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A Novel Framework for Shock Filter Using Partial Differential Equations

1
School of Management Science and Engineering, Shandong Normal University, Jinan 250014, China
2
School of Electrical and Automation, Qilu University of Technology, Jinan 250353, China
*
Authors to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Entropy 2017, 19(4), 142; https://doi.org/10.3390/e19040142
Received: 31 December 2016 / Revised: 12 March 2017 / Accepted: 22 March 2017 / Published: 26 March 2017
(This article belongs to the Section Information Theory, Probability and Statistics)
In dilation or erosion processes, a shock filter is widely used in signal enhancing or image deburring. Traditionally, sign function is employed in shock filtering for reweighting of edge-detection in images and decides whether a pixel should dilate to the local maximum or evolve to the local minimum. Some researchers replace sign function with tanh function or arctan function, trying to change the evolution tracks of the pixels when filtering is in progress. However, analysis here reveals that only function replacement does usually not work. This paper revisits first shock filters and their modifications. Then, a fuzzy shock filter is proposed after a membership function in a shock filter model is adopted to adjust the evolve rate of image pixels. The proposed filter is a parameter tuning system, which unites several formulations of shock filters into one fuzzy framework. Experimental results show that the new filter is flexible and robust and can converge fast. View Full-Text
Keywords: signal enhancing; fuzzy logic; partial differential equation (PDE); shock filter signal enhancing; fuzzy logic; partial differential equation (PDE); shock filter
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Duan, C.; Lu, H. A Novel Framework for Shock Filter Using Partial Differential Equations. Entropy 2017, 19, 142.

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