Estimation of the Number of Endmembers in Hyperspectral Images Using Agglomerative Clustering

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.

DLR HySU - A Benchmark Dataset for Spectral Unmixing

“…1 show that HySime clearly overestimates the real dimensionality of the three smaller subsets, with an increasing error as the dataset gets smaller. This is in line with previous experiments finding HySime to strongly overestimate the number of endmembers when applied to small datasets, such as the Samson dataset [25]: the window in which the algorithm is estimating the noise must be large enough [26], otherwise the analysis can be driven by noise rather than signal [27]. As the size of the image increases, HySime results stabilize and provide a meaningful result for the case of the full subset.…”

“…As the size of the image increases, HySime results stabilize and provide a meaningful result for the case of the full subset. We report HFC performance when setting the false alarm rate t to 10 −3 , 10 −4 , and 10 −5 , because these values are commonly used in the literature [20,25,28] [26,29]. On the other hand, HFC is likely overestimating K on the full dataset.…”

Hyperspectral Image Super-Resolution Based on Spatial Correlation-Regularized Unmixing Convolutional Neural Network

“…However, we have not developed adaptive rules to automatically determine these two parameters. Therefore, our following work will focus on the automatic determination of η and D-for example, using the automatic estimation approaches of endmember numbers in [48][49][50]. Aside from the above analysis of parameters, we also present a brief discussion of the ablation experiments to analyze the mechanism of our proposed approach.…”

“…where E Y ∈ R Λ×D and A Y ∈ R D×N are the spectral endmember matrix and abundance matrix, respectively. D is the number of endmembers, which can be determined by either empirical criteria [6,7] or endmember estimation methods, e.g., thresholding ridge ratio criterion [48], agglomerative clustering [49], saliency-based autonomous endmember detection [50], etc. N Y ∈ R Λ×N is the residual.…”

Editorial for the Special Issue “New Advances on Sub-Pixel Processing: Unmixing and Mapping Methods”

“…In this Special Issue, several stages of sub-pixel image processing are approached incorporating advanced techniques such as neural networks, deep learning, and probabilistic non-Gaussian mixture models. This Special Issue consists of nine research papers [1][2][3][4][5][6][7][8][9]. All the methods proposed in the papers were validated using real hyperspectral data and benchmarked with state-of-the-art methods, thus comprehensively demonstrating the theoretical and practical contributions of the papers.…”