Abstract
The theory of degenerate parabolic equations of the forms u_t=(\\Phi(u_x))\_{x} and v\_{t}=(\\Phi(v))\_{xx} is used to analyze the process of contour enhancement in image processing, based on the evolution model of Sethian and Malladi. The problem is studied in the framework of nonlinear diffusion equations. It turns out that the standard initial-value problem solved in this theory does not fit the present application since it it does not produce image concentration. Due to the degenerate character of the diffusivity at high gradient values, a new free boundary problem with singular boundary data can be introduced, and it can be solved by means of a non-trivial problem transformation, thus obtaining a new type of solutions that fit the desired concentration requirements. The asymptotic convergence to a sharp front is established and rates calculated.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
