Log-Euclidean Bag of Words for Human Action Recognition

TL;DR

This paper introduces a novel Riemannian Bag of Words model for human action recognition that effectively incorporates the geometry of covariance matrices on SPD manifolds, leading to improved classification accuracy.

Contribution

It extends the traditional BoW approach by embedding SPD matrices into Euclidean space using a diffeomorphism, accounting for their Riemannian geometry.

Findings

Achieves higher accuracy than state-of-the-art methods on human action datasets.

Effectively models covariance matrices on SPD manifolds for action recognition.

Demonstrates the benefit of considering non-Euclidean geometry in BoW models.

Abstract

Representing videos by densely extracted local space-time features has recently become a popular approach for analysing actions. In this paper, we tackle the problem of categorising human actions by devising Bag of Words (BoW) models based on covariance matrices of spatio-temporal features, with the features formed from histograms of optical flow. Since covariance matrices form a special type of Riemannian manifold, the space of Symmetric Positive Definite (SPD) matrices, non-Euclidean geometry should be taken into account while discriminating between covariance matrices. To this end, we propose to embed SPD manifolds to Euclidean spaces via a diffeomorphism and extend the BoW approach to its Riemannian version. The proposed BoW approach takes into account the manifold geometry of SPD matrices during the generation of the codebook and histograms. Experiments on challenging human action datasets show that the proposed method obtains notable improvements in discrimination accuracy, in comparison to several state-of-the-art methods.