On the Vector Space in Photoplethysmography Imaging

We study the vector space of visible wavelength intensities from face videos widely used as input features in Photoplethysmography Imaging (PPGI). Based upon theoretical principles of group invariance in the Euclidean space, we derive a change of the topology where the corresponding distance between successive measurements is defined as geodesic on a Riemannian manifold. This lower dimensional embedding of the sensor signal unifies the invariance properties with respect to translation of the features as discussed by several former approaches. The resulting operator acts implicitly on the feature space without requiring any kind of prior knowledge and parameter tuning. The resulting feature's time varying quasi-periodic shaping naturally occurs in form of the canonical state space representation according to the known diffusion process of blood volume changes. This reduces drastically computational complexity and consequently simplifies the implementation. Experiments from face videos on two public databases have shown a competitive estimation performances of heart rate and robustness in comparison with already available methods.