Learning and recognizing three-dimensional shapes by a neural network using solid angles

Abstract

Three-dimensional (3D) shapes differ from two-dimensional (2D) shapes in terms of the amount of data that cat be acquired for each shape. In addition, the information that can be obtained from a 3D shape varies greatly depending on the viewing angle and posture, and there is currently no universal countermeasure for this problem. Therefore, it is difficult to acquire the level of features necessary for machine learning. To learn and recognize 3D shapes, learning approaches using images from various angles, techniques using normal vectors, and approaches based on the acquisition of the overall structure via voxelization have been studied thus far. However, these methods are not always effective because they complicate the preprocessing of data required for learning. In this paper, we propose a method using solid angles as a new quantitative feature for learning and recognition. The solid angle is a 3D angle corresponding to the plane angle of a 2D shape; when a point is fixed, a constant value can be obtained regardless of the posture of the object. In addition, although the calculations required to obtain this value are intensive and time consuming, they can be performed in a relatively simple manner. In this study, primitive shapes are learned and recognized using solid angles as a quantitative feature. As a result, we demonstrate that after learning using a neural network, this method can appropriately recognize a given shape.