# Dynamic level sets for visual tracking

Marc Niethammer, Allen Tannenbaum

January 2003
### Abstract

In this paper we describe two methods for tracking planar curves which are allowed to change topology. In contrast to previous approaches a level set formulation is used that allows for the propagation of state information (here a velocity vector) with every point on a curve. The curve dynamics are derived by minimizing an action integral (based on Hamilton&$#$39;s principle). Incorporating velocity information for every point on a curve lifts the originally two dimensional problem to four dimensions, and thus to a codimeusion three problem. Since basic level set approaches implicitly describe codimension one hypersurfaces, we introduce two methods suitable for codimension three problems within a level set framework. The partial level set approach, which propagates velocity information along with the curve by solving two additional transport equations, and the full level set approach, which is formulated by means of a vector distance function evolution equation. The full level set approach allow for complete topological flexibility (including intersecting curves in the image plane). However, it is computationally expensive. The partial level set approach compromises the topological flexibility for computational efficiency. In particular, the full level set ap proacb has the potential for tracking objects throughout occlusions, when combined with a suitable collision detection algorithm.

Publication

*Proceedings of the Conference on Decision and Control*

###### Professor of Computer Science

My research interests include image registration, image segmentation, shape analysis, machine learning, and biomedical applications.