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.
Manifolds can be also mapped to a reproducing kernel Hilbert space (RKHS) by using kernels. Kernel analysis on SPD matrices and LS has been used for gesture and action recognition in @cite_40 @cite_0 @cite_9 . SPD matrices are embedded into RKHS via a pseudo kernel in @cite_40 . With this pseudo kernel is possible to formulate a locality preserving projections over SPD matrices. Positive definite radial kernels are used to solve the action recognition problem in @cite_0 , where an optimisation algorithm is employed to select the best kernel among the class of positive definite radial kernels on the manifold.
@cite_0 @cite_9 @cite_40
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We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However, the number of known positive definite kernels on manifolds remain very limited. Furthermore, most kernels typically depend on at least one parameter that needs to be tuned for the problem at hand. A poor choice of kernel, or of parameter value, may yield significant performance drop-off. Here, we show that positive definite radial kernels on the unit n-sphere, the Grassmann manifold and Kendall's shape manifold can be expressed in a simple form whose parameters can be automatically optimized within a support vector machine framework. We demonstrate the benefits of our kernel learning algorithm on object, face, action and shape recognition. A convenient way of analysing Riemannian manifolds is to embed them in Euclidean spaces, with the embedding typically obtained by flattening the manifold via tangent spaces. This general approach is not free of drawbacks. For example, only distances between points to the tangent pole are equal to true geodesic distances. This is restrictive and may lead to inaccurate modelling. Instead of using tangent spaces, we propose embedding into the Reproducing Kernel Hilbert Space by introducing a Riemannian pseudo kernel. We furthermore propose to recast a locality preserving projection technique from Euclidean spaces to Riemannian manifolds, in order to demonstrate the benefits of the embedding. Experiments on several visual classification tasks (gesture recognition, person re-identification and texture classification) show that in comparison to tangent-based processing and state-of-the-art methods (such as tensor canonical correlation analysis), the proposed approach obtains considerable improvements in discrimination accuracy.