By Frédéric Cao
In photo processing, "motions through curvature" supply a good method to soft curves representing the boundaries of items. In this kind of movement, every one element of the curve strikes, at any fast, with an ordinary pace equivalent to a functionality of the curvature at this aspect. This booklet is a rigorous and self-contained exposition of the thoughts of "motion via curvature". The method is axiomatic and formulated when it comes to geometric invariance with appreciate to the location of the observer. this is often translated into mathematical phrases, and the writer develops the strategy of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then attracts a whole parallel with one other axiomatic technique utilizing level-set equipment: this results in generalized curvature motions. ultimately, novel, and extremely exact, numerical schemes are proposed permitting one to compute the answer of hugely degenerate evolution equations in a very invariant approach. The convergence of this scheme is usually proved.