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Title: Functional PCA on shape space for gait analysis and assessment Authors:  Nadia Hosni - University of Lille (France)
Boulbaba Ben Amor - Inception Institute of Artificial Intelligence (United Arab Emirates) [presenting]
Hassen Drira - IMT Lille Douai (France)
Faten Chaieb - ENSI (Tunisia)
Abstract: The functional Principal Component Analysis (fPCA) on the Kendall shape space is used to study 3D human shape trajectories. Various problems, including -- gait recognition, gait classification (normal vs. pathological), gender classification and physical performance assessment from 3D skeletal data -- are addressed. The key idea is to transform initial high-dimensional shape trajectories to a compact set of uncorrelated variables. That is, the proposed Kendall fPCA allows representation of their variation around the mean trajectory in a lower dimensional submanifold, in terms of principal modes of variation. Acquired using conventional IR MoCap senors (e.g. Vicon) or cost-effective depth cameras (e.g. Kinect), sequences of skeletal data are first mapped to the shape space of 3D landmark configurations and viewed as time-parameterized shape trajectories. The main barrier to apply fPCA is the non-linear structure of the space of interest. We accommodate fPCA formulation to account for the geometric structure of the Kendall shape space. The elastic metric and the geometric tools previously defined allowed us to align temporally the trajectories and to approximate the Frechet mean trajectory. Kendall fPCA is carried out by log-map the original trajectories to tangent spaces around the Frechet mean, and then performed a classical fPCA on the vector fields lying to the linear tangent spaces of log-mapped data.