A new algorithm for the interrogation of 3D holographic PTV data based on deterministic annealing and expectation minimization optimization

Recently we have presented a new particle tracking algorithm for the interrogation of 2D-PTV data [Kuzmanowski et al. (1998); Stellmacher and Obermayer (2000) Exp Fluids 28: 506-518], which estimates particle correspondences and local flow-field parameters simultaneously. The new method is based on an algorithm recently proposed by Cold et al. [Pattern Recognition (1998) 31:1019-1031], and has two advantages: (1) It allows not only local velocity but also other local components of the flow field such as rotation and shear to be determine; and (2) it allows flow-field parameters also to be reliably determined in regions of high velocity gradients (e.g., vortices or shear flow). In this contribution we extend this algorithm to the interrogation of 3D holographic particle image velocimetry (PIV) data. Benchmarks with cross-correlation and nearest-neighbor methods show that the algorithm retains the superior performance which we have observed for the 2D case. Because PTV methods scale with the square of the number of particles rather than exponentially with the dimension of the interrogation cell, the new method is much faster than cross-correlation-based methods without sacrificing accuracy, and it is well adapted to the low particle seeding densities of holographic PIV methods.