Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map

Bin Wu; Talal Rahman; Xue-Cheng Tai

doi:10.1007/978-3-319-91274-5_3

Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map

Bin Wu^*, Talal Rahman, Xue-Cheng Tai

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

Abstract

A model combining the first-order and the second-order variational regularizations for the purpose of 3D surface reconstruction based on 2D sparse data is proposed. The model includes a hybrid fidelity constraint which allows the initial conditions to be switched flexibly between vectors and elevations. A numerical algorithm based on the augmented Lagrangian method is also proposed. The numerical experiments are presented, showing its excellent performance both in designing cartoon characters, as well as in recovering oriented three dimensional maps from contours or points with elevation information.

Original language	English
Title of host publication	Imaging, Vision and Learning Based on Optimization and PDEs
Subtitle of host publication	IVLOPDE, Bergen, Norway, August 29 – September 2, 2016
Editors	Xue-Cheng Tai, Egil Bae, Marius Lysaker
Publisher	Springer Cham
Pages	47-64
Number of pages	18
Edition	1st
ISBN (Electronic)	9783319912745
ISBN (Print)	9783319912738
DOIs	https://doi.org/10.1007/978-3-319-91274-5_3
Publication status	Published - 19 Nov 2018
Event	International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 - Bergen, Norway Duration: 29 Aug 2016 → 2 Sept 2016

Publication series

Name	Mathematics and Visualization
ISSN (Print)	1612-3786
ISSN (Electronic)	2197-666X

Name	IVLOPDE: International Conference on Imaging, Vision and Learning based on Optimization and PDEs

Conference

Conference	International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016
Country/Territory	Norway
City	Bergen
Period	29/08/16 → 2/09/16

Access to Document

10.1007/978-3-319-91274-5_3

Cite this

Wu, B., Rahman, T., & Tai, X.-C. (2018). Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map. In X.-C. Tai, E. Bae, & M. Lysaker (Eds.), Imaging, Vision and Learning Based on Optimization and PDEs: IVLOPDE, Bergen, Norway, August 29 – September 2, 2016 (1st ed., pp. 47-64). (Mathematics and Visualization), (IVLOPDE: International Conference on Imaging, Vision and Learning based on Optimization and PDEs). Springer Cham. https://doi.org/10.1007/978-3-319-91274-5_3

Wu, Bin ; Rahman, Talal ; Tai, Xue-Cheng. / Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map. Imaging, Vision and Learning Based on Optimization and PDEs: IVLOPDE, Bergen, Norway, August 29 – September 2, 2016. editor / Xue-Cheng Tai ; Egil Bae ; Marius Lysaker. 1st. ed. Springer Cham, 2018. pp. 47-64 (Mathematics and Visualization). (IVLOPDE: International Conference on Imaging, Vision and Learning based on Optimization and PDEs).

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title = "Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map",

abstract = "A model combining the first-order and the second-order variational regularizations for the purpose of 3D surface reconstruction based on 2D sparse data is proposed. The model includes a hybrid fidelity constraint which allows the initial conditions to be switched flexibly between vectors and elevations. A numerical algorithm based on the augmented Lagrangian method is also proposed. The numerical experiments are presented, showing its excellent performance both in designing cartoon characters, as well as in recovering oriented three dimensional maps from contours or points with elevation information.",

author = "Bin Wu and Talal Rahman and Xue-Cheng Tai",

note = "Funding Information: Acknowledgements XC Tai acknowledges the support through ISP-Matematikk (Project no. 239033/F20). The providing us example strokes.; International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016 ; Conference date: 29-08-2016 Through 02-09-2016",

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month = nov,

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doi = "10.1007/978-3-319-91274-5_3",

language = "English",

isbn = "9783319912738",

series = "Mathematics and Visualization",

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Wu, B, Rahman, T & Tai, X-C 2018, Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map. in X-C Tai, E Bae & M Lysaker (eds), Imaging, Vision and Learning Based on Optimization and PDEs: IVLOPDE, Bergen, Norway, August 29 – September 2, 2016. 1st edn, Mathematics and Visualization, IVLOPDE: International Conference on Imaging, Vision and Learning based on Optimization and PDEs, Springer Cham, pp. 47-64, International conference on Imaging, Vision and Learning Based on Optimization and PDEs, IVLOPDE 2016, Bergen, Norway, 29/08/16. https://doi.org/10.1007/978-3-319-91274-5_3

Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map. / Wu, Bin; Rahman, Talal; Tai, Xue-Cheng.
Imaging, Vision and Learning Based on Optimization and PDEs: IVLOPDE, Bergen, Norway, August 29 – September 2, 2016. ed. / Xue-Cheng Tai; Egil Bae; Marius Lysaker. 1st. ed. Springer Cham, 2018. p. 47-64 (Mathematics and Visualization), (IVLOPDE: International Conference on Imaging, Vision and Learning based on Optimization and PDEs).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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N1 - Funding Information: Acknowledgements XC Tai acknowledges the support through ISP-Matematikk (Project no. 239033/F20). The providing us example strokes.

PY - 2018/11/19

Y1 - 2018/11/19

N2 - A model combining the first-order and the second-order variational regularizations for the purpose of 3D surface reconstruction based on 2D sparse data is proposed. The model includes a hybrid fidelity constraint which allows the initial conditions to be switched flexibly between vectors and elevations. A numerical algorithm based on the augmented Lagrangian method is also proposed. The numerical experiments are presented, showing its excellent performance both in designing cartoon characters, as well as in recovering oriented three dimensional maps from contours or points with elevation information.

AB - A model combining the first-order and the second-order variational regularizations for the purpose of 3D surface reconstruction based on 2D sparse data is proposed. The model includes a hybrid fidelity constraint which allows the initial conditions to be switched flexibly between vectors and elevations. A numerical algorithm based on the augmented Lagrangian method is also proposed. The numerical experiments are presented, showing its excellent performance both in designing cartoon characters, as well as in recovering oriented three dimensional maps from contours or points with elevation information.

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Wu B, Rahman T, Tai XC. Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map. In Tai XC, Bae E, Lysaker M, editors, Imaging, Vision and Learning Based on Optimization and PDEs: IVLOPDE, Bergen, Norway, August 29 – September 2, 2016. 1st ed. Springer Cham. 2018. p. 47-64. (Mathematics and Visualization). (IVLOPDE: International Conference on Imaging, Vision and Learning based on Optimization and PDEs). doi: 10.1007/978-3-319-91274-5_3

Sparse-Data Based 3D Surface Reconstruction for Cartoon and Map

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