Comparison of Vertex Componet Analysis (VCA) and Genetic Algorithm Endmember Extraction (GAEE) algorithms for Endmember Extraction
Endmember Extraction is a critical step in hyperspectral image analysis and classification. It is an useful method to decompose a mixed spectrum into a collection of spectra and their corresponding proportions. In this paper, we solve a linear endmember extraction problem as an evolutionary optimization task, maximizing the Simplex Volume in the endmember space. We propose a standard genetic algorithm and a variation with In Vitro Fertilization module (IVFm) to find the best solutions and compare the results with the state-of-art Vertex Component Analysis (VCA) method and the traditional algorithms Pixel Purity Index (PPI) and N-FINDR. The experimental results on real and synthetic hyperspectral data confirms the overcome in performance and accuracy of the proposed approaches over the mentioned algorithms.
Paper Online in https://arxiv.org/abs/1805.10644
@ARTICLE{2018arXiv180510644D,
author = {{Douglas Winston.~R.}, S. and {Laureano}, G.~T. and {Camilo}, Jr, C.~G.
},
title = "{Comparison of VCA and GAEE algorithms for Endmember Extraction}",
journal = {ArXiv e-prints},
archivePrefix = "arXiv",
eprint = {1805.10644},
keywords = {Computer Science - Neural and Evolutionary Computing, Electrical Engineering and Systems Science - Image and Video Processing, 68T20, 68U10},
year = 2018,
month = may,
adsurl = {http://adsabs.harvard.edu/abs/2018arXiv180510644D},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
Envirionment Setup:
Monte Carlo runs: 50
Number of endmembers to estimate: 12
Number of skewers (PPI): 1000
Maximum number of iterations (N-FINDR): 36
Parameters | GAEE | GAEE-IVFm | GAEE-VCA | GAEE-IVFm-VCA |
---|---|---|---|---|
Population Size | 100 | 100 | 100 | 100 |
Number of Generations | 1000 | 1000 | 1000 | 1000 |
Crossover Probability | 1 | 0.7 | 0.5 | 1 |
Mutation Probability | 0.1 | 0.3 | 0.05 | 0.1 |
Comparison between the ground-truth Laboratory Reflectances and extracted endmembers using PPI, N-FINDR, VCA, GAEE, GAEE-IVFm using SAM for the Cuprite Dataset.
Endmembers | PPI | NFINDR | VCA | GAEE | GAEE-IVFm | GAEE-VCA | GAEE-IVFm-VCA |
---|---|---|---|---|---|---|---|
Alunite | 0.3744 | 0.1122 | 0.0939 | 0.1122 | 0.1034 | 0.1043 | 0.1043 |
Andradite | 0.0758 | 0.2068 | 0.1034 | 0.0693 | 0.0760 | 0.1694 | 0.1694 |
Buddingtonite | 0.2081 | 0.1205 | 0.0786 | 0.0798 | 0.0762 | 0.0762 | 0.0762 |
Dumortierite | 0.1907 | 0.0706 | 0.0702 | 0.0735 | 0.0719 | 0.0755 | 0.0755 |
Kaolinite_1 | 0.0795 | 0.0870 | 0.0862 | 0.0952 | 0.0935 | 0.0870 | 0.0870 |
Kaolinite_2 | 0.0820 | 0.0992 | 0.0741 | 0.0649 | 0.0723 | 0.0744 | 0.0782 |
Muscovite | 0.2506 | 0.0961 | 0.1805 | 0.0861 | 0.1091 | 0.0965 | 0.0961 |
Montmonrillonite | 0.1338 | 0.0646 | 0.0651 | 0.0671 | 0.0677 | 0.0688 | 0.0650 |
Nontronite | 0.1033 | 0.0780 | 0.0801 | 0.0711 | 0.0791 | 0.1150 | 0.1150 |
Pyrope | 0.0579 | 0.0865 | 0.0818 | 0.0563 | 0.0623 | 0.0793 | 0.0686 |
Sphene | 0.0673 | 0.0542 | 0.0530 | 0.1121 | 0.0946 | 0.0795 | 0.0901 |
Chalcedony | 0.0871 | 0.0731 | 0.0773 | 0.0738 | 0.0756 | 0.0765 | 0.0861 |
Statistics | PPI | NFINDR | VCA | GAEE | GAEE-IVFm | GAEE-VCA | GAEE-IVFm-VCA |
---|---|---|---|---|---|---|---|
Mean | 0.1425 | 0.1033 | 0.1024 | 0.1016 | 0.0989 | 0.1109 | 0.1090 |
Std | 0.0000 | 0.0225 | 0.0252 | 0.0248 | 0.0255 | 0.0117 | 0.0157 |
p-value | -34.8557 | -0.6562 | 0.0000 | 0.5032 | 2.3017 | -6.4153 | -4.8551 |
Gain | 30.6303 | 4.2790 | 3.3962 | 2.6854 | 0.0000 | 10.8064 | 9.2929 |
Time | 2.1929 | 7.8318 | 0.5106 | 8.9232 | 22.3329 | 8.7494 | 22.1761 |
Comparison between the ground-truth Laboratory Reflectances and extracted endmembers using PPI, N-FINDR, VCA, GAEE, GAEE-IVFm using SID for the Cuprite Dataset.
Endmembers | PPI | NFINDR | VCA | GAEE | GAEE-IVFm | GAEE-VCA | GAEE-IVFm-VCA |
---|---|---|---|---|---|---|---|
Alunite | 0.0000 | 0.0000 | 0.0105 | 0.0170 | 0.0000 | 0.0000 | 0.0145 |
Andradite | 0.0000 | 0.0117 | 0.0052 | 0.0055 | 0.0092 | 0.0077 | 0.0056 |
Buddingtonite | 0.0477 | 0.0196 | 0.0077 | 0.0076 | 0.0108 | 0.0072 | 0.0072 |
Dumortierite | 0.0562 | 0.0071 | 0.0298 | 0.0072 | 0.0181 | 0.0077 | 0.0077 |
Kaolinite_1 | 0.0114 | 0.0104 | 0.0139 | 0.0139 | 0.0128 | 0.0131 | 0.0131 |
Kaolinite_2 | 0.0114 | 0.0058 | 0.0042 | 0.0049 | 0.0029 | 0.0111 | 0.0086 |
Muscovite | 0.0969 | 0.0317 | 0.0148 | 0.0086 | 0.0286 | 0.0285 | 0.0171 |
Montmonrillonite | 0.0230 | 0.0053 | 0.0047 | 0.0052 | 0.0048 | 0.0057 | 0.0060 |
Nontronite | 0.0126 | 0.0083 | 0.0093 | 0.0065 | 0.0082 | 0.0155 | 0.0155 |
Pyrope | 0.0071 | 0.0438 | 0.0229 | 0.0057 | 0.0279 | 0.0593 | 0.0593 |
Sphene | 0.0076 | 0.0912 | 0.0096 | 0.0165 | 0.0086 | 0.0099 | 0.0067 |
Chalcedony | 0.0088 | 0.0093 | 0.0069 | 0.0069 | 0.0096 | 0.0070 | 0.0070 |
Statistics | PPI | NFINDR | VCA | GAEE | GAEE-IVFm | GAEE-VCA | GAEE-IVFm-VCA |
---|---|---|---|---|---|---|---|
Mean | 0.0236 | 0.0257 | 0.0197 | 0.0163 | 0.0194 | 0.0265 | 0.0268 |
Std | 0.0000 | 0.0064 | 0.0107 | 0.0099 | 0.0097 | 0.0065 | 0.0059 |
p-value | -5.2271 | -7.2962 | 0.0000 | 3.8716 | 0.3603 | -7.4272 | -8.2866 |
Gain | 28.7161 | 1.6376 | 0.7304 | 0.0000 | -2.7595 | 8.3452 | 6.7899 |
Time | 2.1929 | 7.8318 | 0.5106 | 8.9232 | 22.3329 | 8.7494 | 22.1761 |