{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T15:30:31Z","timestamp":1776094231184,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T00:00:00Z","timestamp":1592524800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["TEC2017-82408-R"],"award-info":[{"award-number":["TEC2017-82408-R"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008431","name":"Consejer\u00eda de Educaci\u00f3n, Junta de Castilla y Le\u00f3n","doi-asserted-by":"publisher","award":["EDU\/1100\/2017"],"award-info":[{"award-number":["EDU\/1100\/2017"]}],"id":[{"id":"10.13039\/501100008431","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Groupwise image (GW) registration is customarily used for subsequent processing in medical imaging. However, it is computationally expensive due to repeated calculation of transformations and gradients. In this paper, we propose a deep learning (DL) architecture that achieves GW elastic registration of a 2D dynamic sequence on an affordable average GPU. Our solution, referred to as dGW, is a simplified version of the well-known U-net. In our GW solution, the image that the other images are registered to, referred to in the paper as template image, is iteratively obtained together with the registered images. Design and evaluation have been carried out using 2D cine cardiac MR slices from 2 databases respectively consisting of 89 and 41 subjects. The first database was used for training and validation with 66.6\u201333.3% split. The second one was used for validation (50%) and testing (50%). Additional network hyperparameters, which are\u2014in essence\u2014those that control the transformation smoothness degree, are obtained by means of a forward selection procedure. Our results show a 9-fold runtime reduction with respect to an optimization-based implementation; in addition, making use of the well-known structural similarity (SSIM) index we have obtained significative differences with dGW with respect to an alternative DL solution based on Voxelmorph.<\/jats:p>","DOI":"10.3390\/e22060687","type":"journal-article","created":{"date-parts":[[2020,6,19]],"date-time":"2020-06-19T10:43:58Z","timestamp":1592563438000},"page":"687","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Groupwise Non-Rigid Registration with Deep Learning: An Affordable Solution Applied to 2D Cardiac Cine MRI Reconstruction"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5922-4960","authenticated-orcid":false,"given":"Elena","family":"Mart\u00edn-Gonz\u00e1lez","sequence":"first","affiliation":[{"name":"Laboratorio de Procesado de Imagen, E.T.S.I. Telecomunicaci\u00f3n, Universidad de Valladolid, Paseo Bel\u00e9n 15, 47011 Valladolid, Spain"}]},{"given":"Teresa","family":"Sevilla","sequence":"additional","affiliation":[{"name":"Unidad de Imagen Cardiaca, Hospital Cl\u00ednico Universitario de Valladolid, CIBER de Enfermedades Cardiovasculares (CIBERCV), 47005 Valladolid, Spain"}]},{"given":"Ana","family":"Revilla-Orodea","sequence":"additional","affiliation":[{"name":"Unidad de Imagen Cardiaca, Hospital Cl\u00ednico Universitario de Valladolid, CIBER de Enfermedades Cardiovasculares (CIBERCV), 47005 Valladolid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1565-0842","authenticated-orcid":false,"given":"Pablo","family":"Casaseca-de-la-Higuera","sequence":"additional","affiliation":[{"name":"Laboratorio de Procesado de Imagen, E.T.S.I. Telecomunicaci\u00f3n, Universidad de Valladolid, Paseo Bel\u00e9n 15, 47011 Valladolid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3684-0055","authenticated-orcid":false,"given":"Carlos","family":"Alberola-L\u00f3pez","sequence":"additional","affiliation":[{"name":"Laboratorio de Procesado de Imagen, E.T.S.I. Telecomunicaci\u00f3n, Universidad de Valladolid, Paseo Bel\u00e9n 15, 47011 Valladolid, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.media.2018.02.003","article-title":"Intrasubject multimodal groupwise registration with the conditional template entropy","volume":"46","author":"Polfliet","year":"2018","journal-title":"Med. Image Anal."},{"key":"ref_2","first-page":"300","article-title":"Medical image registration: Classification, applications and issues","volume":"32","author":"Alam","year":"2018","journal-title":"JPMI"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.media.2010.10.003","article-title":"Nonrigid registration of dynamic medical imaging data using nD+ t B-splines and a groupwise optimization approach","volume":"15","author":"Metz","year":"2011","journal-title":"Med. Image Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"27650","DOI":"10.1109\/ACCESS.2019.2901580","article-title":"Deep group-wise registration for multi-spectral images from fundus images","volume":"7","author":"Che","year":"2019","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1109\/TMI.2019.2897538","article-title":"VoxelMorph: A learning framework for deformable medical image registration","volume":"38","author":"Balakrishnan","year":"2019","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.media.2019.07.006","article-title":"Unsupervised learning of probabilistic diffeomorphic registration for images and surfaces","volume":"57","author":"Dalca","year":"2019","journal-title":"Med. Image Anal."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1525","DOI":"10.1002\/mrm.25733","article-title":"Nonrigid groupwise registration for motion estimation and compensation in compressed sensing reconstruction of breath-hold cardiac cine MRI","volume":"75","year":"2016","journal-title":"Magn. Reson. Med."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"13112","DOI":"10.1038\/s41598-018-31474-7","article-title":"Groupwise image registration based on a total correlation dissimilarity measure for quantitative MRI and dynamic imaging data","volume":"8","author":"Guyader","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_9","first-page":"1315","article-title":"An open benchmark challenge for motion correction of myocardial perfusion MRI","volume":"21","author":"Cowan","year":"2016","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.media.2018.07.002","article-title":"Weakly-supervised convolutional neural networks for multimodal image registration","volume":"49","author":"Hu","year":"2018","journal-title":"Med. Image Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1394","DOI":"10.1109\/JBHI.2019.2951024","article-title":"Unsupervised 3d end-to-end medical image registration with volume tweening network","volume":"24","author":"Zhao","year":"2019","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Krebs, J., Mansi, T., Mailh\u00e9, B., Ayache, N., and Delingette, H. (2018). Unsupervised Probabilistic Deformation Modeling for Robust Diffeomorphic Registration. Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support, Springer.","DOI":"10.1007\/978-3-030-00889-5_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"34","DOI":"10.3389\/fninf.2019.00034","article-title":"Deep Learning Deformation Initialization for Rapid Groupwise Registration of Inhomogeneous Image Populations","volume":"13","author":"Ahmad","year":"2019","journal-title":"Front. Neuroinform."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Tolxdorff, T., Deserno, T.M., Handels, H., Maier, A., Maier-Hein, K.H., and Palm, C. (2020). Deep Groupwise Registration of MRI Using Deforming Autoencoders. Bildverarbeitung f\u00fcr die Medizin 2020, Springer.","DOI":"10.1007\/978-3-658-29267-6"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1002\/mrm.26745","article-title":"5D whole-heart sparse MRI","volume":"79","author":"Feng","year":"2018","journal-title":"Magn. Reson. Med."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1002\/mrm.24524","article-title":"Motion-adaptive spatio-temporal regularization for accelerated dynamic MRI","volume":"70","author":"Asif","year":"2013","journal-title":"Magn. Reson. Med."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Mench\u00f3n-Lara, R.M., Royuela del Val, J., Godino-Moya, A., Cordero-Grande, L., Simmross-Wattenberg, F., Martin-Fernandez, M., and Alberola-L\u00f3pez, C. (2017). An Efficient Multi-resolution Reconstruction Scheme with Motion Compensation for 5D Free-Breathing Whole-Heart MRI. Molecular Imaging, Reconstruction and Analysis of Moving Body Organs, and Stroke Imaging and Treatment, Springer.","DOI":"10.1007\/978-3-319-67564-0_14"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/TMI.2017.2760978","article-title":"A deep cascade of convolutional neural networks for dynamic MR image reconstruction","volume":"37","author":"Schlemper","year":"2017","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1109\/TMI.2018.2863670","article-title":"Convolutional recurrent neural networks for dynamic MR image reconstruction","volume":"38","author":"Qin","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1109\/TMI.2018.2865356","article-title":"MoDL: Model-based deep learning architecture for inverse problems","volume":"38","author":"Aggarwal","year":"2018","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_21","unstructured":"Mart\u00edn-Gonz\u00e1lez, E., Casaseca-de-la Higuera, P., San-Jos\u00e9-Revuelta, L.M., and Alberola-L\u00f3pez, C. (2019, January 27\u201329). Groupwise Deep Learning-based Approach for Motion Compensation. Application to Compressed Sensing 2D Cardiac Cine MRI Reconstruction. Proceedings of the XXXVII Congreso Anual de la Sociedad Espa\u00f1ola de Ingenier\u00eda Biom\u00e9dica, Santander, Spain."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.media.2018.03.005","article-title":"Vortical features for myocardial rotation assessment in hypertrophic cardiomyopathy using cardiac tagged magnetic resonance","volume":"47","author":"Sevilla","year":"2018","journal-title":"Med. Image Anal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1002\/mrm.26198","article-title":"Jacobian weighted temporal total variation for motion compensated compressed sensing reconstruction of dynamic MRI","volume":"77","year":"2017","journal-title":"Magn. Reson. Med."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/42.796284","article-title":"Nonrigid registration using free-form deformations: Application to breast MR images","volume":"18","author":"Rueckert","year":"1999","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2638","DOI":"10.1109\/TPAMI.2013.74","article-title":"Groupwise elastic registration by a new sparsity-promoting metric: Application to the alignment of cardiac magnetic resonance perfusion images","volume":"35","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-Net: Convolutional Networks for Biomedical Image Segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"34461","DOI":"10.1038\/srep34461","article-title":"Liver DCE-MRI registration in manifold space based on robust principal component analysis","volume":"6","author":"Feng","year":"2016","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Bhatia, K.K., Hajnal, J.V., Puri, B.K., Edwards, A.D., and Rueckert, D. (2004, January 18). Consistent groupwise non-rigid registration for atlas construction. Proceedings of the 2004 2nd IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE Cat No. 04EX821), Arlington, VA, USA.","DOI":"10.1109\/ISBI.2004.1398686"},{"key":"ref_29","unstructured":"Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., and Devin, M. (2020, June 17). TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Available online: tensorflow.org."},{"key":"ref_30","unstructured":"(2020, June 17). Keras. Available online: https:\/\/keras.io."},{"key":"ref_31","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Dalca, A.V., Guttag, J., and Sabuncu, M.R. (2018, January 18\u201322). Anatomical priors in convolutional networks for unsupervised biomedical segmentation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00968"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_34","unstructured":"Theodoridis, S., and Koutroumbas, K. (2003). Pattern Recognition, Copyright 2003, Elsevier."},{"key":"ref_35","first-page":"1","article-title":"Entropy, relative entropy and mutual information","volume":"2","author":"Cover","year":"1991","journal-title":"Elem. Inf. Theory"},{"key":"ref_36","first-page":"1","article-title":"Industrial Light & Magic","volume":"2011","author":"Lewis","year":"1995","journal-title":"Fast Norm. Cross Correl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.neuroimage.2017.07.008","article-title":"Quicksilver: Fast predictive image registration\u2014A deep learning approach","volume":"158","author":"Yang","year":"2017","journal-title":"NeuroImage"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Sokooti, H., De Vos, B., Berendsen, F., Lelieveldt, B.P., I\u0161gum, I., and Staring, M. (2017, January 10\u201314). Nonrigid image registration using multi-scale 3D convolutional neural networks. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Quebec City, QC, Canada.","DOI":"10.1007\/978-3-319-66182-7_27"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1109\/TBME.2015.2496253","article-title":"Scalable high-performance image registration framework by unsupervised deep feature representations learning","volume":"63","author":"Wu","year":"2015","journal-title":"IEEE Trans. Biomed. Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/6\/687\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:40:58Z","timestamp":1760175658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/6\/687"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,19]]},"references-count":39,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["e22060687"],"URL":"https:\/\/doi.org\/10.3390\/e22060687","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,19]]}}}