Support vector machines with time series distance kernels for action classification

2017 IEEE International Conference on Computer Vision (ICCV)

Amor

et al. 2017

In this paper, we study the problem of facial expression recognition using a novel space-time geometric representation. We describe the temporal evolution of facial landmarks as parametrized trajectories on the Riemannian manifold of positive semidefinite matrices of fixed-rank. Our representation has the advantage to bring naturally a second desirable quantity when comparing shapes -the spatial covariance -in addition to the conventional affineshape representation. We derive then geometric and computational tools for rate-invariant analysis and adaptive re-sampling of trajectories, grounding on the Riemannian geometry of the manifold. Specifically, our approach involves three steps: 1) facial landmarks are first mapped into the Riemannian manifold of positive semidefinite matrices of rank 2, to build time-parameterized trajectories; 2) a temporal alignment is performed on the trajectories, providing a geometry-aware (dis-)similarity measure between them; 3) finally, pairwise proximity function SVM (ppfSVM) is used to classify them, incorporating the latter (dis-)similarity measure into the kernel function. We show the effectiveness of the proposed approach on four publicly available benchmarks (CK+, MMI, Oulu-CASIA, and AFEW). The results of the proposed approach are comparable to or better than the state-of-the-art methods when involving only facial landmarks.

show abstract

“…is the geodesic in G(2, n) given by Eq. (4). They also define the closeness between G 1 and G 2 , d S + (G 1 , G 2 ), as the square of the length of this curve:…”

Section: Tangent Space and Riemannian Metricmentioning

confidence: 99%

“…Inspired by a recent work of [4] for action recognition, we adopt the pairwise proximity function SVM (ppfSVM) [16,17]. PpfSVM requires the definition of a (dis-)simlarity measure to compare samples.…”

Section: Classification Of Trajectories Inmentioning

confidence: 99%

A Novel Space-Time Representation on the Positive Semidefinite Cone for Facial Expression Recognition

2017 IEEE International Conference on Computer Vision (ICCV)

Amor

et al. 2017

show abstract

“…Inspired by a recent work of [41] for action recognition, we adopted the pairwise proximity function SVM (ppfSVM) [42], [43]. The ppfSVM requires the definition of a (dis-)similarity measure to compare samples.…”

Section: Pairwise Proximity Function Svm Classifiermentioning

confidence: 99%

“…. , β m G } in T , following [41], a proximity function P T : T × T → R + between two trajectories β 1 G , β 2 G ∈ T is defined as,…”

Section: Pairwise Proximity Function Svm Classifiermentioning

confidence: 99%

See 1 more Smart Citation

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

IEEE Trans. Pattern Anal. Mach. Intell.

Amor

et al. 2020

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.In this document, we provide the mathematical preliminaries to our approach. We also give further details on the conducted experiments and the reported results.

show abstract

The Riemannian and Affine Geometry of Facial Expression and Action Recognition

Paiva

Handbook of Variational Methods for Nonlinear Geometric Data

2020