We present a comparative evaluation of various techniques for action recognition while keeping as many variables as possible controlled. We employ two categories of Riemannian manifolds: symmetric positive definite matrices and linear subspaces. For both categories we use their corresponding nearest neighbour classifiers, kernels, and recent kernelised sparse representations. We compare against traditional action recognition techniques based on Gaussian mixture models and Fisher vectors (FVs). We evaluate these action recognition techniques under ideal conditions, as well as their sensitivity in more challenging conditions (variations in scale and translation). Despite recent advancements for handling manifolds, manifold based techniques obtain the lowest performance and their kernel representations are more unstable in the presence of challenging conditions. The FV approach obtains the highest accuracy under ideal conditions. Moreover, FV best deals with moderate scale and translation changes.
Recently, the traditional sparse representation (SR) on vectors has been generalised to sparse representations in SPD matrices and LS @cite_11 @cite_43 @cite_48 @cite_12 . While the objective of SR is to find a representation that efficiently approximates elements of a signal class with as few atoms as possible, for the Riemannian SR, any given point can be represented as a sparse combination of dictionary elements @cite_43 @cite_48 . @cite_48 , LS are embedded into the space via isometric mapping, which leads to a closed-form solution for updating a LS representation, atom by atom. Moreover, @cite_48 presents a kernelised version of the dictionary learning algorithm to deal with non-linearity in data. @cite_43 outlines the sparse coding and dictionary learning problem for SPD matrices. To this end, SPD matrices are embedded into the RKHS to perform sparse coding.
@cite_43 @cite_48 @cite_12 @cite_11
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Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse 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, which enables us to devise a closed-form solution for updating a Grassmann dictionary, atom by atom. Furthermore, to handle non-linearity in data, we propose a kernelised version of the dictionary learning algorithm. Experiments on several classification tasks (face recognition, action recognition, dynamic texture classification) show that the proposed approach achieves considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelised Affine Hull Method and graph-embedding Grassmann discriminant analysis. Low-rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is naturally described as a clustering problem on Grassmann manifold. The novelty of this paper is to generalize LRR on Euclidean space into the LRR model on Grassmann manifold. The new method has many applications in computer vision tasks. The paper conducts the experiments over two real world examples, clustering handwritten digits and clustering dynamic textures. The experiments show the proposed method outperforms a number of existing methods. A novel framework for action recognition in video using empirical covariance matrices of bags of low-dimensional feature vectors is developed. The feature vectors are extracted from segments of silhouette tunnels of moving objects and coarsely capture their shapes. The matrix logarithm is used to map the segment covariance matrices, which live in a nonlinear Riemannian manifold, to the vector space of symmetric matrices. A recently developed sparse linear representation framework for dictionary-based classification is then applied to the log-covariance matrices. The log-covariance matrix of a query segment is approximated by a sparse linear combination of the log-covariance matrices of training segments and the sparse coefficients are used to determine the action label of the query segment. This approach is tested on the Weizmann and the UT-Tower human action datasets. The new approach attains a segment-level classification rate of 96.74 for the Weizmann dataset and 96.15 for the UT-Tower dataset. Additionally, the proposed method is computationally and memory efficient and easy to implement.