Shape Representation of Fractal Dimension on Point Cloud

In this paper, we study the problem of using the similar dimensions in fractal geometry to describe the shape of a 3D point cloud model. We first calculated the K-nearest neighbor of each point in the point cloud, then performed triangulation the obtained K points, and finally calculated the similarity dimension of each point as a shape attribute of the point cloud model. Our main contribution is to extend the application of fractal geometry in point clouds, which redefine the similarity dimension, in order to fit the representation of the point cloud shape attribute. Based on our proposed expression, we introduce a novel approach to extract global features of point cloud models. We demonstrate the ability of our expressions to express shapes, and the effectiveness of our approach to express global features of point cloud models.