Recovering fluid-type motions using Navier-Stokes potential flow
Recovering fluid-type motions using Navier-Stokes potential flow
复制标题
使用纳维-斯托克斯势流恢复流体类型运动
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Jingyi Yu
中科院分区：
文献类型：
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作者：
Feng Li;Liwei Xu;P. Guyenne;Jingyi Yu
经典光流假设特征点在帧间保持恒定的亮度。对于流体类型的运动，如烟雾或云，恒定亮度的假设并不成立，从它们的图像中准确地估计运动流是困难的。在本文中，我们介绍了一个简单而有效的Navier-Stokes（NS）势流模型恢复流体型运动。我们的方法将图像视为波前表面，并对表面下方的3D势流进行建模。速度势的梯度描述了每个体素处的运动流。我们首先推导出一个一般的亮度约束，明确模型波前（亮度）的变化方面的速度潜力。然后，我们使用一系列的偏微分方程，分别模拟的动态的潜在流。为了求解势流，我们使用Dirichlet-Neumann算子（DNO）将三维体积速度势简化为二维表面速度势。我们通过泰勒展开近似的DNO和开发一个傅立叶域的方法来有效地估计泰勒系数。最后，我们展示了如何使用DNO恢复速度潜力的图像，以及传播波前（图像）随着时间的推移。在合成图像和真实的图像上的实验结果表明，该方法具有较好的鲁棒性和可靠性.
The classical optical flow assumes that a feature point maintains constant brightness across the frames. For fluid-type motions such as smoke or clouds, the constant brightness assumption does not hold, and accurately estimating the motion flow from their images is difficult. In this paper, we introduce a simple but effective Navier-Stokes (NS) potential flow model for recovering fluid-type motions. Our method treats the image as a wavefront surface and models the 3D potential flow beneath the surface. The gradient of the velocity potential describes the motion flow at every voxel. We first derive a general brightness constraint that explicitly models wavefront (brightness) variations in terms of the velocity potential. We then use a series of partial differential equations to separately model the dynamics of the potential flow. To solve for the potential flow, we use the Dirichlet-Neumann Operator (DNO) to simplify the 3D volumetric velocity potential to 2D surface velocity potential. We approximate the DNO via Taylor expansions and develop a Fourier domain method to efficiently estimate the Taylor coefficients. Finally we show how to use the DNO to recover the velocity potential from images as well as to propagate the wavefront (image) over time. Experimental results on both synthetic and real images show that our technique is robust and reliable.