{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T22:12:05Z","timestamp":1782943925424,"version":"3.54.5"},"reference-count":48,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T00:00:00Z","timestamp":1688428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China","award":["62261053"],"award-info":[{"award-number":["62261053"]}]},{"name":"National Science Foundation of China","award":["SAST2019-048"],"award-info":[{"award-number":["SAST2019-048"]}]},{"name":"National Science Foundation of China","award":["BNR2019TD01022"],"award-info":[{"award-number":["BNR2019TD01022"]}]},{"name":"Shanghai Aerospace Science and Technology Innovation Fund","award":["62261053"],"award-info":[{"award-number":["62261053"]}]},{"name":"Shanghai Aerospace Science and Technology Innovation Fund","award":["SAST2019-048"],"award-info":[{"award-number":["SAST2019-048"]}]},{"name":"Shanghai Aerospace Science and Technology Innovation Fund","award":["BNR2019TD01022"],"award-info":[{"award-number":["BNR2019TD01022"]}]},{"name":"Beijing National Research Center for Information Science and Technology (BNRist)","award":["62261053"],"award-info":[{"award-number":["62261053"]}]},{"name":"Beijing National Research Center for Information Science and Technology (BNRist)","award":["SAST2019-048"],"award-info":[{"award-number":["SAST2019-048"]}]},{"name":"Beijing National Research Center for Information Science and Technology (BNRist)","award":["BNR2019TD01022"],"award-info":[{"award-number":["BNR2019TD01022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, a multi-focus image fusion algorithm via the distance-weighted regional energy and structure tensor in non-subsampled contourlet transform domain is introduced. The distance-weighted regional energy-based fusion rule was used to deal with low-frequency components, and the structure tensor-based fusion rule was used to process high-frequency components; fused sub-bands were integrated with the inverse non-subsampled contourlet transform, and a fused multi-focus image was generated. We conducted a series of simulations and experiments on the multi-focus image public dataset Lytro; the experimental results of 20 sets of data show that our algorithm has significant advantages compared to advanced algorithms and that it can produce clearer and more informative multi-focus fusion images.<\/jats:p>","DOI":"10.3390\/s23136135","type":"journal-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T00:53:04Z","timestamp":1688518384000},"page":"6135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Multi-Focus Image Fusion via Distance-Weighted Regional Energy and Structure Tensor in NSCT Domain"],"prefix":"10.3390","volume":"23","author":[{"given":"Ming","family":"Lv","sequence":"first","affiliation":[{"name":"College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7354-7494","authenticated-orcid":false,"given":"Liangliang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qingxin","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Guangxi University, Nanning 530004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhenhong","family":"Jia","sequence":"additional","affiliation":[{"name":"College of Information Science and Engineering, Xinjiang University, Urumqi 830046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liangfu","family":"Chen","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Remote Sensing Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100101, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1785-4024","authenticated-orcid":false,"given":"Hongbing","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.inffus.2021.06.008","article-title":"Image fusion meets deep learning: A survey and perspective","volume":"76","author":"Zhang","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.inffus.2022.09.019","article-title":"Current advances and future perspectives of image fusion: A comprehensive review","volume":"90","author":"Karim","year":"2023","journal-title":"Inf. Fusion"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.inffus.2022.11.014","article-title":"ZMFF: Zero-shot multi-focus image fusion","volume":"92","author":"Hu","year":"2023","journal-title":"Inf. Fusion"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zafar, R., Farid, M., and Khan, M. (2020). Multi-focus image fusion: Algorithms, evaluation, and a library. J. Imaging, 6.","DOI":"10.3390\/jimaging6070060"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Dong, Y., Chen, Z., Li, Z., and Gao, F. (2022). A multi-branch multi-scale deep learning image fusion algorithm based on DenseNet. Appl. Sci., 12.","DOI":"10.3390\/app122110989"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"104020","DOI":"10.1016\/j.dsp.2023.104020","article-title":"A review of image fusion: Methods, applications and performance metrics","volume":"137","author":"Singh","year":"2023","journal-title":"Digit. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"12389","DOI":"10.1007\/s11042-020-10462-y","article-title":"A novel multiscale transform decomposition based multi-focus image fusion framework","volume":"80","author":"Li","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"24303","DOI":"10.1007\/s11042-020-09154-4","article-title":"A novel approach for multi-focus image fusion based on SF-PAPCNN and ISML in NSST domain","volume":"79","author":"Li","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15651","DOI":"10.1007\/s11042-022-13949-y","article-title":"Multi-scale siamese networks for multi-focus image fusion","volume":"82","author":"Wu","year":"2023","journal-title":"Multimed. Tools Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1137\/05064182X","article-title":"Fast discrete curvelet transforms","volume":"5","author":"Candes","year":"2006","journal-title":"Multiscale Model. Simul."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/TIP.2005.859376","article-title":"The contourlet transform: An efficient directional multiresolution image representation","volume":"14","author":"Do","year":"2005","journal-title":"IEEE Trans. Image Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3089","DOI":"10.1109\/TIP.2006.877507","article-title":"The nonsubsampled contourlet transform: Theory, design, and applications","volume":"15","author":"Da","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1137\/060649781","article-title":"Optimally sparse multidimensional representation using shearlets","volume":"39","author":"Guo","year":"2007","journal-title":"SIAM J. Math. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.acha.2007.09.003","article-title":"Sparse directional image representations using the discrete shearlet transform","volume":"25","author":"Easley","year":"2008","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/s40815-022-01379-9","article-title":"An intelligent multimodal medical image fusion model based on improved fast discrete curvelet transform and type-2 fuzzy entropy","volume":"25","author":"Kumar","year":"2023","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2250063","DOI":"10.1142\/S0219649222500630","article-title":"Multimodal medical image fusion with improved multi-objective meta-heuristic algorithm with fuzzy entropy","volume":"22","author":"Kumar","year":"2023","journal-title":"J. Inf. Knowl. Manag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1016\/j.patrec.2008.02.002","article-title":"Multifocus image fusion by combining curvelet and wavelet transform","volume":"29","author":"Li","year":"2008","journal-title":"Pattern Recognit. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.1109\/TIP.2022.3154922","article-title":"Adaptive contourlet fusion clustering for SAR image change detection","volume":"31","author":"Zhang","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Li, L., Lv, M., Jia, Z., and Ma, H. (2023). Sparse representation-based multi-focus image fusion method via local energy in shearlet domain. Sensors, 23.","DOI":"10.3390\/s23062888"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"33248","DOI":"10.1109\/ACCESS.2023.3263183","article-title":"MGFuse: An infrared and visible image fusion algorithm based on multiscale decomposition optimization and gradient-weighted local energy","volume":"11","author":"Hao","year":"2023","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2864","DOI":"10.1109\/TIP.2013.2244222","article-title":"Image fusion with guided filtering","volume":"22","author":"Li","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1007\/s11760-013-0556-9","article-title":"Image fusion based on pixel significance using cross bilateral filter","volume":"9","year":"2015","journal-title":"Signal Image Video Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"10092","DOI":"10.1364\/AO.57.010092","article-title":"Fusion of multi-focus images via a Gaussian curvature filter and synthetic focusing degree criterion","volume":"57","author":"Tan","year":"2018","journal-title":"Appl. Opt."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"104794","DOI":"10.1016\/j.bspc.2023.104794","article-title":"Multimodal medical image fusion based on visual saliency map and multichannel dynamic threshold neural P systems in sub-window variance filter domain","volume":"84","author":"Feng","year":"2023","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10252","DOI":"10.1109\/JSEN.2023.3262775","article-title":"Multi-sensor infrared and visible image fusion via double joint edge preservation filter and non-globally saliency gradient operator","volume":"23","author":"Zhang","year":"2023","journal-title":"IEEE Sens. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1109\/TRPMS.2023.3239520","article-title":"Medical image fusion using a new entropy measure between intuitionistic fuzzy sets joint Gaussian curvature filter","volume":"7","author":"Jiang","year":"2023","journal-title":"IEEE Trans. Radiat. Plasma Med. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1007\/s11042-021-11362-5","article-title":"Multifocus image fusion using a convolutional elastic network","volume":"81","author":"Zhang","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ma, W., Wang, K., and Li, J. (2023). Infrared and visible image fusion technology and application: A review. Sensors, 23.","DOI":"10.3390\/s23020599"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.inffus.2016.12.001","article-title":"Multi-focus image fusion with a deep convolutional neural network","volume":"36","author":"Liu","year":"2017","journal-title":"Inf. Fusion"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"114385","DOI":"10.1109\/ACCESS.2019.2935006","article-title":"Multi-scale visual attention deep convolutional neural network for multi-focus image fusion","volume":"7","author":"Lai","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"105744","DOI":"10.1016\/j.engappai.2022.105744","article-title":"MSE-Fusion: Weakly supervised medical image fusion with modal synthesis and enhancement","volume":"119","author":"Wang","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4527","DOI":"10.1109\/TIP.2022.3184250","article-title":"A self-supervised residual feature learning model for multifocus image fusion","volume":"31","author":"Wang","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/s10489-021-02358-7","article-title":"A multi-focus image fusion method based on attention mechanism and supervised learning","volume":"52","author":"Jiang","year":"2022","journal-title":"Appl. Intell."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1049\/ipr2.12668","article-title":"An unsupervised multi-focus image fusion method based on Transformer and U-Net","volume":"17","author":"Jin","year":"2023","journal-title":"IET Image Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.inffus.2020.08.022","article-title":"MFF-GAN: An unsupervised generative adversarial network with adaptive and gradient joint constraints for multi-focus image fusion","volume":"66","author":"Zhang","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Liu, S., and Yang, L. (2022). BPDGAN: A GAN-based unsupervised back project dense network for multi-modal medical image fusion. Entropy, 24.","DOI":"10.3390\/e24121823"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108062","DOI":"10.1016\/j.sigpro.2021.108062","article-title":"Multi-focus image fusion based on nonsubsampled contourlet transform and residual removal","volume":"184","author":"Li","year":"2021","journal-title":"Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"104659","DOI":"10.1016\/j.bspc.2023.104659","article-title":"Parameter adaptive unit-linking pulse coupled neural network based MRI-PET\/SPECT image fusion","volume":"83","author":"Panigrahy","year":"2023","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.optcom.2010.08.085","article-title":"Multi-focus image fusion using a bilateral gradient-based sharpness criterion","volume":"284","author":"Tian","year":"2011","journal-title":"Opt. Commun."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3347","DOI":"10.1109\/TBME.2013.2282461","article-title":"A neuro-fuzzy approach for medical image fusion","volume":"60","author":"Das","year":"2013","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1650123","DOI":"10.1142\/S0218126616501231","article-title":"Multi-exposure and multi-focus image fusion in gradient domain","volume":"25","author":"Paul","year":"2016","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Xu, H., Ma, J., and Le, Z. (2020, January 7\u201312). FusionDN: A unified densely connected network for image fusion. Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI), New York, NY, USA.","DOI":"10.1609\/aaai.v34i07.6936"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zhang, H., Xu, H., and Xiao, Y. (2020, January 7\u201312). Rethinking the image fusion: A fast unified image fusion network based on proportional maintenance of gradient and intensity. Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI), New York, NY, USA.","DOI":"10.1609\/aaai.v34i07.6975"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ins.2019.08.066","article-title":"Infrared and visible image fusion based on target-enhanced multiscale transform decomposition","volume":"508","author":"Chen","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1109\/TPAMI.2020.3012548","article-title":"U2Fusion: A unified unsupervised image fusion network","volume":"44","author":"Xu","year":"2022","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1508","DOI":"10.3724\/SP.J.1004.2008.01508","article-title":"Image fusion algorithm based on spatial frequency-motivated pulse coupled neural networks in nonsubsampled contourlet transform domain","volume":"34","author":"Qu","year":"2008","journal-title":"Acta Autom. Sin."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Haghighat, M., and Razian, M. (2014, January 15\u201317). Fast-FMI: Non-reference image fusion metric. Proceedings of the IEEE 8th International Conference on Application of Information and Communication Technologies, Astana, Kazakhstan.","DOI":"10.1109\/ICAICT.2014.7036000"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/TPAMI.2011.109","article-title":"Objective assessment of multiresolution image fusion algorithms for context enhancement in night vision: A comparative study","volume":"34","author":"Liu","year":"2012","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/13\/6135\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:05:45Z","timestamp":1760126745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/13\/6135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,4]]},"references-count":48,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["s23136135"],"URL":"https:\/\/doi.org\/10.3390\/s23136135","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,4]]}}}