一种基于最大距离的纯像元指数端元提取算法

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

在高光谱混合像元分解中,PPI算法是一种比较成熟的算法,但PPI算法中每次投影向量的生成都是随机的,多次执行PPI算法后端元提取的结果并不稳定。本文以线性光谱混合模型的凸面几何学描述为基础,利用端元在高光谱图像特征空间中所形成的凸面单形体端点的特点,提出了一种区别于PPI算法的最大距离纯像元指数方法。选取特征空间中所有样本点的光谱均值作为超球的球心,计算所有样本点到球心的欧氏距离,以等于或大于这个最大距离的长度作为半径,在特征空间中设计一个包围所有样本点的超球面,并在超球面上均匀地选取参考点,针对每一个参考点,在样本点中找出与它距离最远的一个,记录每个样本点成为距离最大点的次数,将其作为评价该像元是否为端元的纯像元指数,从而使得每次端元提取的精度得到保证。最后,利用美国内华达州Cuprite获取的AVIRIS数据对算法进行了验证。实验结果表明,采用本文算法提取的端元精度优于N-FINDR算法和VCA算法,而且鲁棒性较好,克服了PPI算法由于随机生成投影向量所带来的端元提取不稳定性。

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 endmem-bers 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 calcu-late 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 re-spect 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 algo-rithm. The experimental results illustrate that the precision of the endmember extraction using the algorithm pro-posed in this paper is better than N-FINDR algorithm and VCA algorithm in general. Moreover, it has a good ro-bustness and could overcome the instability of PPI algorithm caused by random projection.