{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T02:22:20Z","timestamp":1778725340859,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,11]],"date-time":"2021-02-11T00:00:00Z","timestamp":1613001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["107-2118-M-009-006-MY3"],"award-info":[{"award-number":["107-2118-M-009-006-MY3"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology, Taiwan","doi-asserted-by":"publisher","award":["108-2221-E-008-081-MY3"],"award-info":[{"award-number":["108-2221-E-008-081-MY3"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Nowadays, deep learning methods with high structural complexity and flexibility inevitably lean on the computational capability of the hardware. A platform with high-performance GPUs and large amounts of memory could support neural networks having large numbers of layers and kernels. However, naively pursuing high-cost hardware would probably drag the technical development of deep learning methods. In the article, we thus establish a new preprocessing method to reduce the computational complexity of the neural networks. Inspired by the band theory of solids in physics, we map the image space into a noninteraction physical system isomorphically and then treat image voxels as particle-like clusters. Then, we reconstruct the Fermi\u2013Dirac distribution to be a correction function for the normalization of the voxel intensity and as a filter of insignificant cluster components. The filtered clusters at the circumstance can delineate the morphological heterogeneity of the image voxels. We used the BraTS 2019 datasets and the dimensional fusion U-net for the algorithmic validation, and the proposed Fermi\u2013Dirac correction function exhibited comparable performance to other employed preprocessing methods. By comparing to the conventional z-score normalization function and the Gamma correction function, the proposed algorithm can save at least 38% of computational time cost under a low-cost hardware architecture. Even though the correction function of global histogram equalization has the lowest computational time among the employed correction functions, the proposed Fermi\u2013Dirac correction function exhibits better capabilities of image augmentation and segmentation.<\/jats:p>","DOI":"10.3390\/e23020223","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T17:20:38Z","timestamp":1613150438000},"page":"223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Computational Complexity Reduction of Neural Networks of Brain Tumor Image Segmentation by Introducing Fermi\u2013Dirac Correction Functions"],"prefix":"10.3390","volume":"23","author":[{"given":"Yen-Ling","family":"Tai","sequence":"first","affiliation":[{"name":"Bio-Microsystems Integration Laboratory, Department of Biomedical Sciences and Engineering, National Central University, Taoyuan City 32001, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shin-Jhe","family":"Huang","sequence":"additional","affiliation":[{"name":"Bio-Microsystems Integration Laboratory, Department of Biomedical Sciences and Engineering, National Central University, Taoyuan City 32001, Taiwan"},{"name":"Chronic Disease Research Center, National Central University, Taoyuan City 32001, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2058-1263","authenticated-orcid":false,"given":"Chien-Chang","family":"Chen","sequence":"additional","affiliation":[{"name":"Bio-Microsystems Integration Laboratory, Department of Biomedical Sciences and Engineering, National Central University, Taoyuan City 32001, Taiwan"},{"name":"Chronic Disease Research Center, National Central University, Taoyuan City 32001, Taiwan"},{"name":"Shing-Tung Yau Center, National Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4392-3361","authenticated-orcid":false,"given":"Henry Horng-Shing","family":"Lu","sequence":"additional","affiliation":[{"name":"Shing-Tung Yau Center, National Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Institute of Statistics, National Chiao Tung University, Hsinchu 30010, Taiwan"},{"name":"Institute of Statistics, National Yang Ming Chiao Tung University, Hsinchu 30010, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"R97","DOI":"10.1088\/0031-9155\/58\/13\/R97","article-title":"A survey of MRI-based medical image analysis for brain tumor studies","volume":"58","author":"Bauer","year":"2013","journal-title":"Phys. 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