PARALLEL IMPLEMENTATION OF THE N-FINDR ENDMEMBER EXTRACTION ALGORITHM ON COMMODITY GRAPHICS PROCESSING UNITS Sergio S´ anchez, Gabriel Mart´ ın, and Antonio Plaza Department of Technology of Computers and Communications University of Extremadura, Avda. de la Universidad s/n, E-10071 Caceres, Spain Phone: +34 927 257000 (Ext. 51662) - Fax: +34 927 257203 E-mail: {sersanmar, gamahefpi, aplaza}@unex.es ABSTRACT Endmember extraction is an important technique in the con- text of spectral unmixing of remotely sensed hyperspectral data. Winter’s N-FINDR algorithm is one of the most widely used and successfully applied methods for endmember ex- traction from remotely sensed hyperspectral images. De- pending on the dimensionality of the hyperspectral data, the algorithm can be time consuming. In this paper, we propose a new parallel implementation of the N-FINDR algorithm. The proposed implementation is quantitatively assessed in terms of both endmember extraction accuracy and parallel efficiency, using two different generations of commercial graphical processing units (GPUs) from NVidia. Our ex- perimental results indicate that the parallel implementation performs better with latest-generation GPUs, thus taking advantage of the increased processing power of such units. Index Terms— Hyperspectral imaging, parallel process- ing, endmember extraction, GPUs. 1. INTRODUCTION A wide range of techniques for hyperspectral image pro- cessing have been proposed in recent years [1, 2]. One of such techniques is spectral unmixing, a very important task in remotely sensed hyperspectral data exploitation [3]. When the spatial resolution of the sensor is not fine enough to separate different spectral constituents, these can jointly occupy a single pixel and the resulting spectral measure- ment will be a mixed pixel, i.e., a composite of the individ- ual pure spectra [4]. In order to define the mixture prob- lem in mathematical terms, let us assume that a remotely sensed hyperspectral scene with n bands is denoted by X, in which the pixel at the discrete, spatial coordinates (i, j ) of the scene is represented by a feature vector given by X(i, j )=[x 1 (i, j ),x 2 (i, j ), ··· ,x n (i, j )] ∈ℜ n , and ℜ de- notes the set of real numbers corresponding to the pixel’s spectral response x k (i, j ) at sensor channels k =1,...,n. Under a linear mixture model assumption [3], each pixel vec- tor in the original scene can be modeled using the following expression: X(i, j )= p  k=1 Φ k (i, j ) · E k + n(i, j ), (1) where E k denotes the spectral response of the k-th endmem- ber, Φ z (i, j ) is a scalar value designating the fractional abun- dance of the k-th at pixel X(i, j ), p is the total number of endmembers, and n(i, j ) is a noise vector. The solution of the linear spectral mixture problem described in (1) relies on the correct determination of a set of p endmembers denoted by {E k } p k=1 . Over the last decade, several algorithms have been de- veloped for extraction of spectral endmembers directly from the input hyperspectral data set [5]. Winter’s N-FINDR al- gorithm [6] is one of the most widely used and successfully applied methods for that purpose. This approach finds the set of pixels with the largest possible volume by “inflating” a simplex within the data. After reducing the dimensionality of the data from n to p − 1 (this is a feasible step, since typically p << n), a random set of p pixel vectors is initially selected from the input scene. In order to refine the initial estimate of endmembers, every pixel in the image must be evaluated in terms of pixel purity likelihood or nearly pure statehood. To achieve this, the volume is calculated for every pixel in the place of each endmember. A trial volume is calculated for every pixel in each endmember position by replacing that end- member and finding the volume. If the replacement results in a volume increase, the pixel replaces the endmember. This procedure is repeated until there are no more replacements of endmembers. While the endmember determination step of N- FINDR in the commercial version distributed by Pacific Spec- tral Technology 1 has been optimized for high speed process- ing, the computational performance of the algorithm depends on the accuracy of the initial random selection of endmembers and, most importantly, on the dimensions of the hyperspectral scene and the number of endmembers to be found, p. 1 http://www.pacificspectral.com 955 978-1-4244-9566-5/10/$26.00 ©2010 IEEE IGARSS 2010