Tracking Level Set Representation Driven by a Stochastic Dynamics

We introduce a non-linear stochastic filtering technique to track the state of a free curve from image data. The approach we propose is implemented through a particle filter, which includes color measurements characterizing the target and the background respectively. 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. Specific noise models lead to the traditional level set evolution law based on mean curvature motions, while other forms lead to new evolution laws with different smoothing behaviors. In these evolution models, we propose to combine local photometric information, some velocity induced by the curve displacement and an uncertainty modeling of the dynamics. The associated filter capabilities are demonstrated on various sequences with highly deformable objects.