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Fig. 1. Block diagram of the HR estimation system.

approaches as a serial fusion of the Eulerian and the Lagrangian magnification techniques. Recently, Eulerian approaches
have gained popularity since they present more tractable
mathematical models than Lagrangian methods. The latter approaches allow an accurate motion estimation, but they have
a high computational cost and are not suitable to handle occlusion of objects and complex motions as put in evidence in
[9]. In contrast, the Eulerian methods present more tractable
mathematical models. For example, Brieva et al. [11], [12] use
the Hermite transform as a spatial decomposition technique,
showing a better image sequence reconstruction, instead of the
Laplacian pyramid of Wu et al. [9].
In HR estimation, motion-based techniques use an image
sequence, first by calculating the displacement of the pixels of
a certain region and then by tracking these pixels over time on
the sequence. The detection of these subtle motions present in
the skin surface corresponds to the heart pulse to be estimated.
A work using the motion magnification to extract the signal
and the DFT to estimate the HR was also proposed in [11].
In this work, we present an HR estimation method based
on a bio-inspired Eulerian magnification procedure using the
Hermite transform (HT). The magnification is performed on
the changes of chrominance, related to the blood irrigation
process, on the image sequence for extracting the raw pulse
signal. Then, it is used in a feed-forward neural network (NN)
to estimate the HR. The NN was trained using a custom dataset
June 2020

that consists of five healthy subjects with five attempts per participant. The experiments were performed under controlled
conditions of acquisition, and the possible micro-movements
of the subject were not taken into account.

Heart Rate Estimation Based on Motion
Magnification
In this section, we show an overview of our proposal for estimating the HR using a non-contact strategy by a video
recording of the patient. The main stages of our proposal are:
the selection of a region of interest (ROI); the amplification of
changes in chrominance applying an Eulerian video motion
magnification method using the HT; the feature extraction to
construct the raw pulse signal; and the estimation of HR using
a properly trained NN. The overall system is shown in Fig. 1.
For the experiments, we collected data videos using a standard
camera, and we validated the results with respect to a personal
pulse monitoring device.

Video Magnification Using the Hermite Transform
In Fig. 2, we show the proposed video magnification method.
It uses the HT, instead of other spatial decomposition tools
(e.g., Laplacian, or Gaussian pyramid), to amplify the temporal changes of chrominance of a selected ROI into the image
sequence. First, we perform a multi-resolution spatial decomposition of low-frequency components (zero-order coefficient)

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