Computing The Medial Axis Transformation Of Point Cloud

Point cloud processing have emerged in a wide variety of disciplines,including virtual reality technology(VR),reverse engineering,laser remote sensing measurement,CAD and human-computer interaction,etc.It involves a lot of subjects in the field in-cluding graphics,geometric computing and artificial intelligence.In the early stage,the acquisition cost of point cloud is very expensive,so point cloud processing in the development of various applications is very slow.In 2010,Microsoft first introduced consumer-class(RGBD)equipment Kinect,which played an important role in point cloud processing.Samsung,Asus and many other company have introduced more RGBD equipments,which lay a good foundation for the subsequent point cloud pro-cessing.Point cloud processing has become an important research field in computer graph-ics,and a lot of research results have been obtained.However,although we get more and more accurate point cloud,it is still very difficult to obtain a clean point cloud with-out noise and missing data.Thus,3D reconstruction of point cloud is still a challenging task.Point cloud process can be divided into four stage:1.Point cloud acquired phase,including intelligent scanning,point cloud registra-tion and so on.2.Point cloud pre-processing phase,including feature enhancement,point cloud de-noising,normal estimation and so on.3.Point cloud representation phase,including computing medial axis transforma-tion,point cloud rendering and so on.4.Reconstruction of point cloud phase,including dynamic modeling,static model-ing and so on.In the first chapter,we give a brief review of point cloud agaization,point cloud pre-processing,point cloud representation and geometry reconstruction,etc.We discuss the current status and development trend in the field,and introduce the background,and the status,development trend and application of the medial axis transformation in detail.In addition,we also briefly introduce the background,the status,development trend and application of the sparse optimization theory.In the second chapter,we make a survey about computing medial axis transforma-tion.The concept of medial axis was firstly put forward by Blum as an effective tool to describe 2D shapes in image analysis,and it was subsequently generalized to repre-sent geometric objects in higher dimensions,and applied in a wide range of areas such as shape discrimination,object retrieval,object segmentation,shape deformation and robots path planning,etc.In the last two decades,various methods have been proposed to extract medial axis.The purpose of the current paper is to make a comprehensive survey on the related work,and to point out some future research problems.In the third chapter,we propose a robust method to compute the medial axis trans-formation of 2D point cloud possibly with noise and/or missing data.The basic ap-proach is to first compute the signed distance function of a point cloud by solving the Eikonal equation.Then we find an approximation of the signed distance function which can recover the non-smooth ridge of the distance function by sparse optimization tech-nique.The medial axis of point cloud corresponds to the non-smooth ridge of the dis-tance function,which can be extracted by checking the norm of the gradient of the distance function together with a new measure related to derivative jump of the dis-tance function along the gradient direction.A spline representation is finally obtained by fitting the discrete medial axis points.We perform experiments on various examples and compare our method with state-of-the-art methods.Experimental results demon-strate that our method outperforms previous methods in obtaining accurate and stable representations for medial axis transformation of noisy point cloud.In the fourth chapter,we propose a robust method to compute the medial axis transformation of 3D point cloud possibly with noise and/or missing data.As far as we are aware,no previous algorithms have dealt with such situation.The topology of the 3D point cloud is very complex,so computing medial axis transformation of 3D point cloud is very hard.This chapter presents the method of sections and successfully di-viding a high-dimensional problems become lower dimensional problems.We perform experiments on various examples and compare our method with state-of-the-art meth-ods.Experimental results demonstrate that our method produces accurate and robust representations for medial axis transformation of 3D point cloud possibly with noise and/or missing data.In the final,we summarize the work of this paper and make a prospect for the future.