This paper introduces a new approach for generating globally consistent normals for point clouds sampled from manifold surfaces. Given that the generalized winding number (GWN) field generated by a point cloud with globally consistent normals is a solution to a PDE with jump boundary conditions and possesses harmonic properties, and the Dirichlet energy of the GWN field can be defined as an integral over the boundary surface, we formulate a boundary energy derived from the Dirichlet energy of the GWN. Taking as input a point cloud with randomly oriented normals, we optimize this energy to restore the global harmonicity of the GWN field, thereby recovering the globally consistent normals. Experiments show that our method outperforms state-of-the-art approaches, exhibiting enhanced robustness to noise, outliers, complex topologies, and thin structures. Our code can be found at \url{https://github.com/liuweizhou319/BIM}.

翻译：本文提出一种新方法，用于为从流形曲面采样的点云生成全局一致的法向量。鉴于具有全局一致法向的点云所生成的广义环绕数场满足跳跃边界条件的偏微分方程解且具有调和性质，且该GWN场的狄利克雷能量可定义为边界曲面上的积分，我们基于GWN的狄利克雷能量构建了边界能量函数。以随机定向法向的点云作为输入，我们通过优化该能量函数来恢复GWN场的全局调和性，从而重建全局一致的法向量。实验表明，本方法在噪声、离群点、复杂拓扑和薄结构等场景下均优于现有先进方法，展现出更强的鲁棒性。代码发布于 \url{https://github.com/liuweizhou319/BIM}。