Research On Shape Attributes Of Point Cloud Based On Fractal Dimension

With the rapid development of point cloud acquisition technology,point cloud data is applied in various fields,such as mechanical manufacturing,medical assistance,and reverse engineering.Therefore,the registration,recognition and storage of 3D point cloud data has become an important subject,and the shape representation of 3D point cloud model is an important basis for the above applications.And using the shape attribute of the point cloud model to represent the point cloud shape is an important method in the shape representation of3 D point cloud model.Traditional point cloud shape attributes use metric information in Euclidean space,such as the length between two points,the principal curvature of the surface,the angle between normal vectors,which are either short of information or high in computational complexity.Different from Euclidean geometry,fractal geometry is a mathematical theory closest to nature and can be used to describe irregular and discontinuous shapes in nature.In this paper,two kinds of expressions,local shape expression and global shape expression,which are suitable for the expression of 3D geometry shape,are firstly derived through the concept of correlation dimension in fractal geometry.Then,the local shape expression is applied to feature point extraction to prove its ability to describe the local shape of point cloud.Finally,the global shape expression is applied to 3D point cloud model retrieval to verify its ability to express the global shape of point cloud.This paper mainly studies the shape representation of fractal dimension in point cloud,which includes the following work:(1)The fractal dimension is redefined to fit the expression of shapes.There are many definitions of fractal dimension,most of which are used to represent geometry with selfsimilar shapes,but few for geometry with arbitrary shapes.By analyzing the concept of correlation dimension,the expression of similarity dimension and shape similarity parameter is derived.The geometric meanings and properties of the two expressions is analyzed and obtained.The problem of scale sensitivity is found and solved.(2)The local shape expression based on the fractal dimension,which is the similarity dimension,is applied to the feature point extraction,and the geometric meaning of each parameter in the similarity dimension is defined on the point cloud.First,the K-nearest neighbor algorithm is used to obtain the point set S composed of K nearest points of each point in the point cloud data.Next,the area,volume,and radius parameters of the point set S are calculated.Finally,after the parameters are scaled,an expression of the similarity dimension is substituted to express the local shape of the point cloud.Experimental results show that similarity dimension has the ability to express the shape of point cloud.Compared with the traditional algorithm,the volume dimension of similarity dimension can extract more complete feature points from the model.(3)The global shape expression based on the fractal dimension,which is the shape similarity parameter,is applied to the 3D model retrieval.In the expression of shape similarity parameters and similarity dimensions,the required parameters are similar.Due to the limitation of the expression of global features by area parameters,the Alpha Shapes algorithm is applied in the expression of global Shapes.Thus,four different shape similarity parameters are obtained.Firstly,the K-nearest neighbor set S of each point in the point cloud is obtained.Then,the four different parameters were calculated by the Alpha Shapes algorithm and the calculation method defined in the local shape expression.Finally,after scaling,four different shape similarity parameters are substituted into the expressions.The experimental results show that the shape similarity parameter has the ability to express the shape similarity of two point cloud models.Compared with RAH algorithm,the algorithm in this paper is more stable,faster and achieves the same performance.