Shape classification based on solid angles by a support vector machine

Abstract

In the field of computer-aided design (CAD) and three-dimensional (3D) modeling, constructive solid geometry (CSG) representations based on primitive 3D shapes and boundary representations (B-Rep) based on geometry and topology are widely used to represent complex shapes. Therefore, it is important to recognize primitive shapes such as cubes, cones, and cylinders and to accurately judge and classify the deformation of primitive shapes. For this purpose, various techniques have been studied, such as a vector-based determination method, a determination method using multiple images from various angles, and a determination method based on positional relationships between points. However, because large datasets are required to classify these shapes and it is difficult to respond to changes in shape due to rotation, the resulting recognition accuracy is not always high. In this work, we propose a method based on solid angles, which do not depend on the positional relationship of vectors, viewpoints, or changes due to rotation, as feature quantities. We demonstrate the effectiveness of primitive 3D figures using features based on solid angles. In addition, we show that the presence or absence of deformation can be determined when part of a primitive 3D figure is deformed.