基于优化Tikhonov最小二乘模型的曲面重建

Surface Reconstruction Based on Optimized Tikhonov Least Squares Model

摘要: 曲面3D重建是通过SfS系列方法从灰度图像中获取梯度场后，采用L2范数建立深度函数的能量泛函进行重建，这是一个不适定问题。本研究一方面通过将三角测量获取的粗糙深度图Z0与深度函数进行拟合作为Tikhonov正则项，将其转化为适定问题，并用L曲线选取合适的正则化参数；另一方面，利用先离散再优化的方法将上述问题表示为Sylvester矩阵方程，使用Hessenberg-Schur方法求解得到待重建曲面。数值实验表明，优化后的模型抑制噪声和偏差的效果更优，重建精度更高。

Abstract: Surface 3D reconstruction is to obtain gradient field from gray image by SfS series method, and then reconstruct it by using L2 norm to establish the energy functional of depth function, which is an ill-posed problem. In this study, on the one hand, the rough depth map Z0 obtained by triangulation is fitted with the depth function as Tikhonov regular term, which is transformed into an adaptive problem, and the appropriate regularization parameters are selected with L curve. On the other hand, the above problems are expressed as Sylvester matrix equations by the first discretization and then optimization method, and the reconstructed surfaces are obtained by Hessenberg-Schur method. Numerical experiments show that the optimized model can suppress the noise and devia-tion better, and the reconstruction accuracy is higher.