Point Clouds Skeleton Extraction Based On Optimal Transport Theory

Point cloud skeleton extraction has always been a hot topic in computer graphics.In recent years,the use of three-dimensional scanning equipment is becoming more and more wide,and the applications about point cloud are growing rapidly.Due to the large amount of data and other reasons the point cloud data could not be saved easily,while the original point cloud contains a lot of noise it could not be used directly.As a one-dimensional representation of the three-dimensional space of the model,the skeleton can preserve the geometric characteristics of the model completely and attracted the researchers' attention.Since the original scanning point cloud model generally contains a large number of noise and outliers,these noise and outliers will affect the quality of the skeleton to varying degrees,so how to design a robust point cloud skeleton extraction algorithm has always been a difficult problem.Therefore,this paper proposes a robust algorithm for point cloud skeleton extraction for noise and outliers based on the optimal transportation method.The algorithm can guarantee the skeleton continuity while ensuring the skeleton accuracy.The main work of this paper includes:1.An algorithm for point cloud skeleton extraction based on optimal transport theory is proposed.Firstly,the input source model is sampled randomly.On this basis,the probability space is allocated by mass on the point,and then the optimal transportation method is introduced to establish the function model of the skeleton extraction.Secondly,during the optimization of the optimal transport plan,the sample points are contracted to the local center of the model.Finally,the skeleton branches are constructed according to the neighborhood relation of the sample points,and at the end the curve skeleton is obtained which is similar to the ideal structure.2.A skeleton optimization algorithm is proposed.The algorithm first linearly interpolates the skeleton point on the basis of the initial skeleton to ensure that the skeleton can capture more details.Then analyzed the skeleton point distribution,and a regular term is added to the original energy function.The regular term calculate the sum of the distance between the current skeleton point and the center of its adjacent skeleton points.After optimization of the skeleton is not only distributed evenly,thus ensuring the accuracy of the skeleton at the same time,but also improve the continuity of the skeleton.3.Through the skeleton extraction experiment of different point cloud data sets,the obtained curve skeleton can better reflect the shape and topology information of the source point cloud model.By comparing with ROSA algorithm and L1 median algorithm,it is proved that our algorithm is effective.The results can be applied to the field of 3D point cloud recognition,analysis and reconstruction.