糖心TV

Title: Tracking particles by passing messages between images

Abstract:

We report construction of an efficient algorithm for learning parameters of dynamical statistical models, mapping many identical particles/markers from one image to another, given that positions of all the particles in both images are known. Our algorithm belongs to the class of the message-passing algorithms, also known in Computer Science, Information Theory and Statistical Physics under the name of Belief Propagation (BP). The algorithm is distributed thus allowing parallel implementation suitable for computations on multiple machines without significant inter-machine computational overhead. We test our algorithm on a model example of reconstructing diffusion coefficient and velocity gradient tensor from two consecutive images of many particles seed in two-dimensional and three-dimensional flows. Our numerical experiments show that this BP algorithm compares in quality of the parameter prediction with exact Markov Chain Monte-Carlo algorithm, while BP is far more superior in speed. We also suggest and analyze a random-distance model providing theoretical justification for BP accuracy in the diffusion and velocity gradient reconstruction. Our main conclusion is that the developed technique offers a very significant ``software" improvement in speed for Particle Image Velocimetry (PIV) technique, which currently constitutes the main working horse in experimental turbulent research. The talk is based on PNAS 10.1073/pnas.0910994107 published in Apr, 2010.