Combining Multiple Manifold-Valued Descriptors for Improved Object Recognition

We present a learning method for classification using multiple manifold-valued features. Manifold techniques are becoming increasingly popular in computer vision since Riemannian geometry often comes up as a natural model for many descriptors encountered in different branches of computer vision. We propose a feature combination and selection method that optimally combines descriptors lying on different manifolds while respecting the Riemannian geometry of each underlying manifold. We use our method to improve object recognition by combining HOG~cite{Dalal05Hog} and Region Covariance~cite{Tuzel06} descriptors that reside on two different manifolds. To this end, we propose a kernel on the $n$-dimensional unit sphere and prove its positive definiteness. Our experimental evaluation shows that combining these two powerful descriptors using our method results in significant improvements in recognition accuracy.