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A Novel Edge Detection Method Based on the Regularized Laplacian Operation

College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
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Symmetry 2018, 10(12), 697; https://doi.org/10.3390/sym10120697
Received: 12 November 2018 / Revised: 21 November 2018 / Accepted: 22 November 2018 / Published: 3 December 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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Abstract

In this paper, an edge detection method based on the regularized Laplacian operation is given. The Laplacian operation has been used extensively as a second-order edge detector due to its variable separability and rotation symmetry. Since the image data might contain some noises inevitably, regularization methods should be introduced to overcome the instability of Laplacian operation. By rewriting the Laplacian operation as an integral equation of the first kind, a regularization based on partial differential equation (PDE) can be used to compute the Laplacian operation approximately. We first propose a novel edge detection algorithm based on the regularized Laplacian operation. Considering the importance of the regularization parameter, an unsupervised choice strategy of the regularization parameter is introduced subsequently. Finally, the validity of the proposed edge detection algorithm is shown by some comparison experiments. View Full-Text
Keywords: edge detection; Laplacian operation; regularization; parameter selection; performance evaluation edge detection; Laplacian operation; regularization; parameter selection; performance evaluation
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Xu, H.; Xiao, Y. A Novel Edge Detection Method Based on the Regularized Laplacian Operation. Symmetry 2018, 10, 697.

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