Recognition of Symmetric 3D Bodies

Tomáš Suk,Jan Flusser

doi:10.3390/sym6030722

Abstract

The paper deals with the recognition of symmetric three-dimensional (3D) bodies that can be rotated and translated. We provide a complete list of all existing combinations of rotation and reflection symmetries in 3D. We define 3D complex moments by means of spherical harmonics, and the influence of individual symmetry groups on complex moment values is studied. Each particular symmetry pre-defines certain moment values. These moments can no longer differentiate between two objects of the same symmetry, which decreases the recognition power of the feature set. They should not be included when constructing the invariants. Translation and rotation invariants up to the fourth order are presented and their performance is studied on both artificial and real data.

Highlights

Automatic recognition of 2D and 3D objects from their digital images has become a well-established discipline in the last two decades
We paid particular attention to the influence of object symmetry on the feature values and showed how to design features if some of the objects in the dataset are symmetric. This issue has not been systematically studied in 3D so far, most objects we meet in practical applications exhibit certain symmetry
The presented features are based on complex moments and spherical harmonics

Summary

Introduction

Automatic recognition of 2D and 3D objects from their digital images has become a well-established discipline in the last two decades. A lot of feature systems that enable to describe and recognize objects regardless of their particular position, orientation and size have been proposed and tested in the literature. Are sufficient, invariants to more general object deformations exist. When testing most current general-purpose recognition systems, one immediately discovers that they perform poorly on symmetric objects. This fact has a straightforward mathematical explanation.

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Conclusion