New Approaches for Feature Extraction in Hyperspectral Imagery

1. New Approaches for Feature Extraction in Hyperspectral Imagery Stefan A. Robila Lukasz Maciak Department of Computer Science www.csam.montclair.edu/~robila IEEE LISAT, 2006

2. Hyperspectral Images Spectral Image: Image format representation of the measurement of the ”brightness” (for a certain interval of energy frequencies) of a phenomenon, object, region, etc. 2 Stefan A. Robila Department of Computer Science

3. Goal • Develop new feature extraction algorithms for hyperspectral images • Ensure that the new methods meet the particularities of the data 3 Stefan A. Robila Department of Computer Science

4. Increasing Wavelength (in meters) 10 -6 Infrared 10 -11 Gamma Rays 10 -8 Ultraviolet 10 Radio X-Rays 10 -9 Visible 10 -7 Microwaves 10 -2 Hyperspectral Imagery • Data collected as hundreds of images (spectral images or spectral bands), with each image corresponding to narrow contiguous wavelength intervals • Multispectral – Many spectra (bands) • Hyperspectral – Huge numbers of continuous bands Electromagnetic Spectrum 4 Stefan A. Robila Department of Computer Science

5. Hyperspectral Imagery • Pixel vectors (or spectra) - formed of pixel intensities from the same location, across the bands • Each pixel corresponds to a certain region of the scene surveyed and will represent the spectral information for that region. 5 Stefan A. Robila Department of Computer Science

6. Hyperspectral Imagery • Hyperspectral remote sensing provides a continuous, essentially complete record of spectral responses of materials over the wavelengths considered 6 Stefan A. Robila Department of Computer Science

7. Processing Hyperspectral Data Hyperspectral Image Processing: • group in classes pixel vectors with similar spectral characteristics • detect pixel vectors whose spectral characteristics are similar to the ones of known materials Importance • Abundance of data in hyperspectral imagery leads to increased processing accuracy • Hyperspectral sensors have been installed on aircrafts (HYDICE, AVIRIS), satellites (Hyperion), and have been started to be produced commercially (SOC 700) indicating large data availability in the near future Processing of the full image cube is not desirable due to its size as well as its redundancy 7 Stefan A. Robila Department of Computer Science

8. Feature Extraction • The process of projecting the data from the original feature space to a lower dimensional subspace that provides a more effective representation • The efficiency of the representation is viewed through the separation between the classes within each feature • Supervised • uses information provided by subsets of pixel vectors – ground data • - the classes are considered to be represented by the ground data • Unsupervised • no ground data is used • concentrates mainly on redundancy reduction ground data may be unreliable or impossible to obtain class statistics cannot be computed or estimated 8 Stefan A. Robila Department of Computer Science

9. n n Feature (Band) Extraction • Principal Component Analysis • Independent Component Analysis • other… 9 Stefan A. Robila Department of Computer Science

10. Principal Component Analysis (PCA) For the multidimensional random vector x, PCA finds a linear transform W such that the obtained components are uncorrelated: Y=Wx (1) The transform is obtained as: W= AxT (2) Where Ax is the matrix formed of the normalized eigenvectors for the covariance matrix Σx. 10 Stefan A. Robila Department of Computer Science

11. Independent Component Analysis (ICA) Given a random vector s, and a matrix A of size , the problem is to recover this pair (s,A) from the available observations x defined as : x=As (3) knowing that the vector s is formed of independent non-Gaussian components: (4) where p(.) refers to the probability density function and sirefers to the components of the vector s. 11 Stefan A. Robila Department of Computer Science

12. Issues • No clear relationship to hyperspectral imagery • Strong restrictions on the IC / PC transform • Does not fit the (Linear) Mixing Model 12 Stefan A. Robila Department of Computer Science

13. Linear Mixing Model (LMM) Each n-dimensional observed pixel vector x can be expressed as: (6) S is the nxm matrix of spectra (s1, .., sm) – endmembers a is an m-dimensional vector - abundance vector w is the additive noise vector The elements of the abundance vector are assumed to be positive and with unit sum: (7) (8) Linear Unmixing - find the endmembers and their abundances. 13 Stefan A. Robila Department of Computer Science

14. Issues (cont) • In PCA and ICA we have orthogonality of the endmembers • The abundance maps are not positive • The abundance maps do not add up to one 14 Stefan A. Robila Department of Computer Science

15. Nonnegative Matrix Factorization (NMF) Given the observed data x, the goal of NMF is to find s and a linear mixing transform W both positively defined such that: x=Ws (9) This approach can be understood as factorizing a data matrix subject to positive constraints. 15 Stefan A. Robila Department of Computer Science

16. NMF Solution • Constrain positivity • Optimize based on gradient: (10) (11) (12) (function based on the Euclidean norm) 16 Stefan A. Robila Department of Computer Science

17. NMF Algorithm 1. Randomly initialize W and s to positive values 2. Scale the columns of s to sum up to one 3. Repeat: 4. 5. 6. Scale the columns of s to sum up to one while non convergence 17 Stefan A. Robila Department of Computer Science

18. NMF Algorithm • Convergence based on the value of f(W,s) from eq. 12 • Stop when converging to 0 • Alternative stop when value is stable • Epsilon factor used for speedup • Algorithm enforces summation to one for s • Algorithm maintains positivity of W and s 18 Stefan A. Robila Department of Computer Science

19. Experiments Hyperspectral Digital Imagery Collection Experiment (HYDICE) • Foliage scene • spatial resolution of 1.5m • 210 bands with wavelengths between 400nm and 2.5 micron. • Rows of panels made of 8 different materials • Sizes 1mx1m, 2mx2m, 3mx3m • Small forest patch • Exposed ground 19 Stefan A. Robila Department of Computer Science

20. Experiments • Relative fast stability Error rate vs. iteration 20 Stefan A. Robila Department of Computer Science

21. Experiments 21 Stefan A. Robila Department of Computer Science

22. Experiments 22 Stefan A. Robila Department of Computer Science

23. Experiments Surface Optics (SOC 700) • artificial • and • natural vegetation • 120 bands with wavelengths between 400nm and 900nm 23 Stefan A. Robila Department of Computer Science

24. Experiments • Relative fast stability Error rate vs. iteration 24 Stefan A. Robila Department of Computer Science

25. Experiments 25 Stefan A. Robila Department of Computer Science

26. Future Work • Number of features to be extracted • Avoid local optima • Speedup through distributed processing • Real time unmixing tool 26 Stefan A. Robila Department of Computer Science

27. Conclusions • Feature extraction remains an attractive approach in processing hyperspectral images. The current techniques are focused on strong restrictions on the separability of the resulting bands and do not have a natural interpretation for the nature of hyperspectral data. • NMF provides an elegant approach that simply assumes that the features must be separable and positively defined. When adding the condition that the features must also sum up to one pixelwise we discover that NMF also provides a solution to the classical linear unmixing problem. • Results suggest that NMF reaches optimal solutions that clearly separate endmember information for the data. • Consider NMF as a viable approach for feature extraction. 27 Stefan A. Robila Department of Computer Science

28. Thank you 28 Stefan A. Robila Department of Computer Science