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A combination of approximation- and geometry-based point and element outlier rejection improves the rigid registration error by 2.5\u2005mm and meets the real-time constraints (4\u2005min). In addition, the paper raises several questions and presents two open problems for the robust estimation and improvement of registration error in the presence of outliers due to sparse, noisy, and incomplete data. It concludes with preliminary results on leveraging Quantum Computing, a promising new technology for computationally intensive problems like Feature Detection and Block Matching in addition to finite element solver; all three account for 75% of computing time in deformable registration.<\/jats:p>","DOI":"10.3389\/fdgth.2023.1283726","type":"journal-article","created":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T13:14:41Z","timestamp":1702041281000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Comparison of physics-based deformable registration methods for image-guided 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