Rotation invariant spherical harmonic representation of 3D shape descriptors

TLDR

3D shape matching is complicated by rotations, so models must be considered equivalent under rotation, yet explicitly aligning them is usually impractical, leading to two common approaches: rotation‑invariant descriptors or canonical alignment. This paper critiques canonical alignment and proposes using spherical harmonics to obtain rotation‑invariant representations. The authors detail the properties of the spherical‑harmonic tool and demonstrate its application to existing orientation‑dependent descriptors to enhance matching. The method improves descriptor matching accuracy while reducing dimensionality, thereby making model comparisons more efficient.

Abstract

One of the challenges in 3D shape matching arises from the fact that in many applications, models should be considered to be the same if they differ by a rotation. Consequently, when comparing two models, a similarity metric implicitly provides the measure of similarity at the optimal alignment. Explicitly solving for the optimal alignment is usually impractical. So, two general methods have been proposed for addressing this issue: (1) Every model is represented using rotation invariant descriptors. (2) Every model is described by a rotation dependent descriptor that is aligned into a canonical coordinate system defined by the model. In this paper, we describe the limitations of canonical alignment and discuss an alternate method, based on spherical harmonics, for obtaining rotation invariant representations. We describe the properties of this tool and show how it can be applied to a number of existing, orientation dependent descriptors to improve their matching performance. The advantages of this tool are two-fold: First, it improves the matching performance of many descriptors. Second, it reduces the dimensionality of the descriptor, providing a more compact representation, which in turn makes comparing two models more efficient.