{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:19:39Z","timestamp":1760231979438,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T00:00:00Z","timestamp":1665532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61176052"],"award-info":[{"award-number":["61176052"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The diffractive deep neural network (D2NN) can efficiently accomplish 2D object recognition based on rapid optical manipulation. Moreover, the multiple-view D2NN array (MDA) possesses the obvious advantage of being able to effectively achieve 3D object classification. At present, 3D target recognition should be performed in a high-speed and dynamic way. It should be invariant to the typical shifting, scaling, and rotating variance of targets in relatively complicated circumstances, which remains a shortcoming of optical neural network architectures. In order to efficiently recognize 3D targets based on the developed D2NN, a more robust MDA (mr-MDA) is proposed in this paper. Through utilizing a new training strategy to tackle several random disturbances introduced into the optical neural network system, a trained mr-MDA model constructed by us was numerically verified, demonstrating that the training strategy is able to dynamically recognize 3D objects in a relatively stable way.<\/jats:p>","DOI":"10.3390\/s22207754","type":"journal-article","created":{"date-parts":[[2022,10,12]],"date-time":"2022-10-12T22:45:29Z","timestamp":1665614729000},"page":"7754","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The mr-MDA: An Invariant to Shifting, Scaling, and Rotating Variance for 3D Object Recognition Using Diffractive Deep Neural Network"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8255-0051","authenticated-orcid":false,"given":"Liang","family":"Zhou","sequence":"first","affiliation":[{"name":"National Key Laboratory of Science & Technology on Multispectral Information Processing, Huazhong University of Science & Technology, Wuhan 430074, China"},{"name":"School of Artificial Intelligence & Automation, Huazhong University of Science & Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiashuo","family":"Shi","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science & Technology on Multispectral Information Processing, Huazhong University of Science & Technology, Wuhan 430074, China"},{"name":"School of Artificial Intelligence & Automation, Huazhong University of Science & Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Science & Technology on Multispectral Information Processing, Huazhong University of Science & Technology, Wuhan 430074, China"},{"name":"School of Artificial Intelligence & Automation, Huazhong University of Science & Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.neunet.2014.09.003","article-title":"Deep Learning in Neural Networks: An Overview","volume":"61","author":"Schmidhuber","year":"2015","journal-title":"Neural Netw."},{"key":"ref_3","first-page":"84","article-title":"Imagenet classification with deep convolutional neural networks","volume":"60","author":"Krizhevsky","year":"2017","journal-title":"NIPS"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"5408","DOI":"10.1109\/TGRS.2018.2815613","article-title":"Hyperspectral Image Classification with Deep Learning Models","volume":"56","author":"Yang","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1038\/s41591-018-0316-z","article-title":"A guide to deep learning in healthcare","volume":"25","author":"Esteva","year":"2019","journal-title":"Nat. Med."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Sun, K., Xiao, B., Liu, D., and Wang, J. (2019, January 16\u201320). Deep High-Resolution Representation Learning for Human Pose Estimation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00584"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"36","DOI":"10.3389\/frobt.2015.00036","article-title":"A Taxonomy of Deep Convolutional Neural Nets for Computer Vision","volume":"2","author":"Srinivas","year":"2016","journal-title":"Front. Robot. Ai"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1445","DOI":"10.1109\/TPAMI.2020.2975798","article-title":"Deep Multi-View Enhancement Hashing for Image Retrieval","volume":"43","author":"Yan","year":"2021","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"114054","DOI":"10.1016\/j.eswa.2020.114054","article-title":"Deep learning approaches for COVID-19 detection based on chest X-ray images","volume":"164","author":"Ismael","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1038\/s41928-020-0428-6","article-title":"Sign-to-speech translation using machine-learning-assisted stretchable sensor arrays","volume":"3","author":"Zhou","year":"2020","journal-title":"Nat. Electron."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"604","DOI":"10.1109\/TNNLS.2020.2979670","article-title":"A Survey of the Usages of Deep Learning for Natural Language Processing","volume":"32","author":"Otter","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_12","first-page":"497","article-title":"Arabic natural language processing: An overview","volume":"33","author":"Guellil","year":"2021","journal-title":"J. King Saud Univ.-Comput. Inf. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106548","DOI":"10.1016\/j.knosys.2020.106548","article-title":"ASRNN: A recurrent neural network with an attention model for sequence labeling","volume":"212","author":"Lin","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1109\/6.591665","article-title":"Moore\u2019s Law: Past, present, and future","volume":"34","author":"Schaller","year":"1997","journal-title":"IEEE Spectrum"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1004","DOI":"10.1126\/science.aat8084","article-title":"All-optical machine learning using diffractive deep neural networks","volume":"361","author":"Lin","year":"2018","journal-title":"Science"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1038\/nphoton.2016.121","article-title":"Two-photon direct laser writing of ultracompact multi-lens objectives","volume":"10","author":"Gissibl","year":"2016","journal-title":"Nat. Photonics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1364\/OPTICA.5.000756","article-title":"Reinforcement learning in a large-scale photonic recurrent neural network","volume":"5","author":"Bueno","year":"2018","journal-title":"Optica"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1038\/s41586-019-1157-8","article-title":"All-optical spiking neurosynaptic networks with self-learning capabilities","volume":"569","author":"Feldmann","year":"2019","journal-title":"Nature"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5181","DOI":"10.1364\/OE.27.005181","article-title":"Neuromorphic photonics with electro-absorption modulators","volume":"27","author":"George","year":"2019","journal-title":"Opt. Express"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mehrabian, A., Al-Kabani, Y., Sorger, V.J., and El-Ghazawi, T. (2018). PCNNA: A Photonic Convolutional Neural Network Accelerator. IEEE SOCC, 169\u2013173.","DOI":"10.1109\/SOCC.2018.8618542"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"023901","DOI":"10.1103\/PhysRevLett.123.023901","article-title":"Fourier-space Diffractive Deep Neural Network","volume":"123","author":"Yan","year":"2019","journal-title":"Phys. Rev. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"046001","DOI":"10.1117\/1.AP.1.4.046001","article-title":"Class-specific differential detection in diffractive optical neural networks improves inference accuracy","volume":"1","author":"Li","year":"2019","journal-title":"Adv. Photonics"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"25915","DOI":"10.1364\/OE.400364","article-title":"Multi-directional beam steering using diffractive neural networks","volume":"28","author":"Idehenre","year":"2020","journal-title":"Opt. Express"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37686","DOI":"10.1364\/OE.405798","article-title":"Anti-noise diffractive neural network for constructing an intelligent imaging detector array","volume":"28","author":"Shi","year":"2020","journal-title":"Opt. Express"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"eabd7690","DOI":"10.1126\/sciadv.abd7690","article-title":"Spectrally encoded single-pixel machine vision using diffractive networks","volume":"7","author":"Li","year":"2021","journal-title":"Sci. Adv."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4207","DOI":"10.1515\/nanoph-2020-0291","article-title":"Misalignment resilient diffractive optical networks","volume":"9","author":"Mengu","year":"2020","journal-title":"Nanophotonics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1038\/s41467-020-20268-z","article-title":"Terahertz pulse shaping using diffractive surfaces","volume":"12","author":"Veli","year":"2021","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7084","DOI":"10.1364\/OE.419123","article-title":"Robust light beam diffractive shaping based on a kind of compact all-optical neural network","volume":"29","author":"Shi","year":"2021","journal-title":"Opt. Express"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"19807","DOI":"10.1364\/OE.420176","article-title":"768-ary Laguerre-Gaussian-mode shift keying free-space optical communication based on convolutional neural networks","volume":"29","author":"Luan","year":"2021","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1038\/s41377-021-00473-1","article-title":"Ensemble learning of diffractive optical networks","volume":"10","author":"Rahman","year":"2021","journal-title":"Light-Sci. Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.eng.2019.04.002","article-title":"Optically Digitalized Holography: A Perspective for All-Optical Machine Learning","volume":"5","author":"Gu","year":"2019","journal-title":"Engineering"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3388","DOI":"10.1364\/OL.432309","article-title":"Multiple-view D2NNs array: Realizing robust 3D object recognition","volume":"46","author":"Shi","year":"2021","journal-title":"Opt. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1021\/acsphotonics.0c01583","article-title":"Scale-, Shift-, and Rotation-Invariant Diffractive Optical Networks","volume":"8","author":"Mengu","year":"2020","journal-title":"ACS Photonics"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1162\/neco.1995.7.1.108","article-title":"Training with Noise is Equivalent to Tikhonov Regularization","volume":"7","author":"Bishop","year":"1995","journal-title":"Neural Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1162\/neco.1996.8.3.643","article-title":"The Effects of Adding Noise during Backpropagation Training on a Generalization Performance","volume":"8","author":"An","year":"1996","journal-title":"Neural Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0893-6080(91)90033-2","article-title":"Creating artificial neural networks that generalize","volume":"4","author":"Sietsma","year":"1991","journal-title":"Neural Networks"},{"key":"ref_37","unstructured":"David, G. (2011). Computational Fourier Optics: A MATLAB Tutorial, SPIE Press."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1364\/OL.389696","article-title":"Residual D2NN: Training diffractive deep neural networks via learnable light shortcuts","volume":"45","author":"Dou","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1016\/j.eng.2020.07.032","article-title":"Diffractive Deep Neural Networks at Visible Wavelengths","volume":"7","author":"Chen","year":"2021","journal-title":"Engineering"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/20\/7754\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:02Z","timestamp":1760143982000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/20\/7754"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,12]]},"references-count":40,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["s22207754"],"URL":"https:\/\/doi.org\/10.3390\/s22207754","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,10,12]]}}}