Principal component analysis of the color spectra from

Principal component analysis of the color spectra from natural scenes Long Nguyen ECE-499 Advisor: Prof. Shane Cotter

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

Equipments • Portable laptop • Spectrophotometer • Matlab

Collection of Spectral data • Summer in Jackson Gardens

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

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)

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:

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

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

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

Calibration • Aim beam of light with known intensity at the sensor • Convert all garden measurements into radiance ( mol/m 2/s/sr/nm)

Mathematical Analysis • Principal Component Analysis (PCA)

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

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.

PCA • Data Covariance Matrix Eigenvalues & Eigenvectors

Eigen values • 11 Significant Eigen values

Eigen values • 11 Significant Eigen values • 0. 0001 0. 0002 0. 0003 0. 0017 0. 0085 0. 0118 0. 0740 0. 4586 48. 8719

11 Eigenvectors from biggest to smallest Eigen values

11 Eigen Vectors continue….

11 Eigen Vectors continue….

3 eigenvectors represent 98% of the data

3 eigenvectors represent 98% of the data

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

Acknowledgements • Prof. Shane Cotter • Prof. Fleishman