Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 42, Issue 1, Pages 1-14Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2018.2872564
Keywords
Trajectory; Manifolds; Three-dimensional displays; Shape; Emotion recognition; Skeleton; Covariance matrices; Landmark configurations; gram matrices; riemannian geometry; symmetric positive semidefinite manifolds; grassmann manifold; action recognition; emotion recognition from body movements; facial expression recognition
Funding
- PIA, ANR [ANR-11-EQPX-0023]
- Agence Nationale de la Recherche (ANR) [ANR-11-EQPX-0023] Funding Source: Agence Nationale de la Recherche (ANR)
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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.
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