Perfect Spatial Hashing for Point-cloud-to-mesh Registration

Point-cloud-to-mesh registration estimates a rigid transformation that minimizes the distance between a point sample of a surface and a reference mesh of such a surface, both lying in different coordinate systems. Point-cloud-to-mesh-registration is an ubiquitous problem in medical imaging, CAD CAM CAE, reverse engineering, virtual reality and many other disciplines. Common registration methods include Iterative Closest Point (ICP), RANdom SAmple Consensus (RANSAC) and Normal Distribution Transform (NDT). These methods require to repeatedly estimate the distance between a point cloud and a mesh, which becomes computationally expensive as the point set sizes increase. To overcome this problem, this article presents the implementation of a Perfect Spatial Hashing for point-cloud-to-mesh registration. The complexity of the registration algorithm using Perfect Spatial Hashing is O(NYxn) (NY : point cloud size, n: number of max. ICP iterations), compared to standard octrees and kd-trees (time complexity O(NY log(NT)xn), NT : reference mesh size). The cost of pre-processing is O(NT +(NH^3)^2) (NH^3 : Hash table size). The test results show convergence of the algorithm (error below 7e-05) for massive point clouds / reference meshes (NY = 50k and NT = 28055k, respectively). Future work includes GPU implementation of the algorithm for fast registration of massive point clouds.