正态分布变换（Normal Distribution Transformation , NDT）
概率密度函数（ Probability Density Function, PDF）
First proposed for two dimensional scan data registration by Biber & Strasser in 2003.
An NDT is described as a set of PDFs.
The first step of the algorithm is to subdivide the space occupied by the scan into a grid of cells (squares in the 2D case, or cubes in 3D).
A PDF is computed for each cell, based on the point distribution within the cell.
网格中的观测到点𝑥 的概率𝑝(𝑥 )服从正态分布𝑁(𝜇 ,Σ)
The PDF in each cell can be interpreted as a generative process for surface points 𝑥 ⃗ within the cell. In other words, it is assumed that the location of 𝑥 ⃗ has been generated by drawing from this distribution. Assuming that the locations of the reference scan surface points were generated by a D-dimensional normal random process, the likelihood of having measured 𝑥 is
Spatial Representation Models
NDT Occupancy Maps (NDT-OMs)
 Peter Biber and Wolfgang Straßer. The normal distributions transform:A new approach to laser scan matching. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS), pages 2743–2748, Las Vegas, USA, October 2003.
Stoyanov, T. and M. Magnusson (2011). "On the Accuracy of the 3D Normal Distributions Transform as a Tool for Spatial Representation."
Stoyanov, T.D., Reliable Autonomous Navigation in Semi-Structured Environments using the Three-Dimensional Normal Distributions Transform (3D-NDT). 2012.