Finite-Element Level-Set Curve Particles

Particle filters encode a time-evolving probability density by maintaining a random sample from it. Level sets represent closed curves as zero crossings of functions of two variables. The combination of level sets and particle filters presents many conceptual advantages when tracking uncertain, evolving boundaries over time, but the cost of combining these two ideas seems prima facie prohibitive. A previous publication showed that a large number of virtual level set particles can be tracked with a logarithmic amount of work for propagation and update. We now make level- set curve particles more efficient by borrowing ideas from the Finite Element Method (FEM). This improves level-set curve particles in both running time (by a constant factor) and accuracy of the results.