{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T16:06:56Z","timestamp":1780330016094,"version":"3.54.1"},"reference-count":60,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>Robust 3D registration is a fundamental problem in computer vision and robotics, where the goal is to estimate the geometric transformation between two sets of measurements in the presence of noise and outlier contamination. Existing robust registration methods are mainly built on either maximum consensus (MC) estimators, which first identify inliers and then estimate the transformation, or M-estimators, which directly optimize a robust objective. However, MC-based methods typically ignore residual magnitudes during inlier selection, while many M-estimators do not explicitly couple inlier\/outlier identification with model estimation. Thus, a unified and efficient framework that jointly performs inlier identification and accurate transformation estimation remains desirable for challenging 3D registration. In this work, we introduce a unified truncated-loss based formulation for simultaneous inlier identification and model estimation (SIME) and study it in the context of 3D registration. We show that, compared with MC-based robust fitting, SIME can achieve a lower fitting residual because it incorporates residual magnitudes into the inlier selection process. To solve the resulting nonconvex problem, we develop an alternating minimization (AM) algorithm, and further propose an AM method embedded with semidefinite relaxation (AM-R) to alleviate the difficulty caused by the binary inlier variables. We instantiate the proposed framework for 3D rotation search and rigid point-set registration using quaternion-based formulations. Experimental results on both simulated and real-world registration tasks demonstrate that the proposed methods compare favorably with strong baseline solvers, especially in high noise and extreme outliers. In the synthetic experiments, the proposed methods are evaluated under outlier ratios up to 95% and consistently achieve competitive or better accuracy, with clear advantages in high-noise cases. On 3DMatch, SIME (AM) achieves a mean registration success rate of 91.0%. These results show the potential of SIME for reliable 3D registration in practical robotics, computer vision, and geometric perception applications.<\/jats:p>","DOI":"10.3390\/jimaging12060247","type":"journal-article","created":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T15:07:52Z","timestamp":1780326472000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Robust 3D Registration Method via Simultaneous Inlier Identification and Model Estimation"],"prefix":"10.3390","volume":"12","author":[{"given":"Xianyun","family":"Qian","sequence":"first","affiliation":[{"name":"School of Integrated Circuits, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fei","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Integrated Circuits, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peilin","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Integrated Circuits, Shanghai Jiao Tong University, Shanghai 200240, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ao, S., Hu, Q., Wang, H., Xu, K., and Guo, Y. (2023). BUFFER: Balancing Accuracy, Efficiency, and Generalizability in Point Cloud Registration. IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52729.2023.00127"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Chen, H., Yan, P., Xiang, S., and Tan, Y. (2024). Dynamic Cues-Assisted Transformer for Robust Point Cloud Registration. IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52733.2024.02050"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wang, H., Liu, Y., Dong, Z., Guo, Y., Liu, Y.S., Wang, W., and Yang, B. (2023). Robust multiview point cloud registration with reliable pose graph initialization and history reweighting. IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52729.2023.00917"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1145\/358669.358692","article-title":"Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography","volume":"24","author":"Fischler","year":"1981","journal-title":"Commun. ACM"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chum, O., Matas, J., and Kittler, J. (2003). Locally optimized ransac. Pattern Recognition, Springer.","DOI":"10.1007\/978-3-540-45243-0_31"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1109\/TPAMI.2005.199","article-title":"Guided-mlesac: Faster image transform estimation by using matching priors","volume":"27","author":"Tordoff","year":"2005","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chum, O., and Matas, J. (2005). Matching with PROSAC-Progressive sample consensus. IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2005.221"},{"key":"ref_8","unstructured":"Choi, S., Kim, T., and Yu, W. (2009, January 7\u201310). Performance evaluation of RANSAC family. Proceedings of the British Machine Vision Conference (BMVC), London, UK."},{"key":"ref_9","unstructured":"Lebeda, K., Matas, J., and Chum, O. (2012, January 3\u20137). Fixing the locally optimized ransac full experimental evaluation. Proceedings of the British Machine Vision Conference, Guildford, UK."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2022","DOI":"10.1109\/TPAMI.2012.257","article-title":"USAC: A universal framework for random sample consensus","volume":"35","author":"Raguram","year":"2012","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Barath, D., Matas, J., and Noskova, J. (2019). Magsac: Marginalizing sample consensus. IEEE\/CVF Conference on Computer Vision and Pattern Recognition, IEEE.","DOI":"10.1109\/CVPR.2019.01044"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, X., Yang, J., Zhang, S., and Zhang, Y. (2023). 3D Registration with Maximal Cliques. IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52729.2023.01702"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yan, S., Wang, Y., Zhao, K., Shi, P., Zhao, Z., Zhang, Y., and Li, J. (2025). HeMoRa: Unsupervised Heuristic Consensus Sampling for Robust Point Cloud Registration. IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52734.2025.00135"},{"key":"ref_14","unstructured":"Li, H. (2009). Consensus set maximization with guaranteed global optimality for robust geometry estimation. IEEE 12th International Conference on Computer Vision, IEEE."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Sugimoto, S., and Okutomi, M. (2011). Deterministically maximizing feasible subsystem for robust model fitting with unit norm constraint. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2011.5995640"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Speciale, P., Paudel, D.P., Oswald, M.R., Kroeger, T., Gool, L.V., and Pollefeys, M. (2017). Consensus maximization with linear matrix inequality constraints. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2017.536"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Chin, T.J., Purkait, P., Eriksson, A., and Suter, D. (2015). Efficient globally optimal consensus maximisation with tree search. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2015.7298855"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Enqvist, O., Ask, E., Kahl, F., and Astrom, K. (2012). Robust fitting for multiple view geometry. European Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-642-33718-5_53"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Olsson, C., Enqvist, O., and Kahl, F. (2008). A polynomial-time bound for matching and registration with outliers. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2008.4587757"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Olsson, C., Eriksson, A.P., and Hartley, R. (2010). Outlier removal using duality. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2010.5539800"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Purkait, P., Zach, C., and Eriksson, A. (2018). Maximum consensus parameter estimation by reweighted L1 methods. International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, Springer.","DOI":"10.1007\/978-3-319-78199-0_21"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TRO.2019.2943061","article-title":"Efficient algorithms for maximum consensus robust fitting","volume":"36","author":"Wen","year":"2020","journal-title":"IEEE Trans. Robot."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Le, H., Chin, T.J., and Suter, D. (2017). An exact penalty method for locally convergent maximum consensus. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2017.48"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1109\/TPAMI.2019.2939307","article-title":"Deterministic approximate methods for maximum consensus robust fitting","volume":"43","author":"Le","year":"2019","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1023\/A:1007941100561","article-title":"Determining the epipolar geometry and its uncertainty: A review","volume":"27","author":"Zhang","year":"1998","journal-title":"Int. J. Comput. Vis."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1006\/cviu.1999.0832","article-title":"MLESAC: A new robust estimator with application to estimating image geometry","volume":"78","author":"Torr","year":"2000","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Aftab, K., and Hartley, R. (2015). Convergence of iteratively re-weighted least squares to robust m-estimators. IEEE Winter Confereence on Applications of Computer Vision, IEEE.","DOI":"10.1109\/WACV.2015.70"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1127","DOI":"10.1109\/LRA.2020.2965893","article-title":"Graduated nonconvexity for robust spatial perception: From non-minimal solvers to global outlier rejection","volume":"5","author":"Yang","year":"2020","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhou, Q.Y., Park, J., and Koltun, V. (2016). Fast global registration. European Conference on Computer Vision (ECCV), Springer.","DOI":"10.1007\/978-3-319-46475-6_47"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, H., and Carlone, L. (2019). A quaternion-based certifiably optimal solution to the Wahba problem with outliers. IEEE International Conference on Computer Vision (ICCV), IEEE.","DOI":"10.1109\/ICCV.2019.00175"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1109\/TRO.2020.3033695","article-title":"Teaser: Fast and certifiable point cloud registration","volume":"37","author":"Yang","year":"2020","journal-title":"IEEE Trans. Robot."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Huang, T., Peng, L., Vidal, R., and Liu, Y.-H. (2024). Scalable 3D Registration via Truncated Entry-wise Absolute Residuals. IEEE\/CVF Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52733.2024.02594"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Jiang, H., Dang, Z., Wei, Z., Xie, J., Yang, J., and Salzmann, M. (2023). Robust Outlier Rejection for 3D Registration with Variational Bayes. IEEE\/CVF Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52729.2023.00117"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Liu, J., Wang, G., Liu, Z., Jiang, C., Pollefeys, M., and Wang, H. (2023). RegFormer: An Efficient Projection-Aware Transformer Network for Large-Scale Point Cloud Registration. IEEE\/CVF International Conference Computer Vision (ICCV), IEEE.","DOI":"10.1109\/ICCV51070.2023.00776"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Fu, K., Yuan, M., Wang, C., Pang, W., Chi, J., Wang, M., and Gao, L. (2025). Dual Focus-Attention Transformer for Robust Point Cloud Registration. IEEE\/CVF Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR52734.2025.01099"},{"key":"ref_36","unstructured":"Hampel, F.R., Ronchetfi, E.M., Rousseeuw, P.J., and Stahel, W.A. (1986). Robust Statistics: The Approach Based on Influence Functions, John Wiley and Sons."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Blake, A., and Zisserman, A. (1987). Visual Reconstruction, The MIT Press.","DOI":"10.7551\/mitpress\/7132.001.0001"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/BF00131148","article-title":"On the unification of line processes, outlier rejection, and robust statistics with applications in early vision","volume":"19","author":"Black","year":"1996","journal-title":"Int. J. Comput. Vis."},{"key":"ref_39","unstructured":"Medioni, G., and Dickinson, S. (2017). The maximum consensus problem: Recent algorithmic advances. Synthesis Lectures on Computer Vision, Morgan and Claypool Publishers."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF01100205","article-title":"A recipe for semidefinite relaxation for (0, 1)-quadratic programming","volume":"7","author":"Poljak","year":"1995","journal-title":"J. Glob. Optim."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s10107-002-0352-8","article-title":"A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization","volume":"95","author":"Burer","year":"2003","journal-title":"Math. Program."},{"key":"ref_42","unstructured":"Grant, M., Boyd, S., and Ye, Y. (2014). CVX: Matlab Software for Disciplined Convex Programming, CVX Research."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1177\/0278364918784361","article-title":"SE-Sync: A certifiably correct algorithm for synchronization over the special Euclidean group","volume":"38","author":"Rosen","year":"2019","journal-title":"Int. J. Robot. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1287\/moor.23.2.339","article-title":"On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues","volume":"23","author":"Pataki","year":"1998","journal-title":"Math. Oper. Res."},{"key":"ref_45","unstructured":"Boumal, N., Voroninski, V., and Bandeira, A. (2016). The non-convex Burer-Monteiro approach works on smooth semidefinite programs. Advances in Neural Information Processing Systems, NeurIPS."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1006\/jpdc.1997.1381","article-title":"Design and performance of parallel and distributed approximation algorithm for the maxcut","volume":"46","author":"Homer","year":"1997","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_47","unstructured":"Fletcher, R. (1987). Practical Methods of Optimization, John Wiley and Sons. [2nd ed.]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1137\/1007077","article-title":"A least squares estimate of satellite attitude","volume":"7","author":"Wahba","year":"1965","journal-title":"SIAM Rev."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Bazin, J.-C., Seo, Y., Hartley, R., and Pollefeys, M. (2014). Globally optimal inlier set maximization with unknown rotation and focal length. European Conference on Computer Vision (ECCV), Springer.","DOI":"10.1007\/978-3-319-10605-2_52"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/s11263-008-0186-9","article-title":"Global optimization through rotation space search","volume":"82","author":"Hartley","year":"2009","journal-title":"Int. J. Comput. Vis."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Iglesias, J.P., Olsson, C., and Kahl, F. (2020). Global optimality for point set registration using semidefinite programming. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR42600.2020.00831"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Bazin, J.-C., Seo, Y., and Pollefeys, M. (2012). Globally optimal consensus set maximization through rotation search. Asian Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-642-37444-9_42"},{"key":"ref_53","first-page":"439","article-title":"A survey of attitude representations","volume":"41","author":"Shuster","year":"1993","journal-title":"J. Astronaut. Sci."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1364\/JOSAA.4.000629","article-title":"Closed-form solution of absolute orientation using unit quaternions","volume":"4","author":"Horn","year":"1987","journal-title":"J. Opt. Soc. Amer."},{"key":"ref_55","unstructured":"Schmidt, M. (2022, June 01). minFunc: Unconstrained Differentiable Multivariate Optimization in Matlab. Available online: http:\/\/www.cs.ubc.ca\/~schmidtm\/Software\/minFunc.html."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"2868","DOI":"10.1109\/TPAMI.2017.2773482","article-title":"Guaranteed outlier removal for point cloud registration with correspondences","volume":"40","author":"Bustos","year":"2017","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_57","unstructured":"MOSEK ApS (2017). The MOSEK Optimization Toolbox for MATLAB Manual; Version 8.1., MOSEK ApS."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Curless, B., and Levoy, M. (1996). A volumetric method for building complex models from range images. SIGGRAPH \u201996: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, Association for Computing Machinery.","DOI":"10.1145\/237170.237269"},{"key":"ref_59","unstructured":"Zeng, A., Song, S., Nie\u00dfner, M., Fisher, M., and Xiao, J. (2017). 3DMatch: Learning the Matching of Local 3D Geometry in Range Scans. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE."},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Gojcic, Z., Zhou, C., Wegner, J.D., and Wieser, A. (2019). The Perfect Match: 3D Point Cloud Matching with Smoothed Densities. IEEE Conference Computer Vision and Pattern Recognition (CVPR), IEEE.","DOI":"10.1109\/CVPR.2019.00569"}],"container-title":["Journal of Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-433X\/12\/6\/247\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T15:39:13Z","timestamp":1780328353000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-433X\/12\/6\/247"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,1]]},"references-count":60,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["jimaging12060247"],"URL":"https:\/\/doi.org\/10.3390\/jimaging12060247","relation":{},"ISSN":["2313-433X"],"issn-type":[{"value":"2313-433X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,1]]}}}