{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/iterative-inversion-of-deformation-vector","title":"Iterative Inversion of Deformation Vector Fields with Feedback Control","arxiv_id":"1610.08589","date":"2016-10-27","proceeding":null,"authors":["Abhishek Kumar Dubey","Alexandros-Stavros Iliopoulos","Xiaobai Sun","Fang-Fang Yin","Lei Ren"],"abstract":"Purpose: Often, the inverse deformation vector field (DVF) is needed together\nwith the corresponding forward DVF in 4D reconstruction and dose calculation,\nadaptive radiation therapy, and simultaneous deformable registration. This\nstudy aims at improving both accuracy and efficiency of iterative algorithms\nfor DVF inversion, and advancing our understanding of divergence and latency\nconditions. Method: We introduce a framework of fixed-point iteration\nalgorithms with active feedback control for DVF inversion. Based on rigorous\nconvergence analysis, we design control mechanisms for modulating the inverse\nconsistency (IC) residual of the current iterate, to be used as feedback into\nthe next iterate. The control is designed adaptively to the input DVF with the\nobjective to enlarge the convergence area and expedite convergence. Three\nparticular settings of feedback control are introduced: constant value over the\ndomain throughout the iteration; alternating values between iteration steps;\nand spatially variant values. We also introduce three spectral measures of the\ndisplacement Jacobian for characterizing a DVF. These measures reveal the\ncritical role of what we term the non-translational displacement component\n(NTDC) of the DVF. We carry out inversion experiments with an analytical DVF\npair, and with DVFs associated with thoracic CT images of 6 patients at end of\nexpiration and end of inspiration. Results: NTDC-adaptive iterations are shown\nto attain a larger convergence region at a faster pace compared to previous\nnon-adaptive DVF inversion iteration algorithms. By our numerical experiments,\nalternating control yields smaller IC residuals and inversion errors than\nconstant control. Spatially variant control renders smaller residuals and\nerrors by at least an order of magnitude, compared to other schemes, in no more\nthan 10 steps. Inversion results also show remarkable quantitative agreement\nwith analysis-based predictions. Conclusion: Our analysis captures properties\nof DVF data associated with clinical CT images, and provides new understanding\nof iterative DVF inversion algorithms with a simple residual feedback control.\nAdaptive control is necessary and highly effective in the presence of non-small\nNTDCs. The adaptive iterations or the spectral measures, or both, may\npotentially be incorporated into deformable image registration methods.","url_abs":"http://arxiv.org/abs/1610.08589v4","url_pdf":"http://arxiv.org/pdf/1610.08589v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"iterative-inversion-of-deformation-vector","repo_url":"https://github.com/ailiop/idvf","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"4d-reconstruction","task_name":"4D reconstruction"},{"task_slug":"image-registration","task_name":"Image Registration"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}