粒子图像测速技术
Diffeomorphic Particle Image Velocimetry
摘要：
现有的粒子图像测速技术（PIV）没有考虑非直线粒子轨迹的曲率效应，因为从一对粒子图像中获取曲率信息似乎是不可能的。结果，由于直线近似，计算的矢量低估了真实速度，这进一步导致PIV仪器的系统误差。本文首次用定常流场的流线段代替单个矢量来解释两个记录之间的粒子弯曲轨迹，这种思想被称为非纯PIV。具体地说，引入变形场来描述粒子的位移，即，我们试图找到最佳的速度场，其相应的变形矢量场与粒子位移相一致。由于变形函数的变化可以用速度函数的变化来近似，因此纯粒子图像测速可以用迭代粒子图像测速来实现。也就是说，非纯PIV用变形矢量场而不是速度来扭曲图像，并且保持其余与迭代PIV相同。提出了两种非均匀变形方案--前向非均匀变形询问（FDDI）和中心非均匀变形询问（CDDI）。在合成图像上进行测试后，FDDI在不同的单通道位移估计器（互相关、光流、深度学习流）上实现了显著的精度提高。此外，三个真实的PIV图像对的结果表明，不可忽略的曲率效应的CDI为基础的PIV，和我们的FDDI提供更大的速度估计（更准确）在快速弯曲的流线区域。FDDI和精确密度估计器相结合的精度提高意味着我们的双纯PIV为复杂流场测量开辟了一条新的途径。
英文摘要：
The existing particle image velocimetry (PIV) do not consider the curvature effect of the non-straight particle trajectory, because it seems to be impossible to obtain the curvature information from a pair of particle images. As a result, the computed vector underestimates the real velocity due to the straight-line approximation, that further causes a systematic error for the PIV instrument. In this work, the particle curved trajectory between two recordings is firstly explained with the streamline segment of a steady flow (diffeomorphic transformation) instead of a single vector, and this idea is termed as diffeomorphic PIV. Specifically, a deformation field is introduced to describe the particle displacement, i.e., we try to find the optimal velocity field, of which the corresponding deformation vector field agrees with the particle displacement. Because the variation of the deformation function can be approximated with the variation of the velocity function, the diffeomorphic PIV can be implemented as iterative PIV. That says, the diffeomorphic PIV warps the images with deformation vector field instead of the velocity, and keeps the rest as same as iterative PIVs. Two diffeomorphic deformation schemes -- forward diffeomorphic deformation interrogation (FDDI) and central diffeomorphic deformation interrogation (CDDI) -- are proposed. Tested on synthetic images, the FDDI achieves significant accuracy improvement across different one-pass displacement estimators (cross-correlation, optical flow, deep learning flow). Besides, the results on three real PIV image pairs demonstrate the non-negligible curvature effect for CDI-based PIV, and our FDDI provides larger velocity estimation (more accurate) in the fast curvy streamline areas. The accuracy improvement of the combination of FDDI and accurate dense estimator means that our diffeomorphic PIV paves a new way for complex flow measurement.
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