Data-Driven 3D Shape Completion with Product Units

Three-dimensional point clouds play a fundamental role in a wide array of fields, spanning from computer vision to robotics and autonomous navigation. Modeling the 3D shape of objects from these point clouds is important for various applications, including 3D shape completion and object recognition. This paper presents a complex-valued product-unit network for data-driven 3D shape completion. Using product units, sparse superpositions of complex power laws, including sparse polynomial functions, are fitted to incomplete 3D point clouds and used for extrapolating the data in the 3D space. In computer-vision applications, this task occurs frequently, e.g., when only partial views are available or occlusions hinder the acquisition of the full point cloud. We conduct a comparative analysis with a standard neural network to emphasize the superior extrapolation capabilities of product-unit networks within the 3D space. Furthermore, we present a real-world task that serves as a tangible demonstration of the proposed method’s utility in the context of completing incomplete point cloud data acquired with a 3D scanner. This research contributes new insights into the field of neural network applications for 3D point cloud processing, revealing the broad potential of product-unit networks in this domain.