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

Zaiping Zhu,Jianjun Zhang,Andres Iglesias,Liqi Zhou,Lihua You

doi:10.3390/math10040542

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.

Highlights

Publisher’s Note: MDPI stays neu-Surface reconstruction from images is the process of recovering the 3D geometry and structure of objects and scenes based on the information of one or multiple images
Methods of the first type decompose the reconstruction process into two steps; in the first step, 3D point clouds or volumetric data are extracted from multiple images or a single image, followed by 3D
In our previous work [35], we proposed a fourth-order partial differential equation, obtained its closed form solutions, and used one of the obtained closed form solutions to test the applicability of the proposed method in surface reconstruction by reconstructing several simple surface patches from several sets of a few ordered points uniformly sampled from a known surface

Summary

Introduction

Surface reconstruction from images is the process of recovering the 3D geometry and structure of objects and scenes based on the information of one or multiple images It is a widely and deeply researched topic that has been commonly adopted in many areas, such as medical diagnosis, quality inspection, cultural heritage and scene understanding [1,2,3]. Regarding the types of representation of reconstructed surfaces, they mainly can be divided into two classes: explicit surfaces (such as B-spline and NURBS surfaces) and implicit surfaces (such as level set). Both have been widely adopted in surface reconstruction tral with regard to jurisdictional claims in published maps and institutional affiliations

Methods

Results

Conclusion