  Curve evolution is often used to solve computer vision problems. If the curve
evolution fails to converge, we would not be able to solve the targeted problem
in a lifetime. This paper studies the theoretical aspect of the convergence of
a type of general curve evolutions. We establish a theory for analyzing and
improving the stability of the convergence of the general curve evolutions.
Based on this theory, we ascertain that the convergence of a known curve
evolution is marginal stable. We propose a way of modifying the original curve
evolution equation to improve the stability of the convergence according to our
theory. Numerical experiments show that the modification improves the
convergence of the curve evolution, which validates our theory.
