Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization
Euler’s elastica energy regularizer, initially employed in mathematical and physical systems, has recently garnered much attention in image processing and computer vision tasks. Due to the non-convexity, non-smoothness, and high order of its derivative, however, the term has yet to be effectively ap...
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| Format: | Article |
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MDPI AG
2023-11-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/23/12695 |
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| author | Jintao Song Huizhu Pan Yuting Zhang Wenqi Lu Jieyu Ding Weibo Wei Wanquan Liu Zhenkuan Pan Jinming Duan |
| author_facet | Jintao Song Huizhu Pan Yuting Zhang Wenqi Lu Jieyu Ding Weibo Wei Wanquan Liu Zhenkuan Pan Jinming Duan |
| author_sort | Jintao Song |
| collection | DOAJ |
| description | Euler’s elastica energy regularizer, initially employed in mathematical and physical systems, has recently garnered much attention in image processing and computer vision tasks. Due to the non-convexity, non-smoothness, and high order of its derivative, however, the term has yet to be effectively applied in 3D reconstruction. To this day, the industry is still searching for 3D reconstruction systems that are robust, accurate, efficient, and easy to use. While implicit surface reconstruction methods generally demonstrate superior robustness and flexibility, the traditional methods rely on initialization and can easily become trapped in local minima. Some low-order variational models are able to overcome these issues, but they still struggle with the reconstruction of object details. Euler’s elastica term, on the other hand, has been found to share the advantages of both the TV regularization term and the curvature regularization term. In this paper, we aim to address the problems of missing details and complex computation in implicit 3D reconstruction by efficiently using Euler’s elastica term. The main contributions of this article can be outlined in three aspects. Firstly, Euler’s elastica is introduced as a regularization term in 3D point cloud reconstruction. Secondly, a new dual algorithm is devised for the proposed model, significantly improving solution efficiency compared to the commonly used TV model. Lastly, numerical experiments conducted in 2D and 3D demonstrate the remarkable performance of Euler’s elastica in enhancing features of curved surfaces during point cloud reconstruction. The reconstructed point cloud surface adheres more closely to the initial point cloud surface when compared to the classical TV model. However, it is worth noting that Euler’s elastica exhibits a lesser capability in handling local extrema compared to the TV model. |
| first_indexed | 2024-03-09T01:55:49Z |
| format | Article |
| id | doaj.art-7fec7e59b0084a2d8d5b9f2fc0951653 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-09T01:55:49Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-7fec7e59b0084a2d8d5b9f2fc09516532023-12-08T15:11:26ZengMDPI AGApplied Sciences2076-34172023-11-0113231269510.3390/app132312695Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica RegularizationJintao Song0Huizhu Pan1Yuting Zhang2Wenqi Lu3Jieyu Ding4Weibo Wei5Wanquan Liu6Zhenkuan Pan7Jinming Duan8College of Computer Science and Technology, Qingdao University, Qingdao 266071, ChinaSchool of Electrical Engineering, Mathematical Science and Computing, Curtin University, Perth, WA 6102, AustraliaSchool of Computer Science, University of Birmingham, Birmingham B15 2TT, UKTissue Image Analytics Centre, Department of Computer Science, University of Warwick, Coventry CV4 7AL, UKCollege of Computer Science and Technology, Qingdao University, Qingdao 266071, ChinaCollege of Computer Science and Technology, Qingdao University, Qingdao 266071, ChinaSchool of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 510275, ChinaCollege of Computer Science and Technology, Qingdao University, Qingdao 266071, ChinaSchool of Computer Science, University of Birmingham, Birmingham B15 2TT, UKEuler’s elastica energy regularizer, initially employed in mathematical and physical systems, has recently garnered much attention in image processing and computer vision tasks. Due to the non-convexity, non-smoothness, and high order of its derivative, however, the term has yet to be effectively applied in 3D reconstruction. To this day, the industry is still searching for 3D reconstruction systems that are robust, accurate, efficient, and easy to use. While implicit surface reconstruction methods generally demonstrate superior robustness and flexibility, the traditional methods rely on initialization and can easily become trapped in local minima. Some low-order variational models are able to overcome these issues, but they still struggle with the reconstruction of object details. Euler’s elastica term, on the other hand, has been found to share the advantages of both the TV regularization term and the curvature regularization term. In this paper, we aim to address the problems of missing details and complex computation in implicit 3D reconstruction by efficiently using Euler’s elastica term. The main contributions of this article can be outlined in three aspects. Firstly, Euler’s elastica is introduced as a regularization term in 3D point cloud reconstruction. Secondly, a new dual algorithm is devised for the proposed model, significantly improving solution efficiency compared to the commonly used TV model. Lastly, numerical experiments conducted in 2D and 3D demonstrate the remarkable performance of Euler’s elastica in enhancing features of curved surfaces during point cloud reconstruction. The reconstructed point cloud surface adheres more closely to the initial point cloud surface when compared to the classical TV model. However, it is worth noting that Euler’s elastica exhibits a lesser capability in handling local extrema compared to the TV model.https://www.mdpi.com/2076-3417/13/23/12695Euler’s elastica3D reconstructionvariational methoddual method |
| spellingShingle | Jintao Song Huizhu Pan Yuting Zhang Wenqi Lu Jieyu Ding Weibo Wei Wanquan Liu Zhenkuan Pan Jinming Duan Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization Applied Sciences Euler’s elastica 3D reconstruction variational method dual method |
| title | Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization |
| title_full | Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization |
| title_fullStr | Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization |
| title_full_unstemmed | Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization |
| title_short | Three-Dimensional Surface Reconstruction from Point Clouds Using Euler’s Elastica Regularization |
| title_sort | three dimensional surface reconstruction from point clouds using euler s elastica regularization |
| topic | Euler’s elastica 3D reconstruction variational method dual method |
| url | https://www.mdpi.com/2076-3417/13/23/12695 |
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