On template-based reconstruction from a single view: analytical solutions and proofs of well-posedness for developable, isometric and conformal surfaces

Conference item


Bartoli, A., Gerard, Y., Chadebecq, F. and Collins, T. 2012. On template-based reconstruction from a single view: analytical solutions and proofs of well-posedness for developable, isometric and conformal surfaces. 2012 IEEE Conference on Computer Vision and Pattern Recognition. Providence, RI, USA 16 - 21 Jun 2012 IEEE. pp. 2026-2033 https://doi.org/10.1109/CVPR.2012.6247906
TitleOn template-based reconstruction from a single view: analytical solutions and proofs of well-posedness for developable, isometric and conformal surfaces
AuthorsBartoli, A., Gerard, Y., Chadebecq, F. and Collins, T.
Abstract

Recovering a deformable surface's 3D shape from a single view registered to a 3D template requires one to provide additional constraints. A recent approach has been to constrain the surface to deform quasi-isometrically. This is applicable to surfaces of materials such as paper and cloth. Current `closed-form' solutions solve a convex approximation of the original problem whereby the surface's depth is maximized under the isometry constraints (this is known as the maximum depth heuristic). No such convex approximation has yet been proposed for the conformal case. We give a unified problem formulation as a system of PDEs for developable, isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy.

KeywordsSurface reconstruction; Equations; Image reconstruction; Shape; Three dimensional displays; Approximation methods; Numerical models
LanguageEnglish
Conference2012 IEEE Conference on Computer Vision and Pattern Recognition
Page range2026-2033
Proceedings Title2012 IEEE Conference on Computer Vision and Pattern Recognition
ISSN1063-6919
ISBN
Electronic9781467312288
Hardcover9781467312264
PublisherIEEE
Publication dates
Online26 Jul 2012
Publication process dates
Accepted2012
Deposited28 Feb 2024
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.1109/CVPR.2012.6247906
Web of Science identifierWOS:000309166202024
Permalink -

https://repository.mdx.ac.uk/item/z3z5z

  • 11
    total views
  • 0
    total downloads
  • 4
    views this month
  • 0
    downloads this month

Export as

Related outputs

Artificial intelligence and automation in endoscopy and surgery
Chadebecq, F., Lovat, L. and Stoyanov, D. 2023. Artificial intelligence and automation in endoscopy and surgery. Nature Reviews Gastroenterology and Hepatology. 20 (3), pp. 171-182. https://doi.org/10.1038/s41575-022-00701-y
Identifying key mechanisms leading to visual recognition errors for missed colorectal polyps using eye-tracking technology
Ahmad, O., Mazomenos, E., Chadebecq, F., Kader, R., Hussein, M., Haidry, R., Puyal, J., Brandao, P., Toth, D. and Mountney, P. 2023. Identifying key mechanisms leading to visual recognition errors for missed colorectal polyps using eye-tracking technology. Journal of Gastroenterology and Hepatology. 38 (5), pp. 768-774. https://doi.org/10.1111/jgh.16127
SuperPoint features in endoscopy
Leon Barbed, O., Chadebecq, F., Morlana, J., Montiel, J. and Murillo, A. 2022. SuperPoint features in endoscopy. Manfredi, L., Ahmadi, S., Bronstein, M., Kazi, A., Lomanto, D., Mathew, A., Magerand, L., Mullakaeva, K., Papiez, B., Taylor, R. and Trucco, E. (ed.) 1st MICCAI Workshop on Imaging Systems for GI Endoscopy. Singapore 18 - 18 Sep 2022 Cham Springer. https://doi.org/10.1007/978-3-031-21083-9_5
P19 Structure-from-motion analysis may generate an accurate automated bowel preparation score
Chadebecq, F., Mountney, P., Ahmad, O., Kader, R., Lovat, L. and Stoyanov, D. 2021. P19 Structure-from-motion analysis may generate an accurate automated bowel preparation score. BSG Campus 2021. Online 21 - 29 Jan 2021 BMJ. https://doi.org/gutjnl-2020-bsgcampus.94
Refractive two-view reconstruction for underwater 3D vision
Chadebecq, F., Vasconcelos, F., Lacher, R., Maneas, E., Desjardins, A., Ourselin, S., Vercauteren, T. and Stoyanov, D. 2020. Refractive two-view reconstruction for underwater 3D vision. International Journal of Computer Vision. 128 (5), pp. 1101-1117. https://doi.org/10.1007/s11263-019-01218-9
Computer vision in the surgical operating room
Chadebecq, F., Vasconcelos, F., Mazomenos, E. and Stoyanov, D. 2020. Computer vision in the surgical operating room. Visceral Medicine. 36 (6), pp. 456-462. https://doi.org/10.1159/000511934
Automated pick-up of suturing needles for robotic surgical assistance
D'Ettorre, C., Dwyer, G., Du, X., Chadebecq, F., Vasconcelos, F., De Momi, E. and Stoyanov, D. 2018. Automated pick-up of suturing needles for robotic surgical assistance. 2018 IEEE International Conference on Robotics and Automation (ICRA). Brisbane, QLD, Australia 21 - 25 May 2018 IEEE. pp. 1370-1377 https://doi.org/10.1109/ICRA.2018.8461200
Monocular 3D reconstruction of the colon using CNNs trained on synthetic data
Rau, A., Chadebecq, F., Stoyanov, D. and Riordan, P. 2018. Monocular 3D reconstruction of the colon using CNNs trained on synthetic data. 8th Joint Workshop on New Technologies for Computer/Robot Assisted Surgery. London, UK 10 - 11 Sep 2018 CRAS.
Adjoint transformation algorithm for hand-eye calibration with applications in robotic assisted surgery
Pachtrachai, K., Vasconcelos, F., Chadebecq, F., Allan, M., Hailes, S., Pawar, V. and Stoyanov, D. 2018. Adjoint transformation algorithm for hand-eye calibration with applications in robotic assisted surgery. Annals of Biomedical Engineering. 46 (10), pp. 1606-1620. https://doi.org/10.1007/s10439-018-2097-4
Medical-grade sterilizable target for fluid-immersed fetoscope optical distortion calibration
Nikitichev, D., Shakir, D., Chadebecq, F., Tella, M., Deprest, J., Stoyanov, D., Ourselin, S. and Vercauteren, T. 2017. Medical-grade sterilizable target for fluid-immersed fetoscope optical distortion calibration. Journal of Visualized Experiments. 120, p. e55298. https://doi.org/10.3791/55298
Corner-based geometric calibration of multi-focus plenoptic cameras
Nousias, S., Chadebecq, F., Pichat, J., Keane, P., Ourselin, S. and Bergeles, C. 2017. Corner-based geometric calibration of multi-focus plenoptic cameras. 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy 22 - 29 Oct 2017 IEEE. pp. 957-965 https://doi.org/10.1109/ICCV.2017.109
Refractive structure-from-motion through a flat refractive interface
Chadebecq, F., Vasconcelos, F., Dwyer, G., Lacher, R., Ourselin, S., Vercauteren, T. and Stoyanov, D. 2017. Refractive structure-from-motion through a flat refractive interface. 2017 IEEE International Conference on Computer Vision (ICCV). Venice, Italy 22 - 29 Oct 2017 IEEE. pp. 5325-5333 https://doi.org/10.1109/ICCV.2017.568
A continuum robot and control interface for surgical assist in fetoscopic interventions
Dwyer, G., Chadebecq, F., Amo, M., Bergeles, C., Maneas, E., Pawar, V., Poorten, E., Deprest, J., Ourselin, S., De Coppi, P., Vercauteren, T. and Stoyanov, D. 2017. A continuum robot and control interface for surgical assist in fetoscopic interventions. IEEE Robotics and Automation Letters. 2 (3), pp. 1656-1663. https://doi.org/10.1109/LRA.2017.2679902
Cooperative control with distal manipulation for fetoscopic laser photocoagulation
Dwyer, G., Bergeles, C., Chadebecq, F., Pawar, V., Vander Poorten, E., Ourselin, S., Deprest, J., De Coppi, P., Vercauteren, T. and Stoyanov, D. 2016. Cooperative control with distal manipulation for fetoscopic laser photocoagulation. 6th Joint Workshop on New Technologies for Computer/Robot Assisted Surgery. Pisa, Italy 12 - 14 Sep 2016 Leuven, Belgium KU Leuven. pp. 34-35
Real-time mosaicing of fetoscopic videos using SIFT
Daga, P., Chadebecq, F., Shakir, D., Herrera, L., Tella, M., Dwyer, G., David, A., Deprest, J., Stoyanov, D., Vercauteren, T. and Ourselin, S. 2016. Real-time mosaicing of fetoscopic videos using SIFT. SPIE Medical Imaging 2016. San Diego, California, United States 27 Feb - 03 Mar 2016 SPIE. https://doi.org/10.1117/12.2217172
A combined EM and visual tracking probabilistic model for robust mosaicking: application to fetoscopy
Tella-Amo, M., Daga, P., Chadebecq, F., Thompson, S., Shakir, D., Dwyer, G., Wimalasundera, R., Deprest, J., Stoyanov, D. and Vercauteren, T. 2016. A combined EM and visual tracking probabilistic model for robust mosaicking: application to fetoscopy. 2016 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW). Las Vegas, NV, USA 26 Jun - 01 Jul 2016 IEEE. https://doi.org/10.1109/CVPRW.2016.72
Shape-from-template
Bartoli, A., Gerard, Y., Chadebecq, F., Collins, T. and Pizarro, D. 2015. Shape-from-template. IEEE Transactions on Pattern Analysis and Machine Intelligence. 37 (10), pp. 2099-2118. https://doi.org/10.1109/TPAMI.2015.2392759
How big is this neoplasia? Live colonoscopic size measurement using the Infocus-Breakpoint
Chadebecq, F., Tilmant, C. and Bartoli, A. 2015. How big is this neoplasia? Live colonoscopic size measurement using the Infocus-Breakpoint. Medical Image Analysis. 19 (1), pp. 58-74. https://doi.org/10.1016/j.media.2014.09.002
Estimation de l'échelle absolue par vision passive monofocale et application à la mesure 3D de néoplasies en imagerie coloscopique
Chadebecq, F. 2015. Estimation de l'échelle absolue par vision passive monofocale et application à la mesure 3D de néoplasies en imagerie coloscopique. Thesis Blaise Pascal University
Practical dry calibration with medium adaptation for fluid-immersed endoscopy
Chadebecq, F., Vercauteren, T., Wimalasundera, R., Attilakos, G., David, A., Deprest, J., Ourselin, S. and Stoyanov, D. 2015. Practical dry calibration with medium adaptation for fluid-immersed endoscopy. Hamlyn Symposium on Medical Robotics 2015. London, UK 20 - 23 Jun 2015
Multimodal and multimedia image analysis and collaborative networking for digestive endoscopy
d’Orazio, L., Bartoli, A., Baetz, A., Beorchia, S., Calvary, G., Chabane, Y., Chadebecq, F., Collins, T., Laurillau, Y. and Martins-Baltar, L. 2014. Multimodal and multimedia image analysis and collaborative networking for digestive endoscopy. IRBM. 35 (2), pp. 88-93.
Enhanced imaging colonoscopy facilitates dense motion-based 3D reconstruction
Alcantarilla, P., Bartoli, A., Chadebecq, F., Tilmant, C. and Lepilliez, V. 2013. Enhanced imaging colonoscopy facilitates dense motion-based 3D reconstruction. 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Osaka, Japan 03 - 07 Jul 2013 IEEE. pp. 7346-7349 https://doi.org/10.1109/EMBC.2013.6611255
Estimation de l'échelle des néoplasies en coloscopie par détection de la profondeur de défocalisation
Chadebecq, F., Tilmant, C. and Bartoli, A. 2013. Estimation de l'échelle des néoplasies en coloscopie par détection de la profondeur de défocalisation. ORASIS 2013 - Journées francophones des jeunes chercheurs en vision par ordinateur. Cluny, France 10 - 14 Jun 2013 HAL Open Science.
Using the Infocus-Breakpoint to estimate the scale of neoplasia in colonoscopy
Chadebecq, F., Tilmant, C. and Bartoli, A. 2013. Using the Infocus-Breakpoint to estimate the scale of neoplasia in colonoscopy. 2013 IEEE 10th International Symposium on Biomedical Imaging. San Francisco, CA, USA 07 - 11 Apr 2013 IEEE. pp. 354-357 https://doi.org/10.1109/ISBI.2013.6556485
Estimation de l'échelle en coloscopie monoculaire par quantification du flou optique: étude de faisabilité
Chadebecq, F., Tilmant, C., Julien, P., Collins, T. and Bartoli, A. 2012. Estimation de l'échelle en coloscopie monoculaire par quantification du flou optique: étude de faisabilité. Reconnaissance des Formes et Intelligence Artificielle 2012. Lyon, France 24 - 27 Jan 2012 HAL Open Science.
Measuring the size of neoplasia in colonoscopy using depth-from-defocus
Chadebecq, F., Tilmant, C. and Bartoli, A. 2012. Measuring the size of neoplasia in colonoscopy using depth-from-defocus. 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society. San Diego, CA, USA 28 Aug - 01 Sep 2012 IEEE. pp. 1478-1481 https://doi.org/10.1109/EMBC.2012.6346220