2015 , Vol. 17 >Issue 1: 86 - 90

• 徐君 , 1, * ,
• 徐富红 2 ,
• 蔡体健 1 ,
• 王彩玲 3 ,
• 黄德昌 1 ,
• 李伟平 1

• 1. 华东交通大学信息工程学院，南昌 330013
• 2. 华东交通大学计划财务处，南昌 330013
• 3. 西安石油大学计算机学院，西安 710065

要求修回日期: 2014-03-05

网络出版日期: 2015-01-05

A Novel Pure Pixel Index Endmember Extraction Algorithm Based on the Maximum Distance

• XU Jun , 1, * ,
• XU Fuhong 2 ,
• CAI Tijian 1 ,
• WANG Cailing 3 ,
• HUANG Dechang 1 ,
• LI Weiping 1
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• 1. School of Information Engineering, East China Jiaotong University, Nanchang 330013, China
• 2. Division of Planning and Finance, East China Jiaotong University, Nanchang 330013, China
• 3. College of Computer, Xi'an Shiyou University, Xi'an 710065, China
*Corresponding author: XU Jun, E-mail:

Request revised date: 2014-03-05

Online published: 2015-01-05

《地球信息科学学报》编辑部 所有

### Abstract

In hyperspectral unmixing, PPI algorithm is a relatively mature algorithm, but each projection vector in PPI algorithm is generated randomly, and the endmembers extracted by PPI algorithm are not stable. That is, different endmembers can be obtained from the same image by repeatedly running PPI algorithm. This paper, based on the convex geometry description of linear spectral mixing model, utilized the feature that the endmembers are the endpoints of the single convex body enclosed in the hyperspectral image feature space, and proposed a novel pure pixel index algorithm for endmember extraction based on the maximum distance. The average of the spectral vectors of all the sample points is calculated and used as the center of a hypersphere. Next, we calculate the Euclidean distances of all the sample points to the center of the hypersphere, and design a radius of equal to or greater than the maximum distance for the hypersphere in the feature space to include all of the sample points. We evenly select the reference points on the surface of the hypersphere. The farthest sample point with respect to each reference point can be found by calculating the Euclidean distance. Subsequently, every sample point’s frequency of being the most distant to the reference points is recorded as an index to evaluate whether the sample point is an endmember or not. Finally, we use the AVIRIS data of Nevada Cuprite to testify this algorithm. The experimental results illustrate that the precision of the endmember extraction using the algorithm proposed in this paper is better than N-FINDR algorithm and VCA algorithm in general. Moreover, it has a good robustness and could overcome the instability of PPI algorithm caused by random projection.

### 2 最大距离纯像元指数

##### Fig. 1 The schematic diagram of endmember extraction algorithm based on maximum distance pure pixel index

（1）选取特征空间中所有样本点的光谱均值作为超球的球心： $O = X ̅ = 1 n ∑ i = 1 n X i$ i=1,2,…,n, n为特征空间中样本点的个数）,O表示超球的球心, $X i$ 表示特征空间中的样本点的光谱矢量;
（2）计算所有样本点到球心的欧氏距离 $distance ( X i ) = X i - O 2$ ;
（3）根据文献[12],与球心距离最大的样本点必是单形体的顶点之一,以等于或大于这个最大距离作为半径,将所有样本点包含在超球内部, $R ≥ max [ dis tan ce E j - O 2 ]$ ( j=1,2,…,m, m为端元个数, $E j$ 为端元);
（4）在超球面上均匀选择参考点,计算样本点与这些参考点之间的距离,记录每个样本点成为最大距离点的次数作为纯像元指数。
（5）针对上述的纯像元指数做出像元纯净图像,选择合适的阈值,提取其中的端元光谱。

### 3 超球面上均匀选择参考点

PPI算法中,由于投影向量的选取具有随机性,因此造成每次端元提取的结果不稳定。基于上述的最大距离纯像元指数,如果能在包围所有样本的超球面上均匀地选择参考点,就可避免随机无序选择参考点而给端元提取带来的不确定性。

### 5 结论

PPI算法中由于投影向量的选择是随机的,故算法的鲁棒性不高,每次端元提取的结果并不稳定。本文提出了一种最大距离纯像元指数的概念,首先在特征空间中设计一个超球面包围所有样本点,在超球面上均匀地选择参考点,计算参考点与样本点的距离并记录最大者,统计每个样本点成为最大距离点的次数作为纯像元指数来提取端元。相比于传统的PPI算法随机生成投影向量,新的纯像元指数法选取参考点是均匀的、有规律的,因而算法的鲁棒性高,端元提取的结果也更直观和稳定。但由于本文算法需要在超球面上均匀选择参考点,跟PPI算法相比计算的复杂度和耗时有所增大。因此,如何定量地比较本文算法和PPI算法的计算复杂度和运行效率,在保证运算精度的前提下对本文算法进行优化以减少运算量,是今后需深入研究的课题。

The authors have declared that no competing interests exist.

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