Characterizing the Stability of 3D Invariants Derived from 3D Translational Symmetry

Translational symmetry provides a powerful constraint that enables recognition of three-dimensional (3D) objects from a single view. Under ideal conditions, affine invariants of 3D points reconstructed from corresponding points would serve as accurate indices for object recognition. In real images, however, inaccurate 2D coordinates of corresponding points can lead to erroneous invariants. In this paper, we investigate the effects of such errors on the 3D invariants, and discuss some approaches to successful indexing in the presence of these errors. 1 Introduction Symmetry can provide powerful constraints to enable the recognition of three-dimensional objects from a single view. There has been considerable exploration of the properties of rotational symmetry[4] and bi-lateral symmetry [6]. In this paper, we consider the case of translational symmetry. The definition of translational symmetry is illustrated in Figure 1. The geometric configuration of translational symmetry is composed..