A Novel Geometric Framework on Gram Matrix Trajectories for Human Behavior Understanding

Anis Kacem (1, 2) , Mohamed Daoudi (1, 3) , Boulbaba Ben Amor (1, 3) , Stefano Berretti (4) , Juan Carlos Alvarez-Paiva (5, 2)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Université de Lille
3 IMT Lille Douai - Ecole nationale supérieure Mines-Télécom Lille Douai
4 UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence
5 LPP - Laboratoire Paul Painlevé - UMR 8524

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the benefit to bring naturally a second desirable quantity when comparing shapes-the spatial covariance-in addition to the conventional affine-shape representation. We derived then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the underlying manifold. Specifically, our approach involves three steps: (1) landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of fixed-rank to build time-parameterized trajectories; (2) a temporal warping is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; (3) finally, a pairwise proximity function SVM is used to classify them, incorporating the (dis-)similarity measure into the kernel function. We show that such representation and metric achieve competitive results in applications as action recognition and emotion recognition from 3D skeletal data, and facial expression recognition from videos. Experiments have been conducted on several publicly available up-to-date benchmarks.

Mots clés: Emotion Recognition from Body Movements; Action Recognition; Facial Expression Recognition !; Gram matrices; Riemannian Geometry; Symmetric Positive Semidefinite Manifolds; Grassmann Manifold

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]; Intelligence artificielle [cs.AI]

Anis Kacem, Mohamed Daoudi, Boulbaba Ben Amor, Stefano Berretti, Juan Carlos Alvarez-Paiva. A Novel Geometric Framework on Gram Matrix Trajectories for Human Behavior Understanding. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020, 42 (1), pp.1-14. ⟨10.1109/TPAMI.2018.2872564⟩. ⟨hal-01883247⟩