Fast implementation of N-FINDR algorithm for endmember determination in hyperspectral imagery

Abstract

Analysis of hyperspectral imagery requires the extraction of certain basis spectra called endmembers, which are assumed to be the pure signatures in the image data. N-FINDR algorithm developed by Winter [1] is one of the most widely used technique for endmember extraction. This algorithm is based on the fact that in L spectral dimensions, the L-dimensional volume contained by a simplex formed from the purest pixels is larger than any other volume formed from other combination of pixels. Recently proposed algorithm based on virtual dimensionality (VD) determines the number of endmembers present in the dataset, where an endmember initialization algorithm (EIA) is used to select an appropriate set of pixels for initializing the N-FINDR process. In this paper, we proposed a fast algorithm to implement the N-FINDR technique which has much better computational efficiency than the existing techniques. In the proposed technique, we used the VD to find the number of endmembers N. Then we reduced the dimensionality of the hyperspectral dataset to N−1 by using the principal component transformation (PCT) and divided all the pixels into N number of classes by using the spectral angle map (SAM). We extracted N number of the most pure pixels from each group by using the classical N-FINDR algorithm but with exhaustive search. Thus we get N 2 pixels that are most likely to be the actual endmembers. The classical N-FINDR algorithm is then again applied on these selected pixels to find the final N endmember. Grouping the pixels into several classes makes the computation very fast. Since we extracted N number of pixels from each group by exhaustive search, there is no possibility of loosing any endmember due to classification.

Modified N-FINDR endmember extraction algorithm for remote-sensing imagery

“…An additional approach to lower the complexity of MN-FINDR is to reduce the spatial redundancy of the data by removing pixels unlikely to be endmembers in advance or during the interactions. This can be accomplished by applying EIAs (Plaza and Chang 2005;Chowdhury and Alam 2007) to search a feasible region containing all candidate endmembers in advance. Nevertheless, N-FINDR series algorithms can achieve this aim without extra cost due to the fact that choosing pixel replacement is also a method to determine whether a pixel is in the volume-increasing region (Dowler, Takashima, and Andrews 2013).…”

“…The first is to narrow the search region from the entire region to a feasible region, which presumes to include all potential endmembers, using an endmember initialization algorithm (EIA) (Plaza and Chang 2005;Chowdhury and Alam 2007;Wei et al 2011;Dowler, Takashima, and Andrews 2013). The second is to simplify the computation of the matrix determinant in volume calculation (Xiong et al 2011;Dowler, Takashima, and Andrews 2013).…”

Abundance guided endmember selection: An algorithm for unmixing hyperspectral data

“…One of the most popular algorithms of this class, both widely used in performance evaluations [7][8][9] and as a basis for modifications [10][11][12], is N-FINDR [13,14]. This algorithm exploits the structure of the data by expanding a simplex within the data points.…”

Fast implementation of linear and nonlinear simplex growing algorithm for hyperspectral endmember extraction

“…To reduce computational complexity, different modified N-FINDR approaches are developed [15][16][17][18]. As for SGA, different fast volume calculation approaches are also proposed [19][20][21].…”