采用PPI算法改进的一种数学形态学端元提取方法

doi:10.11947/j.AGCS.2019.20180475

摘要/Abstract

摘要： 自动形态学端元提取（automated morphological endmember extraction，AMEE）算法将结构元素内最纯像元与混合度最大的像元之间的光谱角距离定义为形态学离心率指数（morphological eccentricity index，MEI）来定量化地表示像元的纯净度。然而作为参考标准的混合度最大的像元在不同的结构元素内也是不同的，尤其是当结构元素内的纯净像元占大多数时，像元的均值光谱将更接近纯像元，此时像元的MEI越高，纯度反而越低。针对这一问题，本文提出一种像元纯度指数（pure pixel index，PPI）算法与AMEE算法相结合的端元提取算法PPI-AMEE。在结构元素内，利用PPI指数代替AMEE算法中的MEI指数来寻找最纯像元。变换结构元素时，只有最纯净的像元始终能够投影到随机生成的直线的两端，其PPI值会不断累计增大，而其他像元的PPI值则无法持续增大。累计记录每个像元的PPI值，直至满足迭代终止条件，最终形成一幅PPI图像，端元将在PPI值较大的像元中选取。PPI-AMEE算法只在相对较小的结构元素内运行PPI算法，然后再结合数学形态学中的膨胀操作对整幅图像进行处理，其同时兼顾了图像的光谱信息和空间信息。最后，采用模拟数据及美国内华达州Cuprite地区的机载可见光/红外成像光谱仪（airborne visible infrared imaging spectrometer，AVIRIS）高光谱数据对提出的PPI-AMEE算法进行试验验证。试验结果表明，PPI-AMEE算法的端元提取精度总体上优于AMEE算法和PPI算法。

关键词: 高光谱图像, 端元提取, 纯像元指数, 数学形态学

Abstract: Automated morphological endmember extraction(AMEE) algorithm defines the spectral angular distance between the purest pixel and the most mixed pixel in the structural element as the morphological eccentricity index(MEI) to quantitatively denote the purity of the pixel. However, the most mixed pixels as the reference standard are not the same in different structural elements, especially when the pure pixels account for the majority of the structural elements, the mean spectrum of all the pixels will be closer to the pure pixels. At this time, the higher the MEI, the lower the purity of the pixel. To solve this problem, a novel endmember extraction algorithm is proposed in this paper which combines the pixel purity index (PPI) algorithm with AMEE algorithm and is named PPI-AMEE. In the structural element, the PPI is used to replace the MEI index in the AMEE algorithm to find the purest pixel. When the structural element is transformed, only the purest pixel can always be projected to the two ends of the randomly generated line, therefore the PPI value of the purest pixel will increase continuously, while the PPI value of the other pixels will not increase continuously. The PPI value of each pixel is accumulated and recorded until the iterative termination condition is satisfied, and a PPI image is finally obtained. The endmembers are selected from the pixels with higher PPI value. The PPI-AMEE algorithm runs the PPI algorithm in relatively small structural elements, and then processes the whole image with the expansion operation of mathematical morphology, which takes into account both the spectral and spatial information of the image. In the experiment, AVIRIS hyperspectral data from Cuprite area, Nevada, USA are used to validate the proposed PPI-AMEE algorithm. The experimental results show that the endmember extraction accuracy of PPI-AMEE algorithm is better than that of AMEE algorithm and PPI algorithm on the whole.

Key words: hyperspectral image, endmember extraction, pure pixel index, mathematical morphology

中图分类号:

TP391
P237

徐君, 王彩玲, 王丽. 采用PPI算法改进的一种数学形态学端元提取方法[J]. 测绘学报, 2019, 48(8): 996-1003.

XU Jun, WANG Cailing, WANG Li. An improved endmember extraction method of mathematical morphology based on PPI algorithm[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(8): 996-1003.

参考文献

[1] 蓝金辉, 邹金霖, 郝彦爽, 等. 高光谱遥感影像混合像元分解研究进展[J]. 遥感学报, 2018, 22(1):13-27. LAN Jinhui, ZOU Jinlin, HAO Yanshuang, et al. Research progress on unmixing of hyperspectral remote sensing imagery[J]. Journal of Remote Sensing, 2018, 22(1):13-27.
[2] 张春森, 郑艺惟, 黄小兵, 等. 高光谱影像光谱-空间多特征加权概率融合分类[J]. 测绘学报, 2015, 44(8):909-918. DOI:10.11947/j.AGCS.2015.20140544. ZHANG Chunsen, ZHENG Yiwei, HUANG Xiaobing, et al. Hyperspectral image classification based on the weighted probabilistic fusion of multiple spectral-spatial features[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(8):909-918. DOI:10.11947/j.AGCS.2015.20140544.
[3] 王俊淑, 江南, 张国明, 等. 融合光谱-空间信息的高光谱遥感影像增量分类算法[J]. 测绘学报, 2015, 44(9):1003-1013. DOI:10.11947/j.AGCS.2015.20140388. WANG Junshu, JIANG Nan, ZHANG Guoming, et al. Incremental classification algorithm of hyperspectral remote sensing images based on spectral-spatial information[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(9):1003-1013. DOI:10.11947/j.AGCS.2015.20140388.
[4] DELGADO J, MARTÍN G, PLAZA J, et al. Fast spatial preprocessing for spectral unmixing of hyperspectral data on graphics processing units[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2016, 9(2):952-961.
[5] PLAZA A, MARTÍNZE P, PÉREZ R, et al. Spatial/spectral endmember extraction by multidimensional morphological operations[J]. IEEE Transactions on Geoscience and Remote Sensing, 2002, 40(9):2025-2041.
[6] JIMÉNEZ L I, PLAZA J, PLAZA A. Efficient implementation of morphological index for building/shadow extraction from remotely sensed images[J]. Journal of Supercomputing, 2017, 73(1):482-494.
[7] 方俊龙. 高光谱像元解混技术研究[D]. 杭州:杭州电子科技大学, 2016. FANG Junlong. Research on hyperspectral unmixing techniques[D]. Hangzhou:Hangzhou Dianzi University, 2016.
[8] CHANG C I, PLAZA A. A fast iterative algorithm for implementation of pixel purity index[J]. IEEE Geoscience and Remote Sensing Letters, 2006, 3(1):63-67.
[9] LU Xiaoqiang, WU Hao, YUAN Yuan, et al. Manifold regularized sparse NMF for hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2013, 51(5):2815-2826.
[10] HEYLEN R, PARENTE M, GADER P. A review of nonlinear hyperspectral unmixing methods[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2014, 7(6):1844-1868.
[11] CHANG C I, WU Chaocheng. Design and development of iterative pixel purity index[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2015, 8(6):2676-2695.
[12] ZARE A, GADER P, CASELLA G. Sampling piecewise convex unmixing and endmember extraction[J]. IEEE Transactions on Geoscience and Remote Sensing, 2013, 51(3):1655-1665.
[13] LI H C, CHANG C I. Recursive orthogonal projection-based simplex growing algorithm[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(7):3780-3793.
[14] ZHANG Shaoquan, AGATHOS A, LI Jun. Robust minimum volume simplex analysis for hyperspectral unmixing[J]. IEEE Transactions on Geoscience and Remote Sensing, 2017, 55(11):6431-6439.
[15] LI H C, CHANG C I. Geometric simplex growing algorithm for finding endmembers in hyperspectral imagery[C]//Proceedings of 2016 IEEE International Geoscience and Remote Sensing Symposium. Beijing:IEEE, 2016.
[16] 李琳, 孟令博, 孙康, 等. 基于代数余子式的N-FINDR快速端元提取算法[J]. 电子与信息学报, 2015, 37(5):1128-1134. LI Ling, MENG Lingbo, SUN Kang, et al. A fast N-FINDR algorithm based on cofactor of a determinant[J]. Journal of Electronics and Information Technology, 2015, 37(5):1128-1134.
[17] GENG Xiurui, SUN Kang, JI Luyan, et al. Optimizing the endmembers using volume invariant constrained model[J]. IEEE Transactions on Image Processing, 2015, 24(11):3441-3449.
[18] 徐君, 徐富红, 蔡体健, 等. 一种基于最大距离的纯像元指数端元提取算法[J]. 地球信息科学学报, 2015, 17(1):86-90. XU Jun, XU Fuhong, CAI Tijian, et al. A novel pure pixel index endmember extraction algorithm based on the maximum distance[J]. Journal of Geo-Information Science, 2015, 17(1):86-90.
[19] CHANG C I, WU C C, LIU W, et al. A new growing method for simplex-based endmember extraction algorithm[J]. IEEE Transactions on Geoscience and Remote Sensing, 2006, 44(10):2804-2819.
[20] CHANG C I, WU Chaocheng, LO C S, et al. Real-time simplex growing algorithms for hyperspectral endmember extraction[J]. IEEE Transactions on Geoscience and Remote Sensing, 2010, 48(4):1834-1850.
[21] CHAN T H, CHI C Y, HUANG Y M, et al. A convex analysis-based minimum-volume enclosing simplex algorithm for hyperspectral unmixing[J]. IEEE Transactions on Signal Processing, 2009,57(11):4418-4432.
[22] LIU Junmin, ZHANG Jiangshe. A new maximum simplex volume method based on householder transformation for endmember extraction[J]. IEEE Transactions on Geoscience and Remote Sensing, 2012, 50(1):104-118.
[23] 王瀛, 梁楠, 郭雷. 一种基于修正扩展形态学算子的高光谱遥感图像端元提取算法[J]. 光子学报, 2012, 41(6):672-677. WANG Ying, LIANG Nan, GUO Lei. A hyperspectral remote sensing image endmember extraction algorithm based on modified extended-morphological operator[J]. Acta Photonica Sinica, 2012, 41(6):672-677.
[24] SWAYZE G A. The hydrothermal and structural history of the cuprite mining district, southwestern Nevada:An integrated geological and geophysical approach[D]. Boulder:University of Colorado, 1997:399.
[25] CLARK R N, SWAYZE G A. Automated spectral analysis:Mapping minerals, amorphous materials, environmental materials, vegetation, water, ice and snow, and other materials:The USGS tricorder algorithm[C]//Proceedings of the 5th Annual JPL Airborne Earth Science Workshop. Pasadena:JPL Publication, 1995.
[26] BIOUCAS-DIAS J M, NASCIMENTO J M P. Hyperspectral Subspace Identification[J]. IEEE Transactions on Geoscience and Remote Sensing, 2008, 46(8):2435-2445.