New Divide and Conquer Method on Endmember Extraction Techniques

In hyperspectral imagery, endmember extraction (EE) is a main stage in hyperspectral unmixing process where its role lies in extracting distinct spectral signature, endmembers, from hyperspectral image which is considered as the main input for unsupervised hyperspectral unmixing to generate the abundance fractions for every pixel in hyperspectral data. EE process has some difficulties. There are less distinct endmembers than its mixed background; also, there are endmembers that have rare occurrences in data that are considered as difficulties in EE process. In this paper, we propose a new technique that uses divide and conquer method for EE process to find out these difficult (rare or less distinct) endmembers. divide and conquer method is used to divide hyperspectral data scene to multiple divisions and take each division as a standalone scene to enable endmember extraction algorithms (EEAs) to extract difficult endmembers easily and finally conquer all extracted endmembers from all divisions. We implemented this method on real dataset using three EEAs: ATGP, VCA, and SGA and recorded the results that outperform the results from usual endmember extraction techniques methods in all used algorithms. Keywords—Endmember extraction algorithm (EEA); endmember extraction (EE); automatic target generation process (ATGP); hyperspectral imagery; simplex growing algorithm (SGA); hyperspectral unmixing; vertex component analysis (VCA); divide and conquer method INTRODUCTION I. Endmember extraction is considered to be an important and crucial step in hyperspectral data exploitation. A pixel in hyperspectral data may be either a pure pixel or mixed pixel. A pure pixel represents an endmember (EM) that exists in the scene. A mixed pixel contains multiple contributions from a group of different endmembers that exists in the scene. Therefore, endmember is considered as a pure signature for a class [1]. Generally, an endmember is not a pixel; it is a spectral signature which is specified completely by the spectrum of a single material substance. Several endmember extraction methods have been developed to extract pure pixels from hyperspectral data. Here we use three different algorithms for extracting endmembers from hyperspectral data. The first one is Automatic Target Generation Process (ATGP) that finds its targets by using a sequence of orthogonal subspaces with the maximal orthogonal projections [2], [5], [7], [8] where ATGP considered the unsupervised version of Orthogonal Subspace Projection (OSP) algorithm. The second used algorithm is the Simplex Growing Algorithm (SGA) [3], [8] which finds its endmembers by growing a simplex, vertex by vertex, until it reaches the required endmembers represented by vertices of simplex. The last used algorithm is the Vertex Component Analysis (VCA) [4], [8], it is an OP-based EEA that is characterized by computational complexity reduction by replacing simple volume calculation with OP and growing nonnegative convex hulls, vertex by vertex, until it builds a pvertex convex hull (p denotes the endmembers required to be extracted). Authors in [6], demonstrate some EEAs as ATGP, VCA, and SGA and demonstrate their efficiency by using different criteria as sequential or parallel implementation, dimensionality reduction, etc. ATGP, VCA, SGA are most widely used in EE [8]. They are similar in their design but different in preprocessing steps. Some researches work in spatial and spectral information of hyperspectral data to enhance EEAs. Over segmentation based method introduced in [9], exploit spatial and spectral information to enhance computational performance for EEA. A new enhancement for EEAs is suggested in [10] that gives guidance to EE process for spatially homogenous regions and consequently to enhance performance of unmixing process. This paper contributed to enabling EEAs to find difficult endmembers where EEAs alone couldn’t find them without using this proposed method. This paper is organized as follows. Section 2 introduces Linear Mixture Model. Section 3 describes the proposed method. Dataset used is introduced in Section 4. Results and discussions are provided in Section 5. The conclusion is given in Section 6. LINEAR MIXTURE MODEL II. Linear mixture model is a well-known approach used for determination and quantification of materials in hyperspectral images. Hyperspectral image consists of pixels where every pixel is represented by a vector of values for each spectral band which, in its turn, is the reflectance of the material in a specific wavelength. Let r be an L × 1 column vector in a hyperspectral image where L refers to the number of bands. Suppose that there are (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 8, No. 7, 2017 95 | P a g e www.ijacsa.thesai.org p materials in the hyperspectral image and M = [m1 m2 ... mp] is an L × p matrix of material signature, where mj is an L × 1 column vector of the j th material signature in the hyperspectral image. Assume that a is a p × 1 abundance column vector denoted as (a1, a2, ..., ap) T which associated with r (ak represents the abundance fraction of the k th signature exist in the pixel vector r). Linear unmixing can solve this mixed pixel problem. It assumes that spectral signature r can be represented by a linear regression model as in (1) where r is linearly mixed by p material signatures.