Unsupervised iterative manifold alignment via local feature histograms

Abstract

We propose a new unsupervised algorithm for the automatic alignment of two manifolds of different datasets with possibly different dimensionalities. Alignment is performed automatically without any assumptions on the correspondences between the two manifolds. The proposed algorithm automatically establishes an initial set of sparse correspondences between the two datasets by matching their underlying manifold structures. Local feature histograms are extracted at each point of the manifolds and matched using a robust algorithm to find the initial correspondences. Based on these sparse correspondences, an embedding space is estimated where the distance between the two manifolds is minimized while maximally retaining the original structure of the manifolds. The problem is formulated as a generalized eigenvalue problem and solved efficiently. Dense correspondences are then established between the two manifolds and the process is iteratively implemented until the two manifolds are correctly aligned consequently revealing their joint structure. We demonstrate the effectiveness of our algorithm on aligning protein structures, facial images of different subjects under pose variations and RGB and Depth data from Kinect. Comparison with an state-of-the-art algorithm shows the superiority of the proposed manifold alignment algorithm in terms of accuracy and computational time.