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

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.

Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics

“…Wang et al integrate partial differential equation-based geometric modelling and boundary-based surface creation to obtain the first analytical C 0 continuous four-sided PDE patches [35]. Zhu et al use a fourth-order partial differential equation to reconstruct three-dimensional surfaces from multi-view two-dimensional images [36].…”

“…The above figure shows that different combinations of facial blendshape weights create different shapes when the time variable 𝑡 is fixed. Different from the facial blendshapes using Equation (36), where one weight combination can create one new shape only, the facial blendshapes using Equation (39) will enable one weight combination to create many different new shapes by simply setting the time variable 𝑡 to different values. It indicates that the proposed method not only improves the realism of facial interpolation and facial blendshapes but also noticeably raises the capacity to create more facial shapes for facial animation.…”

“…36) where 𝒘 0 is a neutral model, 𝒘 𝑗 ( 𝑗 = 1, 2, 3, … , 𝑁 ) are target models, and 𝜉 𝑗 ( 𝑗 = 1, 2, 3, … , 𝑁) are weights with 𝜉 𝑗 ≥ 0 and ∑ 𝜉 𝑗 With the PDE-based interpolation proposed in this paper, we use Equation(32) to interpolate a neutral expression and the jth target expression and obtain the following quadratic PDE-based interpolation equation for the jth target expression:…”

Enhanced Combined Techniques for Interval-Valued Intuitionistic Fuzzy Multiple-Attribute Group Decision-Making and Applications to Quality Evaluation of Large-Scale Multi-View 3D Reconstruction

“…These applications require rapid and accurate 3D digitization of real scenes to meet huge field needs. The methods for reconstructing 3D models can usually be divided into active and passive methods [7][8][9]. Multi view Iterative reconstruction is a passive reconstruction method that does not require physical contact with the reconstruction object.…”

3D spatial perception for underwater robots using point cloud data from orthogonal multibeam sonars fusion

“…The association process used by OMSF, as shown in Section 4.1, tends to assume a target reconstruction of a shape of a 'solid' surface connecting the 'horizontal' and 'vertical' feature sets, similar to results from other multiview-based reconstruction methods [104]. This is illustrated in Fig.…”