TY - JOUR
T1 - Bootstrap uncertainty evaluation of three-dimensional optical flow technique utilized in flame measurements
AU - Men, Wenqi
AU - Ling, Chen
AU - Wu, Yue
AU - Gao, Yu
AU - Zhang, Hao
N1 - Publisher Copyright:
© 2025
PY - 2025/3
Y1 - 2025/3
N2 - To gain a better understanding of flame propagation and evolution characteristics, this work develops a 3D optical flow method to measure the 3D flame deformation speed, which reflects the variations of flame structure. More importantly, this work focuses on developing a 3D bootstrap uncertainty evaluation method to quantitatively estimate the errors in the 3D optical flow calculation results. The algorithm of 3D optical flow is first developed on the basis of traditional 2D Horn-Schunck optical flow, which iteratively resolves the velocity field by setting up a trade-off between brightness constancy and smoothness of 3D images. Moreover, the algorithm of 3D bootstrap is also developed by running random resampling multiple times in studied 3D images, which provides an effective way in estimating the calculation error from the optical flow. Subsequently, the 3D optical flow method is validated both numerically and experimentally, using three simulated phantoms and a designed laminar cone flame under controlled displacement field. During the numerical validation, the average endpoint and angular errors of velocity fields are reduced to as low as 0.056 voxel and 3.8°, respectively. Moreover, the 3D bootstrap method identifies unreliable velocity vectors without requiring the true velocity field by estimating the uncertainty at all locations. In summary, the ability of the 3D bootstrap method to estimate velocity field errors makes it feasible for further application of 3D optical flow.
AB - To gain a better understanding of flame propagation and evolution characteristics, this work develops a 3D optical flow method to measure the 3D flame deformation speed, which reflects the variations of flame structure. More importantly, this work focuses on developing a 3D bootstrap uncertainty evaluation method to quantitatively estimate the errors in the 3D optical flow calculation results. The algorithm of 3D optical flow is first developed on the basis of traditional 2D Horn-Schunck optical flow, which iteratively resolves the velocity field by setting up a trade-off between brightness constancy and smoothness of 3D images. Moreover, the algorithm of 3D bootstrap is also developed by running random resampling multiple times in studied 3D images, which provides an effective way in estimating the calculation error from the optical flow. Subsequently, the 3D optical flow method is validated both numerically and experimentally, using three simulated phantoms and a designed laminar cone flame under controlled displacement field. During the numerical validation, the average endpoint and angular errors of velocity fields are reduced to as low as 0.056 voxel and 3.8°, respectively. Moreover, the 3D bootstrap method identifies unreliable velocity vectors without requiring the true velocity field by estimating the uncertainty at all locations. In summary, the ability of the 3D bootstrap method to estimate velocity field errors makes it feasible for further application of 3D optical flow.
KW - 3D flame deformation speed
KW - 3D optical flow
KW - Bootstrap
KW - Error estimation
UR - http://www.scopus.com/inward/record.url?scp=85215128417&partnerID=8YFLogxK
U2 - 10.1016/j.optlaseng.2025.108834
DO - 10.1016/j.optlaseng.2025.108834
M3 - Article
AN - SCOPUS:85215128417
SN - 0143-8166
VL - 186
JO - Optics and Lasers in Engineering
JF - Optics and Lasers in Engineering
M1 - 108834
ER -