Implicit Triangular Function For Surface Reconstruction And Its Application

Surface reconstruction is one of the most important problems in pattern recognition and image processing,which is the key technology to model and analyze objects.With the development of 3D scanning equipment and technology,it is easier and more accurate to acquire the sampling points on the surface of the object.The geometric surface model of the object constructed based on the 3D data set provides an important foundation for the research of surface properties and the analysis of object.This paper proposes a novel implicit surface reconstruction method with the triangular function based on the 3D point cloud data of subject,and applies it to the segmentation of liver by the level set method.Firstly,this paper analyzes the existing methods,the current research status at home and abroad and the difficulties of surface reconstruction,studies the methods of explicit and implicit surface representations,and their applicability and mutual conversion,researches the surface reconstruction methods based on implicit function further,studies the basic principles,advantages and disadvantages of 3L implicit polynomial method and implicit B spline method,gives the simulation experiments and analysis of results.Secondly,considering the technology of surface reconstruction by the implicit function,this paper proposes a novel implicit surface reconstruction method by combining 3L algorithm with the triangular function.And the surface curvature constraint item is added to enhance the stability of the proposed method.Then,the least square method is used to obtain the reconstruction coefficients and fitting function.At last,surface is reconstructed from the zero level of the fitting function.The surface reconstruction results are compared with the typical 3L implicit polynomial algorithm and the implicit B spline algorithm in time,accuracy and other aspects of reconstruction to further verify the effectiveness of the algorithm.Finally,this paper applies the proposed method to the segmentation of liver by level set method.By means of reconstructing the surface of liver based on the average point cloud data,the method in this paper can give the initial contours of liver with stratifying method fastly.And then the liver is obtained by region level set method.Six metrics is used to evaluate the results of liver segmentation.It is proved that the method in this paper can improve the efficiency of liver segmentation significantly under the premise of ensuring the quality of liver segmentation,which is of great significance for the preoperative planning and risk assessment of liver surgery.