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Goal

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Goal

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  1. Principal componentanalysis of the color spectra from natural scenesLong Nguyen ECE-499 Advisor: Prof. Shane Cotter

  2. Goal • We wish to determine if there is some small number of underlying components (basis functions) which can be linearly combined to produce the wide variety of spectral data observed in nature

  3. Equipments • Portable laptop • Spectrophotometer • Matlab

  4. Collection of Spectral data • Summer in Jackson Gardens

  5. Collection of Spectral data • Jackson Gardens: • 120 samples of natural color spectrums.

  6. Collection of Spectral data • Jackson Gardens: • 120 samples of natural color spectrums. • 40 samples in open area, 40 in the shade area, and 40 in mixture of both (Up and sideway)

  7. Collection of Spectral data • Jackson Gardens: • 120 samples of natural color spectrums. • 40 samples in open area, 40 in the shade area, and 40 in mixture of both (Up and sideway) • Leaves:

  8. Collection of Spectral data • Jackson Gardens: • 120 samples of natural color spectrums. • 40 samples in open area, 40 in the shade area, and 40 in mixture of both (Up and sideway) • Leaves: • 60 samples of maple leaves

  9. Fig. 1 Open up sky color spectrum of a sunny day

  10. Calibration • Aim beam of light with known intensity at the sensor

  11. Calibration • Aim beam of light with known intensity at the sensor • Convert all garden measurements into radiance (mol/m2/s/sr/nm)

  12. Mathematical Analysis • Principal Component Analysis (PCA)

  13. Mathematical Analysis • Principal Component Analysis (PCA) • PCA is a technique used to reduce multidimensional data sets to lower dimensions for data compression.

  14. Mathematical Analysis • Principal Component Analysis (PCA) • PCA is a technique used to reduce multidimensional data sets to lower dimensions for data compression. • PCA extracts components which are orthogonal to one another. The first component accounts for the greatest variance observed in the data, the second component accounts for variance in an orthogonal direction, and so on until the data is completely accounted for.

  15. PCA • Data Covariance Matrix Eigenvalues & Eigenvectors

  16. Eigen values • 11 Significant Eigen values

  17. Eigen values • 11 Significant Eigen values • 0.0001 0.0001 0.0002 0.0002 0.0003 0.0017 0.0085 0.0118 0.0740 0.4586 48.8719

  18. 11 Eigenvectors from biggest to smallest Eigen values

  19. 11 Eigen Vectors continue….

  20. 11 Eigen Vectors continue….

  21. 3 eigenvectors represent 98% of the data

  22. 3 eigenvectors represent 98% of the data

  23. Future Work • Relate eigenvectors to real spectra • Analyze the leaves data • Independent Component Analysis (ICA)

  24. Acknowledgements • Prof. Shane Cotter • Prof. Fleishman