Keng-Hao Liu and Chein-I Chang Remote Sensing Signal and Image Processing Laboratory (RSSIPL)

1. Dynamic Band Selection For Hyperspectral Imagery 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 keng3@umbc.edu

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. • 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?

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

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. Progressive Band Dimensionality Process (PBDP) • 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. • 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)

6. Band Prioritization (BP) 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. Virtual Dimensionality (VD) • 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.

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 pj is the probability of the occurrence of the source alphabet aj Similarly, assumes mjis material substance signature to be analyzed, then the nj denotes the number of components (bands) required to represent mj. In other word, njis actually determined by how difficult the mjis discriminated in terms of spectral similarity. In conventional BS, it assumes nj=p for allsignatures. 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.

9. Band Dimensionality Allocation (BDA) for signatures BDA Procedures: • 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 qj larger than these self-information. • Define dimensionality allocation then assigned it to jth signature, mj. Determines the number of signatures to be used for data analysis Additional number required for mjto distinguish itself from other signatures.

10. Band Dimensionality Allocation (BDA) for signatures • Three techniques used to find BDA • Shannon coding • Huffman coding • Hamming coding • 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): • Data sample mean • Signature mean or any signature

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

12. Hyperspectral Images Used for Experiments (1) HYDICE Data: 64x64 169 bands hyperspectral image with spatial resolution is 20m. Classifier: FCLS Band De-correlation (BD) is applied after BP with σ= 0.1 Spectral of five panels Image scene p11, p12, p13 interferer p211, p22, p23 p221 grass p311, p312, p32, p33 p411, p412, p42, p43 tree p511, p52, p53 p521 road Ground truth (desired signatures) undesired signatures

13. HYDICE Data Experiments Shannon BDA results of HYDICE Data

14. HYDICE Data Experiments Unmixed abundance fractions of 19 panel pixels by FCLS VD BDA

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

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

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=nVD=9 seems to be insufficient. But they achieve considerable performance within p=2nVD=18. It implies that the BDA provides a better way to predict cut-off band than VD.

18. Hyperspectral Images Used for Experiments (2) AVIRIS (Purdue) Data: 145x145 202 bands hyperspectral image. Data samples are heavily-mixed Classifier: MLC Band De-correlation (BD) is applied after BP with σ= 0.1 Class map Image scene class1 class2 class3 class4 class5 class6 class7 class8 class9 class10 class11 class12 class13 class14 class15 class16 17 Classes maps

19. Purdue Data Experiments BDA results of Purdue Data

20. Purdue Data Experiment MLC classification results of 16 classes Y axis: MLC classification rate in percent% X axis: Number of selected bands, p BDA VD class1 class2 class3 class4 class5 class6 class7 class8 class9 class10 Classes 1 to 10

21. Purdue Data Experiment MLC classification results class11 class12 class13 class14 class15 Classes 11 to 16 BDA range 2VD class16 VD Average performance of 16 classes

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. • 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.

23. Summary of DBS • 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. • 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.

24. Conclusions • 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.

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