On the relationship between parametric and geometric active contours

Geometric active contours have many advantages over parametric active contours, such as computational simplicity and the ability to change the curve topology during deformation. While many of the capabilities of the older parametric active contours have been reproduced in geometric active contours, the relationship between the two has not always been clear. We develop a precise relationship between the two which includes spatially-varying coefficients, both tension and rigidity, and non-conservative external forces. The result is a very general geometric active contour formulation for which the intuitive design principles of parametric active contours can be applied. We demonstrate several novel applications in a series of simulations.