hyper spectral data art

Proceedings of International Joint Conference on Neur al Networks, Atlanta, Georgia, USA, June 14-19, 2009 nalysis Hyperspectral ata with iffusionMapsandFuzzy RT Rui Xu, Louis du Plessis, Steven Damelin, Michael Sears, and Donald C. Wunsch II Abstract-The presence of large amounts of data in hyperspectral images makes itve ry difficult to perform further tractable analyses. Here, we present a method of analyzing real hyperspectral data by dimensionality reduction using di ffusion maps. Diffusion maps interpret the eigenfunctions of Markov matrices as a system of coordinates on the original data set in order to obtain an efficient representation of data geometric descriptions.Aneural network clust eri ngtheory, Fu zzy ART, is further applied to the reduced data to form clusters of the potential minerals. Experimental results on a subset of hyperspectralcore imager data show that the proposed methods are promising in addressing the complicated hyperspectral data and identifying the minerals incore samples. 1. INTRODUCTION T HE advent of new spectral imaging techniques makes hyperspectral data more commonly acce ss ible in recent decades. Spectral imaging refers to the process of sampling an image at several different frequenc ies [1]. Di gi tal color photography is a form of spectral imag ing. Th e picture issampled atthree different fr equencies, one inthe bluerange of the spectrum and the other two n red and green respectively. Every sample gives a ma tr ix of intensit y va lues, which could be plotted to give a gray-scale image. When all three matricesare bl ended toget he r a colorimage isproduced. Multispectral imaging refers to the process of sampli ng an image at more fr equencies. Images ar e commonly sampled in the frequency range between 400 and 2,500 nm, since this is of usef ul illuminati on [1]. In hype rspec tra l imaging the image is sample d at hundreds of freque nc ies, compared to only a few for multispectral imaging. Furthermore, the different frequencies in multis pect ra l imaging ar e us uall y dis tri but ed in an irregular fashion, whereas the bands in hyperspectraI imaging are regularly spaced [1]. Man uscriptreceiv ed January 5, 2009. R. Xu is with the Applied Computational Intelligence Laboratory, Depart me nt of Electri cal & Comput er En gineeri ng, Missouri Universi ty of Science and Technology, MO 65409 USA (phone: 573-341-6811; fax: 573· 341-4521; e-ma il: [email protected]). L. du Plessis is with the School of Computational and Applied Mathematics, University of the Wi twatersrand, Joh annesburg, Sout h Af ri ca (emai l: [email protected]). S. Damelin is with the Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460 USA, and the School of Computational and Applied Mathematics, University of the Wi twat ersrand, Johann e sbu rg, Sou th Africa (e-mail:dameli n @georgiasouth em.edu). M. Sears is with the Sch ol of Computer Science, University of the Witwat ersrand, Johann esburg, South Af rica (email: michae [email protected]. za). D. C. Wunsch [[ is with he Departmen of Electrical & Computer Engin eer ing, Missouri Univer sit y of Science & Technology, Rolla, MO 65409 USA (e-mail: dwu [email protected] du). 978-1 -4244-3553-1/09 / 25.00 ©2009 IEEE q Fig. 1. Thehyperspectraldatacube.Foreveryoneofthe m frequencies sampled, there is an image of p x q of intensity va lues. Similarly, for every one of the pixels in the image, there is a complete spectrum of va lues. Th iscube image isgeneratedwithth e datausedinourstudies. Because of the regular spacing of narrow bands, a continuous spectrum can be drawn for every pixel in the image. Inst ead of ending up with a flat two-dimensional matrix of values, e obtain a hypercube of data, as shown in Fig. 1. This is where the problem in analyzing and storing hyperspectral data comes in. Having more than a hundred bands for every pixel means having enormous amounts of data. I f the hyperspectraI imager scans in m ba nds, then ever y pixel of the hyperspectral image can be seen as an m dimens ion al vec tor . Currently, hyperspectral imaging is mainly used In airborne surveillance te hniques [2]. Some uses for hypersp ectral imaging include crop assessment, environmental applications, and mineral exploitation [3]. Here, we are interested in the identification of minerals in core sample s. Core samples are long pieces of rock that was drilled in ar eas suspecte d of being rich in minerals. Sites for new mines are identified using data collected from core samples. It would be advantageous to automatic all y identi fy the different minerals resident in a piec e of core. AngIoGold Ashanti has constr uct ed the Hypers pectral Core Imager (HC ) that scans in core samples. The HCI scans in 5 meters of core every hour,at400 ba nds, producing 2 gigabytes of data every ho ur [2].Withthisamount of data be ing produced ever y hour, 3390

hyper spectral data art

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