We present a variational approach for surface reconstruction from a set of oriented points with scale information. We focus particularly on scenarios with nonuniform point densities due to images taken from different distances. In contrast to previous methods, we integrate the scale information in the objective and globally optimize the signed distance function of the surface on a balanced octree grid. We use a finite element discretization on the dual structure of the octree minimizing the number of variables. The tetrahedral mesh is generated efficiently with a lookup table which allows to map octree cells to the nodes of the finite elements. We optimize memory efficiency by data aggregation, such that robust data terms can be used even on very large scenes. The surface normals are explicitly optimized and used for surface extraction to improve the reconstruction at edges and corners.

中文翻译：

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十亿点的全球密集多尺度重建

我们提出了一种从一组具有尺度信息的定向点重建表面的变分方法。我们特别关注由于从不同距离拍摄的图像而导致点密度不均匀的场景。与以前的方法相比，我们将目标中的尺度信息整合在一起，并在平衡八叉树网格上全局优化表面的有符号距离函数。我们在八叉树的对偶结构上使用有限元离散化来最小化变量的数量。四面体网格是通过查找表高效生成的，该表允许将八叉树单元映射到有限元的节点。我们通过数据聚合优化内存效率，这样即使在非常大的场景中也可以使用健壮的数据项。