相似性维数在点云中的应用

3D点云配准、分割、识别等任务中都需要获取形状属性，传统的形状属性对尺度变化敏感且计算复杂，表达的几何意义简单。结合分形几何中相似性维数的概念，给出了一种可作为点云模型形状属性的维数定义。首先，求取模型中每个点的k邻域得到一个点集，计算其外接球半径；其次，计算由该点集组成的体积与面积信息，并通过缩放处理解决尺度敏感的问题；最后，利用相似性维数表达式计算点云模型中每个点的维数值，使用该值来表示点云模型的形状属性。实验结果表明，相似性维数具有表达形状的能力，并且能够清晰地表达模型的全局特征。

Application of similarity dimension in point cloud

Shape attribute acquisition is necessary in 3D point cloud registration, segmentation, recognition and other tasks. Traditional shape attributes are sensitive to scale changes, complicated to calculate，and simple to express the geometric meaning. Thus, combined with the concept of similarity dimension in fractal geometry, we propose a dimension definition that can be used as the shape attribute of the point cloud model. Firstly, we obtain a set of points that composed of the k neighborhood of each point in the model, and calculate the radius of the circumscribed sphere of the set of points. Secondly, we calculate the volume and area of the set of points, and solve the scale-sensitive problem by scaling. Finally, the dimension value of each point in the point cloud model is calculated using the similarity dimension expression, and the value is used to represent the shape attribute of the point cloud model. Experimental results show that the similarity dimension has the ability to express the shape and can clearly express the global characteristics of the model.