We introduce a stochastic filtering technique for the tracking of closed curves from image sequence. For that purpose, we design a continuous-time dynamics that allows us to infer inter-frame deformations. The curve is defined by an implicit level-set representation and the stochastic dynamics is expressed on the level-set function. It takes the form of a stochastic partial differential equation with a Brownian motion of low dimension. The evolution model we propose combines local photometric information, deformations induced by the curve displacement and an uncertainty modeling of the dynamics. Specific choices of noise models and drift terms lead to an evolution law based on mean curvature as in classic level set methods, while other choices yield new evolution laws. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background photometric probability densities respectively. The merit of this filter is demonstrated on various satellite image sequences depicting the evolution of complex geophysical flows.