Point Set Registration via Particle Flow Filtering

This thesis project presents an innovative registration algorithm using the particle flow filter. This is the first known approach to image registration using the particle flow filter. The particle flow filter is a Bayesian filter that uses particles to represent probability densities. Others have approached image registration as a Bayesian filtering problem; however, none have used the particle flow filter. The particle flow filter is not constrained to the highly restrictive unimodal, linear, and Gaussian assumptions of many Bayesian filters such as the Kalman filter. The particle flow filter works for any probability density function. Additionally, the particle flow filter is computationally more efficient than other multimodal filters such as the better-known particle filter. Unlike the particle filter, the particle flow filter does not require particle resampling or importance weight updates. Rather, the proposal density is formed by flowing the a priori probability density to the a posteriori using the Fokker-Planck equation. Moreover, the particle flow filter is more parallelizable than the particle filter. Regarding image registration, the particle flow filter is more robust to noise and outliers than other methods. The particle flow filter algorithms were implemented in MATLAB for both 2D and 3D rigid body point-set registration. Additionally, the particle filter method proposed by and iterative closest point algorithms were implemented for comparison. All three registration techniques were tested with a high degree of initial misalignment and noise. For the same alignment accuracy, the new particle flow filter algorithms were 244% faster than the particle filter for certain challenging problems. For the same alignment time, the particle flow filter reduced misalignment by as much as 35% compared to the particle filter. The particle flow filter achieved 100% alignment with enough particles, and reduced misalignment by as much as 75% over that of iterative closest point. These results demonstrate that image registration via the particle flow filter significantly outperforms the particle filter and iterative closest point algorithms in the presence of noise and a high degree of initial misalignment. Future areas of research for particle flow filter image registration include deformable registration and GPU parallelization