A new approach to the temporal evolution of a family of curves

In this study the problem of modeling a family of curves is addressed. The need of such modeling appears frequently in many aspects of image processing where many linear structures keep spatial relationships during their evolution. We present a modeling tool well suited to the spatial modeling of a family of curves, and which can be very useful for motion tracking and curve evolution as well. The family of curves is represented as the line paths (orbits) of a "spline vector field", i.e. a vector field interpolating data using a framework similar to the theory of spline curves. The model is exemplified with oceanic satellite data. Its usefulness for curve evolution modeling is also presented.