CSV

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