Three-dimensional particle cluster tracking algorithm using affine transformation

In Particle Image Velocimetry (PIV), the cross correlation tracking technique is widely used to analyze the particle images. The technique assumes that the fluid motion, within small regions of the flow field, is given by parallel movements over short time intervals. However, actual flow fields may have some distorted motion, such as rotation and shear. Therefore, if the distortion of the flow field is not negligible, the fluid motion can not be tracked well using the cross correlation technique. The author proposed a new particle tracking technique, based on the particle cluster matching using linear Affine Transformation. The algorithm can be applied to flow fields which exhibit characteristics such as rotation and shear. The deformation of the cluster pattern is expressed by the linear Affine Transformation. The parameter of the transformation can be determined using the least square technique from the particle positions. The effectiveness of the tracking techniques, including 3D cross correlation, Spring Model and Affine Transformation, were evaluated with synthetic data of three-dimensional flow field. The cross correlation technique could be applicable to the small deformation cases. When the deformation of particle pattern between two images are very large, the pattern deformation could not be expressed by the Affine Transformation, i.e., linear transformation, resulting in mis-tracking. However, the Spring Model technique was found to be more effective even in the larger deformation condition, because the Spring Model does not assume the linear transformation.