Figure 1:Shape collections typically come with inconsistent orientations (a). PCA-based alignment (b), or aligning to an arbitrarily chosen base model (c) is prone to error. The problem with pairwise alignments is attributed to several minima in alignment distances (E_pair), arising due to near-symmetries of shapes. We introduce an autocorrelation-guided algorithm to efficiently sample the minima (red boxes) and jointly co-align the input models (d).

Abstract

Co-aligning a collection of shapes to a consistent pose is a common problem in shape analysis with applications in shape matching, retrieval, and visualization. We observe that resolving among some orientations is easier than others, for example, a common mistake for bicycles is to align front-to-back, while even the simplest algorithm would not erroneously pick orthogonal alignment. The key idea of our work is to analyze rotational autocorrelations of shapes to facilitate shape co-alignment. In particular, we use such an autocorrelation measure of individual shapes to decide which shape pairs might have well-matching orientations; and, if so, which configurations are likely to produce better alignments. This significantly prunes the number of alignments to be examined, and leads to an efficient, scalable algorithm that performs comparably to state-of-the-art techniques on benchmark datasets, but requires significantly fewer computations, resulting in 2-16$\times$ speed improvement in our tests.