Building Deep Networks on Grassmann Manifolds

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean network paradigm to Grassmann manifolds. In particular, we design full rank mapping layers to transform input Grassmannian data to more desirable ones, exploit re-orthonormalization layers to normalize the resulting matrices, study projection pooling layers to reduce the model complexity in the Grassmannian context, and devise projection mapping layers to respect Grassmannian geometry and meanwhile achieve Euclidean forms for regular output layers. To train the Grassmann networks, we exploit a stochastic gradient descent setting on manifolds of the connection weights, and study a matrix generalization of backpropagation to update the structured data. The evaluations on three visual recognition tasks show that our Grassmann networks have clear advantages over existing Grassmann learning methods, and achieve results comparable with state-of-the-art approaches.Comment: AAAI'18 pape

Pooling Faces: Template based Face Recognition with Pooled Face Images

We propose a novel approach to template based face recognition. Our dual goal is to both increase recognition accuracy and reduce the computational and storage costs of template matching. To do this, we leverage on an approach which was proven effective in many other domains, but, to our knowledge, never fully explored for face images: average pooling of face photos. We show how (and why!) the space of a template's images can be partitioned and then pooled based on image quality and head pose and the effect this has on accuracy and template size. We perform extensive tests on the IJB-A and Janus CS2 template based face identification and verification benchmarks. These show that not only does our approach outperform published state of the art despite requiring far fewer cross template comparisons, but also, surprisingly, that image pooling performs on par with deep feature pooling.Comment: Appeared in the IEEE Computer Society Workshop on Biometrics, IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), June, 201