{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:20:40Z","timestamp":1760059240192,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T00:00:00Z","timestamp":1748908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Key Laboratory of Advanced Computing of Gansu Province, Key Talent Project of gansu province, Fundamental Research Funds for the Central Universities of China","doi-asserted-by":"publisher","award":["lzujbky-2022-pd12","22YF7GA006","22JR5RA492"],"award-info":[{"award-number":["lzujbky-2022-pd12","22YF7GA006","22JR5RA492"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Gansu Province, China","award":["lzujbky-2022-pd12","22YF7GA006","22JR5RA492"],"award-info":[{"award-number":["lzujbky-2022-pd12","22YF7GA006","22JR5RA492"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Pulse-coupled neural networks (PCNNs) are capable of segmenting digital images in a multistage unsupervised fashion; however, optimal output selection remains challenging. To address the above problem, this paper emphasizes the role of the step size, which influences the decreasing speed of the membrane potential and the dynamic threshold profoundly. A dynamic-step-size mechanism is proposed, utilizing trigonometric functions to adaptively control segmentation granularity, along with the supervised optimization of a single parameter \u03d5 via intersection over union (IoU) maximization, reducing tuning complexity. Thus, the number of groups of image segmentation becomes controllable and the model itself becomes more adaptive than ever for various scenarios. Experimental results further demonstrate the enhanced robustness under noise (92.1% Dice at \u03c3=0.2), outperforming SPCNN and PCNN with IoU = 0.8863, Dice = 0.901, and 0.8684 s\/image.<\/jats:p>","DOI":"10.3390\/e27060597","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T06:21:51Z","timestamp":1748931711000},"page":"597","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Dynamic-Step-Size Regulation in Pulse-Coupled Neural Networks"],"prefix":"10.3390","volume":"27","author":[{"given":"Jiayi","family":"Geng","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fanqing","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shouliang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yulin","family":"Shen","sequence":"additional","affiliation":[{"name":"Gansu Computing Center, Lanzhou 730030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,3]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Ma, Y., Lin, D., Zhang, B., Liu, Q., and Gu, J. 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