Adaptive Mathematical Morphology with Fuzzy Structuring Element


  • Mingzhu Zhang College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China
  • Mengdi Sun Dong’e Nanhu Xingzhi School, Liaocheng, China
  • Huichao Sun School of Information Science and Engineering, Shandong Normal University, Jinan, China
  • Zhonggui Sun School of Mathematical Sciences, Liaocheng University, Liaocheng, China



Adaptive morphology, fuzzy structuring element, serial implementation, stability


As a well-known nonlinear tool, mathematical morphology (MM) is still active in image processing. Benefiting from the fixed structuring element (SE), traditional MM (TMM) gets solid theoretical foundation. However, due to the inherent diversity of pixels in an image, the rigid SE paradigm is not always practical. As a result, the development of morphology with adaptive SE, known as adaptive MM (AMM), has been a significant challenge. In this work, we present a novel approach for designing adaptive SE using the \boldsymbolα-cut of a fuzzy set. By implementing dilation and erosion operations serially, we obtain an AMM (named SAMM) that is both adaptive to image content and robust to noise. Additionally, the operators in SAMM inherit important properties from TMM as much as possible. We provide theoretical proofs and simulated results to support our conclusion. Preliminary experiments on edge detection and noise reduction confirm the effectiveness of our SAMM both quantitatively and perceptually. In the denoising experiments, SAMM achieves the best performance in the nine algorithms involved, with its PSNR value surpassing the second-ranked approach by more than 0.6 dB overall. Additionally, its SSIM quantification metric also ranks prominently among the top performers.


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How to Cite

Zhang, M., Sun, M., Sun, H., & Sun, Z. (2024). Adaptive Mathematical Morphology with Fuzzy Structuring Element. COMPUTING AND INFORMATICS, 43(2), 317–342.



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