A stochastic flow for feature extraction

In recent years evolution of level sets of two-dimensional functions or images in time through a partial differential equation has emerged as an important tool in image processing. Curve evolutions, which may be viewed as an evolution of a single level curve, has been applied to a wide variety of problems such as smoothing of shapes, shape analysis and shape recovery. We give a stochastic interpretation of the basic curve smoothing equation, the so called geometric heat equation, and show that this evolution amounts to a rotational diffusion movement of the particles along the contour. Moreover, assuming that a priori information about the orientation of objects to be preserved is known, we present new flows which amount to weighting the geometric heat equation nonlinearly as a function of the angle of the normal to the curve at each point.