PDE-Based 3D Surface Reconstruction from Multi-View 2D Images

Zaiping Zhu, Andres Iglesias, Liqi Zhou, Lihua You and Jianjun Zhang
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Zaiping Zhu: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Andres Iglesias: Department of Applied Mathematics and Computational Sciences, University of Cantabria, 39005 Cantabria, Spain
Liqi Zhou: China Railway Construction Engineering Group, Beijing 100160, China
Lihua You: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK
Jianjun Zhang: The National Center for Computer Animation, Faculty of Media & Communication, Bournemouth University, Poole BH12 5BB, UK

Mathematics, 2022, vol. 10, issue 4, 1-17

Abstract: 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.

Keywords: shape reconstruction; explicit fourth-order partial differential equation; point clouds reconstruction from multi-view images; point cloud parameterization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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