Discrete Approach to Curve Evolution
We propose a simple approach to evolution of digital planar curves that is specially designed to fit discrete nature of curves in digital images. The obtained curve evolution method by digital linearization has many advantages in comparison to curve evolutions in scale-space theories that are usually guided by diffusion equations. We will show that it leads to simplification of shape complexity, analog to evolutions guided by diffusion equations, but with no blurring (i.e., shape rounding) effects and no dislocation of relevant features. Moreover, in our approach the problem to determine the size of discrete steps for numerical implementations does not occur, since our evolution method leads in a natural way to a finite number of discrete evolution steps which are just the iterations of a basic procedure of digital linearization.
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