论文标题
Infinity Laplacian的非本地梯度方法，具有$γ$ -Convergence
A non-local gradient based approach of infinity Laplacian with $Γ$-convergence
论文作者
论文摘要
我们提出了一种无限拉普拉斯方法，以解决非结构化点云上插值的问题。在此过程中，我们发现具有其梯度最小的无穷大标准的标签函数。通过引入非本地梯度，连续功能以离散形式近似。离散的问题是凸，可以通过分裂的布雷格曼方法有效地解决。实验结果表明，即使在极端低采样率的情况下，我们的方法提供了一致的插值，并且获得的标记函数在全球平稳。更重要的是，使用$γ$ convergence和Compacts证明了离散最小化器与最佳连续标签函数的收敛性，这保证了在各种潜在应用中无限Laplacian方法的可靠性。
We propose an infinity Laplacian method to address the problem of interpolation on an unstructured point cloud. In doing so, we find the labeling function with the smallest infinity norm of its gradient. By introducing the non-local gradient, the continuous functional is approximated with a discrete form. The discrete problem is convex and can be solved efficiently with the split Bregman method. Experimental results indicate that our approach provides consistent interpolations and the labeling functions obtained are globally smooth, even in the case of extreme low sampling rate. More importantly, convergence of the discrete minimizer to the optimal continuous labeling function is proved using $Γ$-convergence and compactness, which guarantees the reliability of the infinity Laplacian method in various potential applications.
