Zhonggui Sun^1,2, Meiqi Lyu¹, Jie Li², Ying Wang², Xinbo Gao³

　

1 School of Mathematical Sciences, Liaocheng University

2 Video and Image Processing System Laboratory, School of Electronic Engineering, Xidian University

3 The Chongqing Key Laboratory of Image Cognition, Chongqing University of Posts and Telecommunications
 
　

Abstract

Mathematical morphology (MM) is traditional and yet applied in many areas. Among the relevant researches, nonlocal extensions have been studied due to their advantages of adaptivity and nonlocal self-similarity. However, these extensions are fragile to noises and easily result in gray value deviation (the maximum grayscale value is changed significantly). In this paper, a local-nonlocal mathematical morphology (LNLMM) is proposed: we use flat structuring element (SE) to avoid gray value deviation and introduce local information to suppress noises. Moreover, to speed up the nonlocal computation involved, we construct the SE in low-dimensional space. Benefiting from the constraint of k-reciprocal nearest neighbors (KRNN) on the SE, the operators of LNLMM theoretically inherit the important mathematical properties from traditional MM, that gives solid supports in applications. With denoising experiments, the powerful performance of LNLMM is preliminarily verified.


　

Paper

Z. Sun, S. M. Lyu, J. Li et al.,  A local-nonlocal mathematical morphology. in Neurocomputing, 2022. [pdf|code]

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