# On the Vector Space in Photoplethysmography Imaging

## TL;DR

This paper introduces a novel Riemannian manifold approach to analyze face video signals for photoplethysmography imaging, improving robustness and simplicity in heart rate estimation.

## Contribution

It develops a topology change based on group invariance principles, enabling parameter-free, low-complexity feature extraction for PPGI from face videos.

## Key findings

- Achieved robust heart rate estimation on public face video datasets.
- Unifies invariance properties with a low-dimensional embedding.
- Operates implicitly without prior knowledge or parameter tuning.

## Abstract

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 implicit on the feature space without requiring any kind of prior knowledge and does not need 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. The computational complexity is low and the implementation becomes fairly simple. During experiments the operator achieved robust and competitive estimation performance of heart rate from face videos on two public databases.