The Stability of Convergence of Curve Evolutions in Vector Fields
This addresses stability issues in curve evolutions for computer vision applications, but it is incremental as it builds on existing methods with theoretical improvements.
The paper tackles the problem of ensuring convergence in curve evolutions used for computer vision by establishing a theory to analyze and improve stability, showing that a known evolution is marginally stable and proposing a modification that enhances convergence in numerical experiments.
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.