Level-Set Curve Particles

In many applications it is necessary to track a moving and deforming boundary on the plane from infrequent, sparse measurements. For instance, each of a set of mobile observers may be able to tell the position of a point on the boundary. Often boundary components split, merge, appear, and disappear over time. Data are typically sparse and noisy and the underlying dynamics is uncertain. To address these issues, we use a particle filter to represent a distribution in the large space of all plane curves and propose a full-fledged combination of level sets and particle filters. Our main contribution is in controlling the potentially high expense of multiplying the cost of a level set representation of boundaries by the number of particles needed. Experiments on tracking the boundary of a colon in tomographic imagery from sparse edge measurements show the promise of the approach.