基于各向异性扩散PDE的曲面重建

Surface Reconstruction Based on Anisotropic Diffusion Paritial Differential Equation

摘要: Possion方程是曲面重建中能够保持曲面平滑的简单有效方法之一，由于该方程是各向同性扩散的，因此不可避免会平滑曲面尖锐特征。本研究通过选取合适的高斯核与结构张量进行卷积构造能够保留曲面细节的扩散张量，在Possion方程中引入该扩散张量为梯度设置各向异性的权重，从而建立能够兼顾曲面平滑和尖锐特征的基于各向异性扩散PDE重建模型；使用Guass消元法求解离散后的模型得到高度值。数值实验结果表明，本研究方法能够保持物体的尖锐及边缘特征，重建效果更佳。

Abstract: Possion equation is one of the simple and effective methods to keep the surface smooth in surface reconstruction. Since the equation is isotropic diffusion, it will inevitably smooth the sharp features of the surface. In this study, the diffusion tensor that can retain the details of the surface was con-structed by convolution of Gaussian kernel and structure tensor, and the diffusion tensor was in-troduced into Possion equation to set the weight of anisotropy for gradient, so as to establish a re-construction model based on anisotropic diffusion paritial differential equation that can give con-sideration to both smooth and sharp features of the surface. Guass elimination method was used to solve the discrete model to get the height value. Numerical experimental results show that the proposed method can preserve the sharp and edge features of the object, and the reconstruction effect is better.