CCSM: Cross correlogram spectral matching F. Van Der Meer & W. Bakker Published online: 25 Nov 2010.

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3 int. j. remote sensing, 1997, vol. 18, no. 5, 1197± 1201 C CSM: cross correlogram spectral matching F. VAN DER MEER International Institute for Aerospace Survey and Earth Sciences ITC, Department of Earth Resources Surveys, Hengelosestraat 99, P.O. Box 6, 7500 AA Enschede, The Netherlands and W. BAKKER International Institute for Aerospace Survey and Earth Sciences ITC, Department of Geoinformatics, Hengelosestraat 99, P.O. Box 6, 7500 AA Enschede, The Netherlands (Received 12 June 1996; in nal form 30 October 1996) Abstract. Cross correlogram spectral matching (CCSM) is a new approach towards mineral mapping from imaging spectrometer data. A cross correlogram is constructed by calculating the cross correlation at di erent match positions between a test spectrum (i.e., a remotely-sensed spectrum) and a reference spectrum (i.e., a laboratory mineral spectrum). To assess the sensitivity of the cross correlogram as a means of spectral matching, the technique is applied to laboratory spectra. In each experiment, the cross correlogram function was derived, a test of signi cance of the correlations was conducted and a moment of skewness was calculated to characterize the curve shape of the correlogram. The cross correlogram for a perfect spectral match had a parabolic shape with the maximum correlation of one at match position zero and a symmetry around the central match number. The cross correlation is found to be insensitive to di erences in gain and thus allows to compare materials of di erent albedos. The cross correlogram is relatively insensitive to noise which will reduce the overall correlation but does not a ect the shape of the correlogram. Relative small di erences in absorption band position and shape between the test and reference spectrum a ect the shape, signi cance and correlation of the correlogram values. 1. Introduction The advent of imaging spectrometers with typically more than 200 spectral bands requires new analytical tools that can be automated to a large extent to extract relevant information from hyperspectral data sets. Imaging spectrometers are devices that acquire data in many, narrow and contiguous spectral bands over large portions of the electromagnetic spectrum producing laboratory-like re ectance spectra for each pixel. Visual comparison of remote and laboratory spectra may allow positive identi cation of surface mineralogy. This is laborious and subjective. Alternatively, standard remote sensing techniques such as colour compositing and ratioing can be used. However, an enormous amount of possible two or three-band combinations arise from imaging spectrometer data sets. Several techniques have been developed to extract information in a semi-automated manner from imaging spectrometer data sets. It is outside the scope of this Letter to review these, the interested reader is referred to recent review papers by Cloutis (1996) and Ichoku and Karnieli (1996). In this letter, we present a new approach to hyperspectral data analysis that is based on the cross correlogram. A cross correlogram is constructed for each image 0143± 1161/97 $12.00 Ñ 1997 Taylor & Francis Ltd

4 1198 F. van der Meer and W. Bakker pixel by calculating the linear correlation coe cient between a test (i.e., a remotely sensed) spectrum and a reference (i.e., laboratory) spectrum at di erent match positions (i.e. spectral channel shifts). We demonstrate that the cross correlogram (e.g., the plot of match positions versus cross correlation) provides important statistical information that can be used to develop spectral curve matching algorithms that ultimately allow single-component mineral mapping as well as sub-pixel analysis. Through a set of experiments on laboratory spectra we will show the potential of the cross correlogram. 2. The cross correlogram for spectral matching 2.1. Basic calculations A cross correlogram is constructed by calculating the cross correlation coe cient between a test spectrum, usually a remotely-sensed spectrum, and a reference spectrum, usually a laboratory spectrum at di erent match positions (or lags). By convention, we move the reference spectrum and refer to a negative match position when shifting towards shorter wavelengths and to a positive match position when shifting toward a longer wavelength. Thus match position Õ 1 means that we are calculating the cross correlation between the test spectrum and the reference spectrum in which all channels have been shifted by one channel position number to the lower end of the spectrum. The cross correlation, rm, at each match position, m, is equivalent to the ordinary linear correlation coe cient and is de ned as the product of the covariance and the sum of the standard deviations as rm = COVt,r where COVt,r is the covariance between the overlapped portions of the test spectrum, t, and reference spectrum, r, and st and sr are the corresponding standard deviations. If we denote the test and reference spectrum as lt and lr, respectively, and de ne n as the number of overlapping positions, the cross correlation for match position m can be calculated as rm = stsr n lrlt Õ lr lt Ó [n l 2 r Õ ( lr ) 2 ][n l 2 t Õ ( lt ) 2 ] (1) (2) This is analogous to the approach (in a complete di erent context) of Mahle and Ashley (1979) and McFee et al. (1994). However, Mahle and Ashley (1979) did not use the correlation coe cient as a similarity index while McFee et al. (1994) only exploited the correlation at m=0 rather than calculating the full correlogram function. The signi cance of the cross correlation coe cient can be assessed by the following t-test S nõ 2 t=rm 1Õ r 2 m (3) which has (nõ 2) degrees of freedom and tests the null hypothesis stating that the correlation between the two spectra at a speci c match position is zero.

5 Remote Sensing L etters Sensitivity analysis To test the sensitivity of the cross correlogram as a tool for spectral matching, we applied the method in a number of experiments to re ectance spectra from the NASA-JPL laboratory spectral library (Grove et al. 1992). Spectra in this library were measured on a Beckman UV 5240 spectrophotometer which has a sampling interval of 1 nm in the wavelength range of 0 4 to 0 8 mm, and a sampling interval of 4 nm in the wavelength range of 0 8 to 2 5 mm. Bandwidth ranges from 1 nm at 0 4 mm to 40 nm at 2 5 mm with a spectral resolution (de ned as bandwidth/wavelength) better than 2 per cent at all wavelengths. As a reference spectrum we have selected kaolinite between 2 0 and 2 3 mm and compared it with two other clay minerals; alunite and buddingtonite. Kaolinite has a strong absorption feature at 1 4 mm and a double absorption feature centred at 2 16 mm and 2 2 mm. Due to the lack of H2O, the feature at 1 9 mm is weakly developed or missing. Alunite is characterized by absorption features at 2 16 mm and 2 20 mm. Due to OH frequency stretching and a nearly symmetrical shape in the 2 08± 2 28 mm region. A second broad absorption feature occurs at 2 32 mm. An absorption feature at 2 02 mm and a vibrational absorption feature due to NH4 at 2 11 mm are the main diagnostic features distinguishing buddingtonite spectrally from other clay minerals. Experiment 1 was a cross correlogram with the kaolinite spectrum both as test and reference spectrum in the wavelength region of the characteristic doublet. The correlogram found was symmetric around the match position zero which also has the highest correlation value of one. The symmetry can be expressed in the moment of skewness which we calculate as the correlation at match position minus ten subtracted from the correlation at match position plus ten. The results of the t-test indicated that for all match positions the correlation was found to be signi cant indicating that the two spectra are dependent, non-random series. To demonstrate that the cross correlogram is insensitive to di erences in albedo, in another experiment the test spectrum was o set by 10 per cent re ectance which had no e ect on the correlogram ( gure 1). The e ect of noise on the correlogram was tested by adding a component of 5 per cent random noise to the test spectrum which did not a ect the shape characteristics of the correlogram, but resulted in a decrease of the cross correlation values by 5 per cent ( gure 2). Adding 10 per cent random noise to the test spectrum and 5 per cent random noise to the reference spectrum caused a minute e ect on the shape characteristic of the correlogram (skewness of ) and a decrease of the cross correlation values of 7 5 per cent. The cross correlogram for the spectral matching of kaolinite (as reference spectrum) versus buddingtonite, alunite and kaolinite (as test spectrum) is shown in gure 3. The function for buddingtonite is highly skewed with the negative moment of skewness indicating that the peak of the correlation coe cients is found when shifting the kaolinite spectrum toward shorter wavelengths. Note that the correlation coe cients were found insigni- cant for all match positions. The cross correlogram for alunite versus kaolinite shows a peak at match position minus six which corresponds to a shift of the kaolinite reference spectrum of 24 nm toward shorter wavelength. 3. Conclusions Cross correlogram spectral matching (CCSM) is a simple and straightforward technique that allows the quanti cation of the spectral similarity existing between remotely-sensed and laboratory spectra. Assessment of the statistical signi cance of the spectral match is an integral part of the matching process. The cross correlogram

6 1200 F. van der Meer and W. Bakker Figure 1. Library and test spectrum ( left) and corresponding cross correlogram (right) for kaolinite versus kaolinite o set by 10 per cent re ectance. The vertical dashed line on the top of the right-hand chart indicates the match positions for which the correlation coe cients were found to be signi cant according to the t-test of equation (2). Figure 2. Library and test spectrum ( left) and corresponding cross correlogram (right) for kaolinite versus kaolinite with 5 per cent random noise added. The vertical dashed line on the top of the right-hand chart indicates the match positions for which the correlation coe cients were found to be signi cant according to the t-test of equation (2). outlined is insensitive to gain factors and random noise a ects the values of the correlation coe cients equally at each match position without a ecting the shape of the correlogram. The position of the correlation peak in the correlogram is directly related to the relative position of the spectral absorption features that are being compared and the t-test provides a means of testing the signi cance of the correlation coe cients found. Finally, the cross correlogram provides a statistically meaningful comparison between test and reference spectra that can lead to automated mineral

7 Remote Sensing L etters 1201 Figure 3. Library and test spectrum ( left) and corresponding cross correlogram (right) for kaolinite versus kaolinite, alunite and buddingtonite. The vertical lines in the diagram above the right-hand chart indicate the match positions for which the correlation coe cients were found to be signi cant according to the t-test of equation (2). Note that for the mineral buddingtonite all correlation coe cients were insigni cant and that the peak of the correlogram occurs outside of the mapped area to the left. mapping using imaging spectrometer data. We are currently developing and testing algorithms to apply CCSM to imaging spectrometer data by addressing problems related to the mixed nature of remotely-sensed spectra and problems arising from di erences in bandpasses and spectral response function of eld and imaging spectral devices. Referen ces Cloutis, E. A., 1996, Hyperspectral geological remote sensing: evaluation of analytical techniques. International Journal of Remote Sensing, 17, 2215± Grove, C. I., Hook, S. J. and Paylor, II, E. D., 1992, L aboratory Re ectance Spectra of 160 minerals, 0 4 to 2 5 Micrometers (Pasadena: Jet Propulsion Laboratory), NASA-JPL Publication 92± 2. Ichoku, C. and Karnieli, A., 1996, A review of mixture modelling techniques for sub-pixel land cover estimation. Remote Sensing Reviews, 13, 161± 186. Mahle, N. H. and Ashley, J. W., 1979, Application of a correlation coe cient pattern recognition technique to low resolution mass spectra. Computers & Chemistry, 3, 19± 23. McFee, J. E., Achal, S. and Anger, C., Scatterable mine detection using CASI. Proceedings of the First International Airborne Remote Sensing Conference and Exhibition, Strasbourg, France, 12± 15 September 1994 (Ann Arbor: ERIM), pp. 587± 599.