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浙江大学学报(工学版)
浙江大学学报(工学版)  2021, Vol. 55 Issue (4): 658-664    DOI: 10.3785/j.issn.1008-973X.2021.04.007
计算机技术、电信技术     
强度传输方程和神经网络融合的三维重构算法
程鸿(),胡佳杰,刘勇,叶远青
安徽大学 电子信息工程学院，安徽 合肥 230601
Three-dimensional reconstruction algorithm based on fusion of transport of intensity equation and neural network
Hong CHENG(),Jia-jie HU,Yong LIU,Yuan-qing YE
School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
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摘要：

针对原有强度传输方程法所恢复的相位精度不够精确的缺点，提出强度传输方程和神经网络融合的三维重构算法. 利用强度传输方程求解出物体不同角度的初始相位，利用神经网络算法进行优化，根据不同角度的最终恢复相位结合乘法技术重构出三维体信息. 该算法具有精度高的特点，可以为三维成像技术的应用提供参考. 对于实验中的示例图像，该算法将强度传输方程得到的相位误差从21.40%降低为5.26%，重构三维物体与模拟真实物体的相关程度为显著相关.
关键词： 三维重构;  强度传输方程;  人工神经网络;  乘法技术;  相位恢复    
Abstract:

A three-dimensional reconstruction algorithm based on the fusion of transport of intensity equation and neural network was proposed in order to improve the accuracy of the phase retrieved by the original transport of intensity equation method. The initial phases of different angles of the object were solved by transport of intensity equation and optimized by the neural network algorithm. Then the three-dimensional information was reconstructed according to the final retrieval phases with different angles and the multiplicative technique. The algorithm has the characteristics of high precision, and can provide reference for the application of three-dimensional imaging technology. The phase error obtained by the transport of intensity equation was reduced from 21.40% to 5.26% for the example image in the experiment. The correlation degree between the reconstructed three-dimensional object and the simulated object was significant.
Key words: three-dimensional reconstruction    transport of intensity equation    artificial neural network    multiplicative technique    phase retrieval
收稿日期: 2020-07-04 出版日期: 2021-05-07
CLC:  O 436  
基金资助: 国家自然科学基金资助项目（61605002）；安徽省高等学校自然科学研究资助项目（KJ2020ZD02，KJ2019ZD04）；安徽省自然科学基金资助项目（2008085MF209）
作者简介: 程鸿（1981—），女，副教授，从事计算信号处理的研究. orcid.org/0000-0002-3712-1485. E-mail： chenghong@ahu.edu.cn
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程鸿
胡佳杰
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引用本文:

程鸿,胡佳杰,刘勇,叶远青. 强度传输方程和神经网络融合的三维重构算法[J]. 浙江大学学报(工学版), 2021, 55(4): 658-664.

Hong CHENG,Jia-jie HU,Yong LIU,Yuan-qing YE. Three-dimensional reconstruction algorithm based on fusion of transport of intensity equation and neural network. Journal of ZheJiang University (Engineering Science), 2021, 55(4): 658-664.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2021.04.007    或    http://www.zjujournals.com/eng/CN/Y2021/V55/I4/658

图 1  强度差分原理图
图 2  TIE与ANN融合原理图
图 3  MT重构过程（以4个角度为例）
图 4  模拟生成物体及不同角度的投影图
图 5  基于TIE的初始相位结果
图 6  基于ANN的优化相位结果与对应的精确相位
图 7  精确相位图、初始相位图及优化相位图的三维显示
算法 ${ { {E} }_{{\rm{tr}}} }/{\text{%} }$ ${ { {E} }_{{\rm{tes}}} }/{\text{%} }$ ${ { {E} }_{{\rm{exa}}} }/{\text{%} }$ ${ {T} }/{\rm{s}}$
TIE 20.66 20.56 21.40 0.57
TIE+ANN 0.42 4.06 5.26 0.91
表 1  2种不同算法的误差比较
图 8  基于MT的三维重构
相关系数 相关程度
0~0.3 微相关
0.3~0.5 实相关
0.5~0.8 显著相关
0.8~1.0 高度相关
表 2  相关系数与相关程度的关系
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