1. 1 Keng-Hao Liu and Chein-I Chang Remote Sensing Signal and Image Processing Laboratory (RSSIPL) Department of Computer Science and Electrical Engineering University of Maryland, Baltimore County (UMBC) Baltimore, MD 21250 Dynamic Band Selection For Hyperspectral Imagery keng3@umbc.edu

2. 2 Motivation Band Selection (BS) is one of commonly used approaches that take advantage of high inter- band correlation to remove band redundancy in order to achieve a wide range of applications. Band Selection (BS) is one of commonly used approaches that take advantage of high inter- band correlation to remove band redundancy in order to achieve a wide range of applications. However, there are several crucial issues arising in implementation of BS. One of these issues is how to estimate the number of bands, p, required to be selected? However, there are several crucial issues arising in implementation of BS. One of these issues is how to estimate the number of bands, p, required to be selected? How to find p? How to find p?

3. 3 Outline Dynamic Band Selection (DBS) Dynamic Band Selection (DBS) - Virtual Dimensionality (VD) - Band Dimensionality Allocation (BDA) - Progressive Band Dimensionality Process (PBDP) - Criteria for Band Prioritization (BP) Experiments Experiments - HYDICE - AVIRIS (Purdue) Data Conclusions Conclusions

4. 4 Issues of Conventional BS Require knowing the number of bands required for BS, p, a priori The value of p is fixed at a constant and cannot be adaptive. Need an exhaustive search required to find an optimal set of p bands among all possible combinations out of the total number of bands.

5. 5 Progressive Band Dimensionality Process (PBDP) Using a criterion prioritizes all L spectral bands and removes highly correlated bands then selects bands progressively in a forward or backward manner depending upon how to retain band information in increasing or decreasing order. Using a criterion prioritizes all L spectral bands and removes highly correlated bands then selects bands progressively in a forward or backward manner depending upon how to retain band information in increasing or decreasing order.  Forward Progressive Band Dimensionality Process (FPBDP)  Backward Progressive Band Dimensionality Process (BPBDP) The PBDP process is continued on until it reaches a specific number of bands, p. So the p is considered as variable instead of fixed value. The PBDP process is continued on until it reaches a specific number of bands, p. So the p is considered as variable instead of fixed value.

6. 6 Band Prioritization (BP) Criteria for PBDP Band Prioritization Criteria for PBDP Band Prioritization Criteria for PBDP Second order statistic-based BP criteria - Variance - Signal-to-Noise Ratio (SNR or MNF) High order statistic-based BP criteria - Skewness - Kurtosis Infinite order Statistics BP criteria - Entropy - Information Divergence (ID) ) - Neg-entropy (combination of 3rd and 4th order)

7. 7 Virtual Dimensionality (VD) Use VD [Chang 2003] to determine the number of components required for Hyperspectral images. Use VD [Chang 2003] to determine the number of components required for Hyperspectral images. We assume one spectrally distinct signature can be accommodated by one band. So the number of bands required to be selected must be equal or greater than the VD. We assume one spectrally distinct signature can be accommodated by one band. So the number of bands required to be selected must be equal or greater than the VD.

8. Band Dimensionality Allocation (BDA) Concept is derived from information theory where a source S is emitted by a set of source alphabets that are used to represent the source with a given probability distribution where p j is the probability of the occurrence of the source alphabet a j Concept is derived from information theory where a source S is emitted by a set of source alphabets that are used to represent the source with a given probability distribution where p j is the probability of the occurrence of the source alphabet a j Similarly, assumes m j is material substance signature to be analyzed, then the n j denotes the number of components (bands) required to represent m j. In other word, n j is actually determined by how difficult the m j is discriminated in terms of spectral similarity. Similarly, assumes m j is material substance signature to be analyzed, then the n j denotes the number of components (bands) required to represent m j. In other word, n j is actually determined by how difficult the m j is discriminated in terms of spectral similarity. In conventional BS, it assumes n j =p for all signatures. In this cases all substance are assumed to have equal difficulty to be discriminated by spectral similarity. Generally it is not true in hyperspectral data. In conventional BS, it assumes n j =p for all signatures. In this cases all substance are assumed to have equal difficulty to be discriminated by spectral similarity. Generally it is not true in hyperspectral data. 8

9. 9 Band Dimensionality Allocation (BDA) for signatures Select a spectral similarity measure and a reference signature s. Calculate spectral similarity values for each signature and normalize them to a probability vector. Find self-information. Find the smallest integer q j larger than these self- information. Define dimensionality allocation then assigned it to jth signature, m j. BDA Procedures: Determines the number of signatures to be used for data analysis Additional number required for m j to distinguish itself from other signatures.

10. 10 Band Dimensionality Allocation (BDA) for signatures Three techniques used to find BDA Three techniques used to find BDA   Shannon coding   Huffman coding   Hamming coding Candidates that can be used for spectral similarity measure: Candidates that can be used for spectral similarity measure: Spectral angle mapper (SAM) Spectral information divergence (SID) Candidates that can be used as reference signature (s): Candidates that can be used as reference signature (s): Data sample mean Signature mean or any signature

11. 11 Dynamic Band Selection (DBS) Custom design a criterion for Band Prioritization (BP) Custom design a criterion for Band Prioritization (BP) Implement PBDP Implement PBDP Apply Band De-correlation (BD) Apply Band De-correlation (BD) Band Dimensionality Allocation (BDA) Band Dimensionality Allocation (BDA) DBS steps:

12. 12 Hyperspectral Images Used for Experiments (1) HYDICE Data: 64x64 169 bands hyperspectral image with spatial resolution is 20m. Ground truth (desired signatures) Image scene p 11, p 12, p 13 p 211, p 22, p 23 p 221 p 311, p 312, p 32, p 33 p 411, p 412, p 42, p 43 p 511, p 52, p 53 p 521 interferer grass tree road undesired signatures Spectral of five panels Classifier: FCLS Band De-correlation (BD) is applied after BP with σ= 0.1

13. 13 HYDICE Data Experiments signature m j n VD πjπj qjqj n j (BDA) Shannon coding m 1 =p 1 (panels in row1) 9 SID0.017215 SAM0.046214 m 2 =p 2 (panels in row2) 9 SID0.029515 SAM0.077913 m 3 =p 3 (panels in row3) 9 SID0.035814 SAM0.089713 m 4 =p 4 (panels in row4) 9 SID0.069513 SAM0.100413 m 5 =p 5 (panels in row5) 9 SID0.107013 SAM0.114013 m 6 (grass) 9 SID0.100713 SAM0.139612 m 7 (road) 9 SID0.056514 SAM0.103513 m 8 (tree) 9 SID0.286912 SAM0.147912 m 9 (interferer) 9 SID0.296911 SAM0.180812 Shannon BDA results of HYDICE Data

14. 14 HYDICE Data Experiments Unmixed abundance fractions of 19 panel pixels by FCLS n VD Shannon codingHuffman codingHamming coding2n VD totalOptimal p = Number of selected bands915141318 65 to 70 p 11 Variance0.440.630.60.540.730.78(65)0.78(32) Skewness0.270.84 0.820.850.81(70)0.92(36) Entropy0.830.870.850.840.880.77(68)1(24) p 12 Variance0.660.460.480.510.430.56(65)0.68(11) Skewness0.540.530.360.30.520.56(70)0.68(38) Entropy0.930.90.86 0.720.53(68)0.93(10) p 13 Variance000000(65)0(10) Skewness000000.05(70)0.23(34) Entropy0.680.690.670.690.670.01(68)0.83(12) p = Number of selected bands915141318 p 211 Variance0.850.87 0.89(65) Skewness0.840.950.960.95 0.89(70)0.99(36) Entropy1.20.880.87 0.880.92(68)1.2(9) p 221 Variance0.530.710.7 0.720.75(65) Skewness0.720.950.96 0.77(70)1(37) Entropy00.210.190.250.220.81(68)1(38) p 22 Variance0.750.86 0.850.810.78(65)0.86(14) Skewness0.870.740.750.80.70.79(70)0.87(9) Entropy0.640.60.620.610.60.77(68)0.78(67) p 23 Variance0.460.49 0.480.46(65)0.49(14) Skewness0.380.24 0.220.45(70) Entropy00.230.190.180.190.44(68) VDBDA

15. HYDICE Data Experiments ROC performance of 5 row panels using FCLS Panels in row 1Panels in row 2Panels in row 3 Panels in row 4 Panels in row 5 BDA VD 15 Y axis: Area under curve of ROC (P D versus P F ) X axis: Number of selected bands, p

16. 16 HYDICE Data Experiments Average ROC performance of 5 row panels Average performance of 5 row panels BDA range VD 2VD

17. 17 Some notes for HYDICE Data Experiments Classifying subpixels panels requires more bands than pure pixels. High order statistics BPC generally requires a smaller number of bands than 2nd order statistic BPC. The skewness seems to work the best for HYDICE data. To unmix panels, p=n VD =9 seems to be insufficient. But they achieve considerable performance within p=2n VD =18. It implies that the BDA provides a better way to predict cut-off band than VD.

18. 18 Hyperspectral Images Used for Experiments (2) Class map AVIRIS (Purdue) Data: 145x145 202 bands hyperspectral image. Image scene class1class2class3class4class5class6class7class8class9class10 class11class12class13class14class15class16 17 Classes maps Data samples are heavily-mixed Classifier: MLC Band De-correlation (BD) is applied after BP with σ= 0.1

19. 19 Purdue Data Experiments BDA results of Purdue Data signature m j n VD πjπj q j j n j (BDA) Shannon coding m 1 (class 1)29SID0.012836 m 2 (class 2)29SID0.043734 m 3 (class 3)29SID0.039234 m 4 (class 4)29SID0.014036 m 5 (class 5)29SID0.134132 m 6 (class 6)29SID0.031634 m 7 (class 7)29SID0.004237 m 8 (class 8)29SID0.010436 m 9 (class 9)29SID0.015436 m 10 (class 10)29SID0.054334 m 11 (class 11)29SID0.048034 m 12 (class 12)29SID0.043034 m 13 (class 13)29SID0.027735 m 14 (class 14)29SID0.229332 m 15 (class 15)29SID0.058034 m 16 (class 16)29SID0.210532 m 17 (BKG)29SID0.023935

20. 20 Purdue Data Experiment MLC classification results of 16 classes class1class2class3class4class5 class6class7class8class9class10 BDA VD Y axis: MLC classification rate in percent% X axis: Number of selected bands, p Classes 1 to 10

21. 21 Purdue Data Experiment Average performance of 16 classes MLC classification results class11class12class13class14class15 class16 VD 2VD BDA range Classes 11 to 16

22. 22 Some Notes for Purdue Data Experiments Second order statistic BPC generally perform better than High order statistic BPC due to - the land covers of this particular scene are large - the data samples are heavily mixed because of low spatial resolution and their contributions to statistics are mainly 2nd order statistics In most of classes using fewer dimensions for MLC can perform as well the using all bands. For instance, classes 7, 9, 13, and 16 do not require more bands to produce the best results. In most of classes using fewer dimensions for MLC can perform as well the using all bands. For instance, classes 7, 9, 13, and 16 do not require more bands to produce the best results. Only 5 classes, 2, 3, 4, 8, and 15 which required almost full dimensions to produce the best MLC results. Only 5 classes, 2, 3, 4, 8, and 15 which required almost full dimensions to produce the best MLC results. DBS provide some guidelines in selecting appropriate p for MLC to perform reasonably. DBS provide some guidelines in selecting appropriate p for MLC to perform reasonably.

23. 23 Summary of DBS The DBS is achieved by implementing the PBDP conjunction with BDA. The DBS is achieved by implementing the PBDP conjunction with BDA. DBS provides a guideline to decide how many bands is needed for each different signature. DBS provides a guideline to decide how many bands is needed for each different signature. The selection of BP criteria has huge influence on the unmixing/classification results. Different applications may requires different BP criteria to produce the best performance. The selection of BP criteria has huge influence on the unmixing/classification results. Different applications may requires different BP criteria to produce the best performance. VD is indeed a good estimate. VD is indeed a good estimate.

24. 24 Progressive Band Dimensionality Process (PBDP) provides a way to estimate p adaptively by increasing bands in a forward manner and decreasing bands in a backward manner. Progressive Band Dimensionality Process (PBDP) provides a way to estimate p adaptively by increasing bands in a forward manner and decreasing bands in a backward manner. Since various material substance signatures require different values of the p for data processing, the Band Dimensionality Allocation (BDA) is further developed to determine different numbers of spectral bands required by individual signatures. Since various material substance signatures require different values of the p for data processing, the Band Dimensionality Allocation (BDA) is further developed to determine different numbers of spectral bands required by individual signatures. Conclusions

25. 25 Thank You ! keng3@umbc.eduhttp://www.umbc.edu/rssipl/