Eulerian Biometric Signal & Flow Analyzer

Overview

This single-page application combines spatial-temporal modeling and biological signal extraction. It simulates how non-contact sensors capture a subject's heart rate and facial micro-vascular blood flow velocity from raw video sequences.

The system is split into two halves: the Spatial Domain and the Temporal-Spectral Domain. On the left, a detailed vector wireframe profile of a human face is overlaid with a circular region on the cheek, representing a skin area centered over the transverse facial artery. Applying spatial video magnification principles allows you to visually observe color changes as cardiac blood flow cycles. On the right, the application converts these local spatial fluctuations into a live time-domain plot (simulating photoplethysmogram signal processing) and a frequency-domain spectrum showing the isolated heart rate peak calculated via a fast Fourier transform model.

How to Use

• Play / Pause: Toggles the animation loop and graph buffers. Freeze the loop to inspect static measurements of localized flow vectors or spectral frequencies.
• Reset: Immediately returns all states, coordinates, noise matrices, and hardware configurations back to baseline values.
• Active Target Probe: Click or tap anywhere inside the cheek patch on the face. A crosshair target telemetry probe will snap to that location, updating the digital signal processing parameters on the live graph displays to track that specific coordinate.
• Adjust Sliders:
  • Heart Rate (BPM): Modifies the fundamental frequency of the vascular contraction, altering the speed of the face color changes and shifting the FFT frequency peak.
  • Signal Amplitude: Scales the strength of the color variations, showing how weak signals can become buried under noise.
  • Motion Noise: Simulates noise from movement and fluctuating lighting, challenging the robustness of the filter.
• Opt-in Sonification: Enabling sound maps the cardiac cycle to low-frequency synth beeps that align with the peak systolic output, demonstrating acoustic tracking of photoplethysmogram waveforms.

Technical Details

Eulerian Spatial-Temporal Transformation

In contrast to Lagrangian computer vision models, which track moving features like landmarks, Eulerian Video Magnification (EVM) isolates static coordinates and measures intensity changes over time. By observing fluctuations in the red, green, and blue color channels of individual facial pixels, EVM extracts vital signs without requiring the subject to remain perfectly still. Green channels are particularly useful, as hemoglobin has a high absorption peak around 520–580 nm, making it highly sensitive to changes in blood volume.

Fourier Spectral Extraction

To identify the heart rate from noisy time-series data, the application simulates a Fourier Transform. This operation decomposes the continuous time-domain signal $x(t)$ into its constituent frequencies: $$X(f) = \int_{-\infty}^{\infty} x(t) e^{-i 2 \pi f t} dt$$ The resulting power spectrum shows relative energy amplitudes across a range of frequencies (expressed in beats per minute). The highest, most prominent peak corresponds to the fundamental cardiac frequency, allowing for precise heart rate measurement even in the presence of random white noise or simulated motion artifacts.

Future Directions

• Clinical-Grade Motion Tracking: Implementing active face-mesh tracking (e.g., MediaPipe) to maintain a steady ROI (Region of Interest) during patient motion, preventing signal loss.
• Continuous Wavelet Transform (CWT): Replacing standard FFT models with wavelets to analyze non-stationary signals, helping to capture transient heart rate variability (HRV) and respiratory cycles.
• Oxygen Saturation Mapping (SpO2): Modeling dual-wavelength illumination (660 nm red and 940 nm infrared) to non-invasively map arterial oxygen saturation across different areas of the face.