PDE-Based 3D Surface Reconstruction from Multi-View 2D Images
Partial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be naturally maint...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/4/542 |
| _version_ | 1827654179822239744 |
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| author | Zaiping Zhu Andres Iglesias Liqi Zhou Lihua You Jianjun Zhang |
| author_facet | Zaiping Zhu Andres Iglesias Liqi Zhou Lihua You Jianjun Zhang |
| author_sort | Zaiping Zhu |
| collection | DOAJ |
| description | Partial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be naturally maintained when certain conditions are satisfied, and the physics-based nature is also kept. Although some works applied implicit PDEs to 3D surface reconstruction from images, there is little work on exploiting the explicit solutions of PDE to this topic, which is more efficient and accurate. In this paper, we propose a new method to apply the explicit solutions of a fourth-order partial differential equation to surface reconstruction from multi-view images. The method includes two stages: point clouds data are extracted from multi-view images in the first stage, which is followed by PDE-based surface reconstruction from the obtained point clouds data. Our computational experiments show that the reconstructed PDE surfaces exhibit good quality and can recover the ground truth with high accuracy. A comparison between various solutions with different complexity to the fourth-order PDE is also made to demonstrate the power and flexibility of our proposed explicit PDE for surface reconstruction from images. |
| first_indexed | 2024-03-09T21:30:51Z |
| format | Article |
| id | doaj.art-c28fec4e8c8441cf8c81d8d7aaddb04d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:30:51Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c28fec4e8c8441cf8c81d8d7aaddb04d2023-11-23T20:56:21ZengMDPI AGMathematics2227-73902022-02-0110454210.3390/math10040542PDE-Based 3D Surface Reconstruction from Multi-View 2D ImagesZaiping Zhu0Andres Iglesias1Liqi Zhou2Lihua You3Jianjun Zhang4The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKDepartment of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Cantabria, SpainChina Railway Construction Engineering Group, Beijing 100160, ChinaThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKThe National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UKPartial differential equation (PDE) based surfaces own a lot of advantages, compared to other types of 3D representation. For instance, fewer variables are required to represent the same 3D shape; the position, tangent, and even curvature continuity between PDE surface patches can be naturally maintained when certain conditions are satisfied, and the physics-based nature is also kept. Although some works applied implicit PDEs to 3D surface reconstruction from images, there is little work on exploiting the explicit solutions of PDE to this topic, which is more efficient and accurate. In this paper, we propose a new method to apply the explicit solutions of a fourth-order partial differential equation to surface reconstruction from multi-view images. The method includes two stages: point clouds data are extracted from multi-view images in the first stage, which is followed by PDE-based surface reconstruction from the obtained point clouds data. Our computational experiments show that the reconstructed PDE surfaces exhibit good quality and can recover the ground truth with high accuracy. A comparison between various solutions with different complexity to the fourth-order PDE is also made to demonstrate the power and flexibility of our proposed explicit PDE for surface reconstruction from images.https://www.mdpi.com/2227-7390/10/4/542shape reconstructionexplicit fourth-order partial differential equationpoint clouds reconstruction from multi-view imagespoint cloud parameterization |
| spellingShingle | Zaiping Zhu Andres Iglesias Liqi Zhou Lihua You Jianjun Zhang PDE-Based 3D Surface Reconstruction from Multi-View 2D Images Mathematics shape reconstruction explicit fourth-order partial differential equation point clouds reconstruction from multi-view images point cloud parameterization |
| title | PDE-Based 3D Surface Reconstruction from Multi-View 2D Images |
| title_full | PDE-Based 3D Surface Reconstruction from Multi-View 2D Images |
| title_fullStr | PDE-Based 3D Surface Reconstruction from Multi-View 2D Images |
| title_full_unstemmed | PDE-Based 3D Surface Reconstruction from Multi-View 2D Images |
| title_short | PDE-Based 3D Surface Reconstruction from Multi-View 2D Images |
| title_sort | pde based 3d surface reconstruction from multi view 2d images |
| topic | shape reconstruction explicit fourth-order partial differential equation point clouds reconstruction from multi-view images point cloud parameterization |
| url | https://www.mdpi.com/2227-7390/10/4/542 |
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