Vertex Component Analysis: A~Fast Algorithm to Extract Endmembers Spectra from Hyperspectral Data

Abstract

Abstract. Linear spectral mixture analysis, or linear unmixing, has proven to be a useful tool in hyperspectral remote sensing applications. It aims at estimating the number of reference substances, also called endmembers, their spectral signature and abundance fractions, using only the observed data (mixed pixels). This paper presents new method that performs unsupervised endmember extraction from hyperspectral data. The algorithm exploits a simple geometric fact: endmembers are vertices of a simplex. The algorithm complexity, measured in floating points operations, is O(n), where n is the sample size. The effectiveness of the proposed scheme is illustrated using simulated data.

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

“…where (26) is obtained by using (22) to turn (25) to (23) (with a proper index reordering), and then applying (24). We call the resulting algorithm successive N-FINDR (SC-N-FINDR) since it is very similar to the SC-N-FINDR proposed in [38].…”

Visualization and characterisation of defined hair follicle compartments by Fourier transform infrared (FTIR) imaging without labelling

“…2) where perturbation due to liquid nitrogen refill was evident. N-FINDR, a spectral unmixing method similar to vertex component analysis (VCA) [23] and iterated constrained endmembers (ICE) algorithm [24], was applied to the pre-processed data to extract five endmembers [10]. The algorithm assumes that ''pure'' spectra are present in the dataset and that they span the largest volume in the n-dimensional volume spanned by the spectral points of all the spectra present in the data set.…”

Hyperspectral Endmember Extraction Techniques

“…The OP based EE approaches, makes the orthogonal projection of all data samples onto a set of selected vectors and considers the data samples producing extreme (either minimal or maximal) projections with these selected vectors as a final set of endmembers. The popular OP based EE algorithms are Pixel Purity Index (PPI) [7], VCA [8] and Sequential Maximum Angle Convex Cone (SMACC) [9]. The SV based EE approaches, assumes that the simplex formed by a set of pure signatures as vertices should produce the maximum volume among all simplexes formed by the same number of signatures as vertices.…”

“…The vertex component analysis (VCA) algorithm [8,22,23] is an unsupervised endmember extraction algorithm and works with the assumption that, in linear spectral mixing, every pixel signature is composed with the linear combinations of endmember spectra available within the scene. The VCA algorithm explores two facts: One, the endmembers are found to be the vertices of the simplexes and two, the affine transformation of every simplex is too simplex.…”