Pendulum Motion Tracking & Analysis

Computer vision pipeline for tracking a spring-pendulum system from multi-camera video, extracting dominant oscillation modes via PCA, and estimating physical parameters analytically.

Project Report

The full project report is available at: mech0107_coursework1_final.pdf

The coursework specification is available at: MECH0107_CW1_2526.pdf

Notebooks

Notebook	Description
Notebooks/main.ipynb	Main analysis notebook — full pipeline using the PendulumTracker class
Notebooks/testing_and_viz.ipynb	Exploratory development and visualisation notebook

Pipeline Overview (main.ipynb)

1. Data Loading — loads .mat files from three camera views; rotates Camera 3 to align orientation
2. Pre-processing — grayscale conversion and Gaussian blur
3. Area of Interest — manually confirmed bounding regions for each camera
4. Detection Pipeline — median background subtraction, thresholding, morphological dilation, contour detection
5. Centroid Tracking — frame-by-frame centroid extraction with interpolation for missed detections
6. Frequency Analysis — FFT-based dominant frequency detection per camera signal
7. PSD Filtering — noise reduction by zeroing low-power spectral components
8. Gabor Transform — time-frequency spectrogram to confirm frequency stationarity
9. PCA — 6-component PCA on standardised centroid data to isolate oscillation modes
10. Analytical Modeling — estimates spring constant $k$ (from PC1) and pendulum length $L$ (from PC2), compared against undamped cosine solutions

Data

Raw .mat files are stored in data/matlab_files/ (not tracked by git due to size).

File	Contents
cam1.mat	vidFrames1_4 — 480×640×3×392 frames
cam2.mat	vidFrames2_4 — 480×640×3×405 frames
cam3.mat	vidFrames3_4 — 640×480×3×394 frames (rotated on load)

Requirements

pip install -r requirements.txt

Key dependencies: numpy, scipy, opencv-python, scikit-image, scikit-learn, matplotlib.