Schlieren imaging is a widely used technique for flow visualization in turbulence and combustion investigations due to its high sensitivity, flexibility and easiness in use. With the development of digital imaging and image processing techniques, it is possible to retrieve velocity measurements using time-resolved schlieren imaging sequences. In this paper, an optimization and parametric study has been conducted on a newly proposed schlieren motion estimation (SME) algorithm, based on the high speed schlieren images of a jet flow and the transient ignition process of impinging flames. The SME algorithm is optimized using a graduated non-convexity (GNC) computing scheme, which employs a three stage strategy by linearly combining a convex quadratic function and a slightly non-convex generalized Charbonnier function. The Euler–Lagrange equations have been derived, while the penalty function was separated so that penalty functions can be changed conveniently. Parametric investigations have been conducted to discuss the influence of weight parameters, while the suitable ranges have been obtained after intensive calculations. Comprehensive comparisons have been made between the SME and GNC-SME methods, which indicates that the GNC scheme can preserve the boundary well and avoid local divergence and over-smoothness at the same time. The suitable weight parameter range is also broadened by using the GNC technique. The better robustness of GNC-SME method makes it more adaptive to various applications.

Schlieren成像技术具有很高的灵敏度，灵活性和易用性，是湍流和燃烧研究中流动可视化的一种广泛使用的技术。随着数字成像和图像处理技术的发展，可以使用时间分辨的纹影成像序列来检索速度测量值。本文基于射流的高速schlieren图像和撞击火焰的瞬时点火过程，对新提出的schlieren运动估计（SME）算法进行了优化和参数研究。SME算法使用分级非凸度（GNC）计算方案进行了优化，该方案采用三阶段策略，通过线性组合凸二次函数和略微非凸广义Charbonnier函数。推导了Euler-Lagrange方程，同时分离了惩罚函数，以便可以方便地更改惩罚函数。已经进行了参数研究以讨论重量参数的影响，而经过大量计算后获得了合适的范围。SME和GNC-SME方法之间进行了全面的比较，这表明GNC方案可以很好地保留边界并同时避免局部差异和过度平滑。通过使用GNC技术，还可以扩大合适的重量参数范围。GNC-SME方法具有更好的鲁棒性，使其更适合各种应用。已经进行了参数研究以讨论重量参数的影响，而经过大量计算后获得了合适的范围。SME方法和GNC-SME方法之间进行了全面的比较，这表明GNC方案可以很好地保留边界，同时避免局部差异和过度平滑。通过使用GNC技术，还可以扩大合适的重量参数范围。GNC-SME方法具有更好的鲁棒性，使其更适合各种应用。已经进行了参数研究以讨论重量参数的影响，而经过大量计算后获得了合适的范围。SME方法和GNC-SME方法之间进行了全面的比较，这表明GNC方案可以很好地保留边界，同时避免局部差异和过度平滑。通过使用GNC技术，还可以扩大合适的重量参数范围。GNC-SME方法具有更好的鲁棒性，使其更适合各种应用。这表明GNC方案可以很好地保留边界，同时避免局部发散和过度平滑。通过使用GNC技术，还可以扩大合适的重量参数范围。GNC-SME方法具有更好的鲁棒性，使其更适合各种应用。这表明GNC方案可以很好地保留边界，并同时避免局部发散和过度平滑。通过使用GNC技术，还可以扩大合适的重量参数范围。GNC-SME方法具有更好的鲁棒性，使其更适合各种应用。