This paper focuses on the tracking of free curves using non-linear stochastic filtering techniques. It relies on a particle filter which includes color measurements. The curve and its velocity are defined through two coupled implicit level set representations. The stochastic dynamics of the curve is expressed directly on the level set function associated to the curve representation and combines a velocity field captured from the additional second level set attached to the past curve's points location. The curve's dynamics combines a lowdimensional noise model and a data-driven local force. We demonstrate how this approach allows the tracking of highly and rapidly deforming objects, such as convective cells in infra-red satellite images, while providing a location-dependent assessment of the estimation confidence.