用于随机粒子追踪的非平衡最优输运
Unbalanced optimal transport for stochastic particle tracking
AI总结：
本文针对粒子追踪测速中重建误差导致的轨迹估计难题，提出一种基于非平衡最优输运的全局一致最近邻追踪算法，在高斯测度空间中优化二元输运计划并自动确定匹配粒子数，最终通过3D打印脑动脉瘤体外实验验证其鲁棒性。
摘要：
非侵入式流场测量技术（如粒子追踪测速）通过在连续时间步中配对示踪粒子位置来解析三维速度场。这些轨迹对于评估涡量、剪切应力、压力和相干结构等物理量至关重要。传统方法通过追踪算法确定性地重建粒子位置并提取粒子轨迹。然而，由于高粒子密度、粒子图像重叠以及错误重建的三维粒子位置所导致的测量噪声，可靠的轨迹估计面临挑战。为克服这一挑战，概率方法对粒子位置的不确定性进行量化，通常采用高斯概率分布。然而，依赖最近邻搜索的标准确定性追踪算法不能直接扩展到概率设定中。此外，此类算法未必能找到对重建误差具有鲁棒性的全局一致解。本文旨在开发一种全局一致的最近邻算法，从所有帧中重建的高斯粒子分布中鲁棒地提取随机粒子轨迹。我们的追踪算法依赖于高斯测度度量空间中的非平衡最优输运理论。具体而言，我们优化一个二元输运计划，以在时间帧之间高效地移动重建粒子位置的高斯分布。我们通过在高斯测度度量空间中计算部分Wasserstein距离来实现这一目标。我们的追踪算法对位置重建误差具有鲁棒性，因为它通过超参数优化自动检测应匹配的粒子数量。最后，我们使用三维打印的脑动脉瘤进行体外流动实验来验证我们的方法。
英文摘要：
Non-invasive flow measurement techniques, such as particle tracking velocimetry, resolve 3D velocity fields by pairing tracer particle positions in successive time steps. These trajectories are crucial for evaluating physical quantities like vorticity, shear stress, pressure, and coherent structures. Traditional approaches deterministically reconstruct particle positions and extract particle tracks using tracking algorithms. However, reliable track estimation is challenging due to measurement noise caused by high particle density, particle image overlap, and falsely reconstructed 3D particle positions. To overcome this challenge, probabilistic approaches quantify the epistemic uncertainty in particle positions, typically using a Gaussian probability distribution. However, the standard deterministic tracking algorithms relying on nearest-neighbor search do not directly extend to the probabilistic setting. Moreover, such algorithms do not necessarily find globally consistent solutions robust to reconstruction errors. This paper aims to develop a globally consistent nearest-neighborhood algorithm that robustly extracts stochastic particle tracks from the reconstructed Gaussian particle distributions in all frames. Our tracking algorithm relies on the unbalanced optimal transport theory in the metric space of Gaussian measures. Specifically, we optimize a binary transport plan for efficiently moving the Gaussian distributions of reconstructed particle positions between time frames. We achieve this by computing the partial Wasserstein distance in the metric space of Gaussian measures. Our tracking algorithm is robust to position reconstruction errors since it automatically detects the number of particles that should be matched through hyperparameter optimization. Finally, we validate our method using an in vitro flow experiment using a 3D-printed cerebral aneurysm.
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