Abstract
Many tasks in hyperspectral imaging, such as spectral unmixing and sub-pixel matching, require knowing how many substances or materials are present in the scene captured by a hyperspectral image. In this paper, we present an algorithm that estimates the number of materials in the scene using agglomerative clustering. The algorithm is based on the assumption that a valid clustering of the image has one cluster for each different material. After reducing the dimensionality of the hyperspectral image, the proposed method obtains an initial clustering using K-means. In this stage, cluster densities are estimated using Independent Component Analysis. Based on the K-means result, a model-based agglomerative clustering is performed, which provides a hierarchy of clusterings. Finally, a validation algorithm selects a clustering of the hierarchy; the number of clusters it contains is the estimated number of materials. Besides estimating the number of endmembers, the proposed method can approximately obtain the endmember (or spectrum) of each material by computing the centroid of its corresponding cluster. We have tested the proposed method using several hyperspectral images. The results show that the proposed method obtains approximately the number of materials that these images contain.
Highlights
Some tasks in hyperspectral imaging, such as classification and unmixing, require knowing how many pure substances or materials are present in a scene [1]
The information captured by a hyperspectral sensor with N cells and L spectral bands can be represented by an L × N matrix, X = [x1, . . . , xN], where each column of X is a pixel of the image
We present the results provided by the proposed method in the estimation of the number of endmembers of four hyperspectral images (Samson, Jasper Ridge, Urban, and Wasington DC)
Summary
Some tasks in hyperspectral imaging, such as classification and unmixing, require knowing how many pure substances or materials are present in a scene [1]. Some algorithms have been proposed to estimate the number of materials in a hyperspectral image [2,3,4,5,6,7,8]. Each material in a scene has a representative L-band spectrum, called endmember. Devising an algorithm to estimate the number of endmembers requires assuming a certain model for the generation of the hyperspectral image. The most commonly used model is the linear mixing model (LMM) [2] In this model, each pixel x is a random vector of the form. CK}, called abundances, are random variables that represent the fraction of each endmember in x; and the noise term, n, is a random vector that accounts for any model or measurement error. Under the LMM, a hyperspectral image matrix X can be written as
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