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 discuss the limitations of canonical alignment and present a new mathematical tool, 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 advantage of this is twofold: 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.
Kazhdan et al. (2003) studied this question.