Edge-Preserving Smoothing by Convex Minimization
This work presents a new approach for analyzing the problem of edge-preserving image smoothing using convex minimization and for selecting smoothing parameters. The close-form (global) solution is derived as the response of a convex smoothing model to the ideal step edge. Insights into how the minimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution are drawn from the analytic expression of the close-form solution. Based on this, a scheme is proposed for selecting parameters to achieve desirable response at edges.