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Axioms 2018, 7(3), 53; https://doi.org/10.3390/axioms7030053

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

1
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong
2
Centre de Mathématiques et de Leurs Applications, ENS de Cachan, 94230 Paris, France
*
Author to whom correspondence should be addressed.
Received: 18 June 2018 / Revised: 1 August 2018 / Accepted: 1 August 2018 / Published: 2 August 2018
(This article belongs to the Special Issue Advanced Numerical Methods in Applied Sciences)
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Abstract

The goal of edge-histogram specification is to find an image whose edge image has a histogram that matches a given edge-histogram as much as possible. Mignotte has proposed a non-convex model for the problem in 2012. In his work, edge magnitudes of an input image are first modified by histogram specification to match the given edge-histogram. Then, a non-convex model is minimized to find an output image whose edge-histogram matches the modified edge-histogram. The non-convexity of the model hinders the computations and the inclusion of useful constraints such as the dynamic range constraint. In this paper, instead of considering edge magnitudes, we directly consider the image gradients and propose a convex model based on them. Furthermore, we include additional constraints in our model based on different applications. The convexity of our model allows us to compute the output image efficiently using either Alternating Direction Method of Multipliers or Fast Iterative Shrinkage-Thresholding Algorithm. We consider several applications in edge-preserving smoothing including image abstraction, edge extraction, details exaggeration, and documents scan-through removal. Numerical results are given to illustrate that our method successfully produces decent results efficiently. View Full-Text
Keywords: edge-histogram; edge-preserving smoothing; histogram specification edge-histogram; edge-preserving smoothing; histogram specification
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Chan, K.C.K.; Chan, R.H.; Nikolova, M. A Convex Model for Edge-Histogram Specification with Applications to Edge-Preserving Smoothing. Axioms 2018, 7, 53.

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