Anisotropic Octrees: a Tool for Fast Normals Estimation on Unorganized Point Clouds

With the recent advances in remote sensing of objects and environments, point cloud processing has become a major field of study. Three-dimensional point cloud collected with remote sensing instruments may be very large, containing up to several tens of billions of points. This imposes the use for efficient and automatic algorithms to extract geometric or structural elements of the scanned surfaces. In this paper, we focus on the estimation of normal directions in an unorganized point cloud and provide a curvature indicator. We avoid point-wise operations to accelerate the running time for normals estimation. Instead, our method rely on an innovative anisotropic partitioning of the point cloud using an octree structure guided by the geometric complexity of the data and generates patches of points. These patches are then approximated by a quadratic surface in order to estimate the normal directions and curvatures. Our method has been applied to six models of various types presenting different characteristics and performs, in average, 2.65 times faster than multi-threads implementations available in current pieces of software. The results obtained are a compromise between running time efficiency and normals accuracy. Moreover, this work opens up promising perspectives and can be easily inserted in wide range of workflows.