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The goal of edge-histogram specification is to find an image whose edge imagehas a histogram that matches a given edge-histogram as much as possible.Mignotte has proposed a non-convex model for the problem [M. Mignotte. Anenergy-based model for the image edge-histogram specification problem. IEEETransactions on Image Processing, 21(1):379--386, 2012]. In his work, edgemagnitudes of an input image are first modified by histogram specification tomatch the given edge-histogram. Then, a non-convex model is minimized to findan output image whose edge-histogram matches the modified edge-histogram. Thenon-convexity of the model hinders the computations and the inclusion of usefulconstraints such as the dynamic range constraint. In this paper, instead ofconsidering edge magnitudes, we directly consider the image gradients andpropose a convex model based on them. Furthermore, we include additionalconstraints in our model based on different applications. The convexity of ourmodel allows us to compute the output image efficiently using eitherAlternating Direction Method of Multipliers or Fast IterativeShrinkage-Thresholding Algorithm. We consider several applications inedge-preserving smoothing including image abstraction, edge extraction, detailsexaggeration, and documents scan-through removal. Numerical results are givento illustrate that our method successfully produces decent results efficiently.

A Convex Model for Edge-Histogram Specification with Applications to Edge-preserving Smoothing