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<p><b>Abstract</b>—This work presents a new approach for the analysis of convex minimization-based edge-preserving image smoothing and the parameter selection therein. The global solution, that is, the response of a convex smoothing model to the ideal step edge, is derived in close-form. By analyzing the close-form solution, insights are drawn into how the optimal solution responds to edges in the data and how the parameter values affect resultant edges in the solution. Based on this, a scheme is proposed for selecting parameters to achieve desirable responses at edges. The theoretic results are substantiated by experiments.</p>
Convexity, edge preservation, energy minimization, image smoothing, Markov random field (MRF), maximum a posteriori (MAP), parameter selection, regularization.

S. Z. Li, "Close-Form Solution and Parameter Selection for Convex Minimization-Based Edge-Preserving Smoothing," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 20, no. , pp. 916-932, 1998.
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