Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

Dynamic gesture recognition using PCA with multi-scale theory and HMM

In this paper, a dynamic gesture recognition system is presented which requires no special hardware other than a Webcam. The system is based on a novel method combining Principal Component Analysis (PCA) with hierarchical multi-scale theory and Discrete Hidden Markov Models (DHMM). We use a hierarchical decision tree based on multiscale theory. Firstly we convolve all members of the training data with a Gaussian kernel, which blurs differences between images and reduces their separation in feature space. This reduces the number of eigenvectors needed to describe the data. A principal component space is computed from the convolved data. We divide the data in this space into two clusters using the k-means algorithm. Then the level of blurring is reduced and PCA is applied to each of the clusters separately. A new principal component space is formed from each cluster. Each of these spaces is then divided into two and the process is repeated. We thus produce a binary tree of principal component spaces where each level of the tree represents a different degree of blurring. The search time is then proportional to the depth of the tree, which makes it possible to search hundreds of gestures in real time. The output of the decision tree is then input into DHMM to recognize temporal information

Continuous Action Recognition Based on Sequence Alignment

Continuous action recognition is more challenging than isolated recognition because classification and segmentation must be simultaneously carried out. We build on the well known dynamic time warping (DTW) framework and devise a novel visual alignment technique, namely dynamic frame warping (DFW), which performs isolated recognition based on per-frame representation of videos, and on aligning a test sequence with a model sequence. Moreover, we propose two extensions which enable to perform recognition concomitant with segmentation, namely one-pass DFW and two-pass DFW. These two methods have their roots in the domain of continuous recognition of speech and, to the best of our knowledge, their extension to continuous visual action recognition has been overlooked. We test and illustrate the proposed techniques with a recently released dataset (RAVEL) and with two public-domain datasets widely used in action recognition (Hollywood-1 and Hollywood-2). We also compare the performances of the proposed isolated and continuous recognition algorithms with several recently published methods