NDT概念
正態分布變換（Normal Distribution Transformation , NDT）
概率密度函數（ 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.
NDT及其改進
將二維空間划分為固定大小網格，每個網格至少包括3個點（一般5個）
計算網格中點集的均值𝜇
計算網格中點集的協方差矩陣Σ
網格中的觀測到點𝑥 的概率𝑝(𝑥 )服從正態分布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
標准的NDT方法
多尺度NDT
NDT tree
聚類NDT/區域生長NDT
Spatial Representation Models
其它
NDT interpolation
NDT格網划分后，每個方格或者體素中的點用正態分布描述，整幀掃描的分布並不連續。通過重疊NDT和內插NDT可以一定程度解決此問題。
NDT Occupancy Maps (NDT-OMs)
類似於占用概率地圖，用NDT分布網格表達整幅地圖。
Color-NDT
利用圖像的顏色信息進行NDT匹配。
NDT-MCL
NDT匹配為蒙特卡洛方法提供初值。
基於NDT的掃描匹配
參考文獻
[1] 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.
[2]Stoyanov, T. and M. Magnusson (2011). "On the Accuracy of the 3D Normal Distributions Transform as a Tool for Spatial Representation."
[3]Stoyanov, T.D., Reliable Autonomous Navigation in Semi-Structured Environments using the Three-Dimensional Normal Distributions Transform (3D-NDT). 2012.