The Mathematics Methods Application For Airborne LiDAR Data Processing

In recent years, Airborne LiDAR has made a big progression. The number of ap-plication of it increases continuously. Now, the accuracy of Airborne LiDAR has beenimproved to contain several points even within a centimeter. The high accuracy is agood news for scanning the information of cities. The higher the scanning accuracy,the more information people can obtain. And it leads to a better result of description ofthe real situation of the region which is scanned. However, the data obtained by Air-borne LiDAR are uniform. That is, there is a large part in the data that people do notinterested. So, it is necessary to remove the uninteresting part by data processing.There are several methods to extract the data scanned by Airborne LiDAR, in-cluding deciding the result directly, and method of mathematics. Comparing with themathematics methods, there more deciding methods among the existing methods be-cause that the fields of application are a little far from mathematics. The good comingof these methods is easy to be comprehended. It means that people can understand thiskindofmethodeasily, withoutanydifficultyinthetheory. Butthiskindofmethodoftenfaces problems among the flexibility. This is because that there are several assumptionsbefore using the methods of deciding. These assumptions are about the ceratin situa-tions of the scanned data. In a result, there must be a large part of scanned data whichdonotfittheassumptions. Anditleadstheproblemswhenusingthemethodofdeciding.In this paper, I try to discuss the application of mathematics tools in the data pro-cessing about data scanned by Airborne LiDAR, in the perspective of mathematics. Inthe first step of the data processing, the author puts forward a method of Curved Sur-faceApproaching. Thisisamethodbasedonlinearizednonlinearregression. Thepaperpresents the basic concept of regression, and the least squared method. Then, the au-thor distinguish the ground points and the points above the ground by using the CurvedSurface Approaching method. The result of experiment is very well. Curved SurfaceApproaching method leads to a good result in different ground situations. It shows thatthe Curved Surface Approaching method is a way with flexibility. The author use amethod of fuzzy clustering to differentiate the building points and other items. Thepaper presents the basic concept of fuzzy and fuzzy clustering briefly. And then, theauthor use this method to extract the building point, and obtain a good result. Amongthe application above, the author has found that this method is a little slow, and thiscan influence the application. So, this paper discusses a method of extracting the build-ing points based on dimensionality reduction. This method can improve the calculationspeed sharply by causing only1%comparing with the method without dimensionalityreduction. So it is a effective method.