Online publication date: 14 December 2010

Transcription

1 This article was downloaded by: [Canadian Research Knowledge Network] On: 13 January 2011 Access details: Access Details: [subscription number ] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK International Journal of Remote Sensing Publication details, including instructions for authors and subscription information: A technique based on non-linear transform and multivariate analysis to merge thermal infrared data and higher-resolution multispectral data Linhai Jing a ; Qiuming Cheng ab a Department of Earth and Space Science and Engineering, York University, Toronto, Ontario, Canada b State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan, China Online publication date: 14 December 2010 To cite this Article Jing, Linhai and Cheng, Qiuming(2010) 'A technique based on non-linear transform and multivariate analysis to merge thermal infrared data and higher-resolution multispectral data', International Journal of Remote Sensing, 31: 24, To link to this Article: DOI: / URL: PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

2 International Journal of Remote Sensing Vol. 31, No. 24, 20 December 2010, A technique based on non-linear transform and multivariate analysis to merge thermal infrared data and higher-resolution multispectral data LINHAI JING* and QIUMING CHENG Department of Earth and Space Science and Engineering, York University, Toronto, Ontario, Canada M3J 1P3 State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan, China (Received 3 January 2006; in final form 21 January 2009) A thermal infrared (TIR) image is a measure of the Earth s surface temperature and TIR emittance; however, its low spatial resolution severely limits its potential applications. Image fusion techniques can be used to fuse a TIR image with higher spatial resolution reflective bands to generate a synthetic TIR image. Because of the weak correlation between TIR and reflective data, such a synthetic image typically contains significant spectral distortion. In this paper, a multivariate analysis technique is used to derive a variable as a linear function of multiple reflective bands and their non-linearly transformed versions, to produce the maximum correlation with the TIR image. The spatial details of the variable are then injected into the TIR image to yield a synthetic image with reduced spectral distortion. In an experiment on Landsat Thematic Mapper (TM) TIR and reflective data, the fusion method proposed in this paper outperforms several existing methods in preserving the spectral characteristics of TIR data. 1. Introduction Earth surface temperatures measured by remote sensing techniques are related to important applications, such as monitoring atmospheric and climatic conditions, estimation of agricultural parameters, and geological target identification. Some spaceborne sensors measure the thermal infrared (TIR) flux emitted from the Earth s surface; for instance, the TIR sensors onboard the Landsat Thematic Mapper (TM) and Enhanced Thematic Mapper Plus (ETMþ), the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), the Advanced Very High Resolution Radiometer (AVHRR), and the Moderate-resolution Imaging Spectroradiometer (MODIS). Each radiance value observed is a function of the temperature and TIR emittance of the pixel observed, its surroundings, and the atmosphere column above it. Because of low TIR flux and sensor design constraints, the spatial resolutions of TIR images are typically several times lower than those of reflective images, severely limiting the applications of TIR images. For instance, the Landsat TM TIR band 6 (TM6) with 120-m spatial resolution is too coarse to delineate surface temperatures of urban areas with large spectral and spatial diversities. In many cases, high spatial *Corresponding author. jlh@yorku.ca International Journal of Remote Sensing ISSN print/issn online # 2010 Taylor & Francis DOI: /

3 6460 L. Jing and Q. Cheng resolution TIR images are required to provide temperature information with accurate locations. To satisfy this requirement, image fusion techniques are used to fuse low spatial resolution TIR data with high spatial resolution reflective data to synthesize high spatial resolution TIR images. Numerous image fusion methods are available to fuse low spatial resolution multispectral (MS) images with high spatial resolution panchromatic (PAN) bands (e.g. Chavez et al. 1991, Munechika et al. 1993, Pohl and van Genderen 1998, Laporterie and Flouzat 2003, González-Audícana et al. 2004, Otazu et al. 2005, Aiazzi et al. 2007, Lillo- Saavedra and Gonzalo 2007). Multiresolution analysis techniques, such as filtering, wavelet, à trous ( with holes ), and pyramids (Dutilleux 1989, Mallat 1989, Aiazzi et al. 1997, 1999, Flouzat et al. 2001), are currently widely used in image fusion. In a multiresolutionbased image fusion method (e.g. Schowengerdt 1980, Yocky 1996, Núñez et al. 1999, Aiazzi et al. 2002, Nencini et al. 2007), one high spatial resolution PAN band is typically decomposed into an approximation and the corresponding spatial details, which are then injected into each MS band to obtain a synthetic band. Multiresolution-based image fusion methods have significantly reduced the spectral distortion in synthetic images. Current image fusion methods are generally based upon the assumption that the correlation between PAN and MS bands or between a PAN band and a variable of multiple MS bands is significant. However, the TIR spectral range is far from the reflective spectral range, and the correlation between TIR and reflective data is generally weak. Although diverse image fusion methods are available for reflective MS and PAN images, only a few in the literature are claimed to be suitable for TIR and reflective data, such as the Price (1987), Moran (1990), Model 2 of the ARSIS (Amélioration de la Résolution Spatiale par Injection de Structures) (Wald and Baleynaud 1999, Ranchin and Wald 2000) and Pixel Block Intensity Modulation (PBIM; Liu and Moore 1998) methods. In the Price method, if the ith MS band (M i, i ¼ 1,...,n) is strongly correlated with the PAN band, the fused ith MS band (M i,f ) is calculated as follows: M i ¼ ap L þ b (1) I T ¼ ap þ b (2) I T M i;f ¼ M i (3) I TL where coefficients a and b are calculated using the least squares approach, P stands for each pixel value in the PAN band, P L for a degraded PAN band obtained using averaging (L being the label of P), I T for an intermediate image (T being the label of I), and I TL for a degraded I T image obtained using averaging. Both P L and I TL have the same pixel size as the MS band. If the correlation between the MS and PAN bands is weak, a look-up table can be generated to link each PAN value and an expected value of the MS band, and then a fused band can be generated using the look-up table and equation (3). In the Moran method, as a square window slides across a low spatial resolution TIR image that has been previously bicubically upsampled to match the pixel size of the reflective image, neighbouring pixels with a similar Normalized Difference Vegetation Index (NDVI) of the centre pixel of the window are delineated. The synthetic TIR value of the centre pixel is then set to be the statistical mode of the TIR values of the selected pixels. This method is dependent upon a strong linear relationship existing between the NDVI and the surface temperature for a given crop (Hope 1986). However, such a

4 A fusion method for TIR and reflective data 6461 relationship does not exist over areas with no vegetation. For instance, a building and its shadow typically have different TIR pixel values yet similar NDVI values. The ARSIS Model 2 method makes use of the wavelet technique and of the ARSIS concept (Ranchin et al. 1996, 2003, Ranchin and Wald 2000). In this method, the spatial details of a high spatial resolution near-ir band, such as TM band 4, are extracted and injected into a low spatial resolution TIR image to generate a synthetic TIR image. In the PBIM method, a synthetic TIR image (M TIR,f ) is calculated as follows: P tmp M TIR;f ¼ M TIR (4) P tmp;l where M TIR stands for a TIR image, P tmp for a weighted sum of multiple MS bands, and P tmp,l for a degraded P tmp image obtained using an averaging approach. In this method, a compromise solution is used to refine the edges with high albedo contrast within a low spatial resolution pixel. In the Price and the ARSIS Model 2 fusion methods for TIR and reflective data, a relationship between a TIR band and an individual reflective band is used. In the Moran and the PBIM methods, a relationship between a TIR band and a variable of the reflective bands is used. However, a weak linear correlation between TIR and reflective data indicates that their relationship is non-linear and a TIR band cannot be accurately linearly accounted for by an individual reflective band. Because a significant correlation between TIR and reflective data is the key for their successful fusion, multivariate analysis (Mardia et al. 1979) may be used as a tool to derive a variable, as a linear function of multiple reflective bands, to have a maximum correlation with the TIR band. As mentioned previously, a TIR pixel value is a mixed measure of two components: the temperature and TIR emittance of the Earth s surface. As the Earth s surface temperature is closely related to the Earth s surface reflectance and topographic effects that are recorded in reflective data, it may be assumed that this component can be linearly explained by the reflective data. As the Earth s surface TIR emittance is approximately equal to one minus the Earth s surface TIR reflectance, it may be assumed that the second component can be accounted for by a different set of reflective data,forinstanceasetofnon-linearly transformed reflective bands. Based upon these concepts, an image fusion method using a non-linear transform and multivariate analysis (denoted the NMV method) is proposed in this paper to merge weakly correlated TIR and reflective data. 2. Methodologies The ith reflective band (M i, i ¼ 1,...,n) can be degraded to an approximation (M i,l ) with the same pixel size as the TIR image using an averaging approach. The spatial details (M i,h, where h is a label of M) of the reflective band may be defined as the difference between the band and its degraded version: M i;h ¼ M i M i;l (5) where M i,l is previously bicubically upsampled to match the pixel size of the reflective band. Similarly, the spatial details (M i,h,t ) of the reflective band raised to the power t may be expressed as follows: M i;h;t ¼ ðm i Þ t t M i;l (6) A multivariate regression of a TIR image, multiple reflective bands, and multiple reflective bands raised to the power t can be established as follows:

5 6462 L. Jing and Q. Cheng M TIR ¼ Xn i¼1 c i ðm i Þ t þa i M i þ b þ e (7) where c i, a i and b are coefficients, e is the residual, and the M TIR is the TIR image. Given a value of t, equation (7) becomes an ordinary multivariate linear regression. Its regression coefficients c i, a i and b can be estimated using the least squares approach. The TIR image is previously bicubically upsampled to match the pixel size of the reflective bands. In multiresolution-based fusion methods (Schowengerdt 1997), a synthetic MS band is equal to the corresponding low spatial resolution MS band plus weighted spatial details of the PAN band. Similarly, a synthetic TIR image (M TIR,f ) can be set to be a sum of the corresponding low spatial resolution TIR image, the spatial details of multiple reflective bands, and the spatial details of multiple non-linearly transformed reflective bands, as follows: M TIR;f ¼ M TIR þ Xn i¼1 c i M i; h; t þ a i M i; h As demonstrated by equation (8), different exponents result in diverse synthetic images. If the exponent is equal to 0 or 1, the non-linearly transformed reflective bands will be ignored, and the NMV method will only be based upon the multivariate analysis of a TIR image and the original reflective bands. This special case of the NMV method is denoted as MV for brevity. 3. Experiment and results 3.1 Test data, fusion methods for comparison, and evaluation criteria A Landsat TM Beijing subscene acquired on 21 September 1997 was used to evaluate the NMV and MV image fusion methods proposed in this paper. The subscene consists of 30-m reflective bands 1 5 and 7 with spectral ranges , , , , and mm, respectively, and one 120-m TIR band ( mm) (TM6). The sizes of the reflective and TIR bands are 2048 pixels 2048 pixels and 512 pixels 512 pixels, respectively. The correlations between the TIR band and reflective bands 1 5 and 7 spatially degraded by a factor of 4 using an averaging approach are 0.62, 0.56, 0.60, 0.22, 0.44 and 0.68, respectively. Such low correlations, especially the correlation between the TIR band and band 4, indicate that it is difficult to merge the TIR band and each individual reflective band to yield a synthetic TIR image with high spectral accuracy. As demonstrated in TIR subsets (figures 1(b), 2(b), 3(b) and3(e)), water areas and agricultural fields with vegetation are represented by dark tones, whereas bare soil and constructed areas are mostly represented by light tones. Two false-colour composites (bands 1, 4 and 7 as red, green and blue channels, respectively) within figures 3(a) and3(d) reveal the patterns of the agricultural fields and of the streets and buildings in urban areas, respectively. Using the TM reflective bands 1 5 and 7, we carried out two fusion processes: NMV, based on multivariate analysis and a non-linear transform with an exponent of 2, and MV, based only on multivariate analysis. For comparison, three other image fusion methods were applied to the test data: the Price method using TM band 7; the ARSIS Model 2 method using the Daubechies-2 wavelet (Daubechies 1988) and TM band 4; and the PBIM method. (8)

6 A fusion method for TIR and reflective data 6463 All resulting synthetic TIR images had a spatial resolution of 30 m and need be compared with a 30-m TM6 image to assess their quality. As the latter image did not exist, spatially degraded images were used in this study. The original TIR and reflective bands were degraded to 480-m and 120-m spatial resolutions, respectively, to simulate the fusion of TIR and reflective bands with a spatial resolution ratio of 4:1. Figures 1(a) and 2(a) are subsets of the degraded reflective bands, and figures 1(c) and 2(c) are subsets of the degraded TIR band. All fusion experiments were carried out on the degraded data to allow quantitative scores to be measured between each synthetic TIR image and real 120-m TM6 image using three quality indices (Wald et al. 1997): mean bias, correlation coefficient, and standard deviation of the error. 3.2 Visual comparison Figures 1(d) 1(h) illustrate subsets of all the 120-m synthetic TIR images. The MV, NMV and Price synthetic images are nearly identical to the reference TIR image (a) (b) (c) (d) (e) (f) (g) (h) Figure pixels 100 pixels original and synthetic images: (a) 120-m MS image; (b) 120-m TM6 image; (c) 480-m TM6 image; (d) MV fusion; (e) NMV fusion; (f) Price fusion; (g) ARSIS fusion; (h) PBIM fusion.

7 6464 L. Jing and Q. Cheng (figure 1(b)). It is clear that fewer anomalously bright pixels are present within the NMV synthetic image than within the MV synthetic image. More anomalies are distributed within the Price synthetic image. Most of the bright features within the ARSIS synthetic image have significant discrepancies with the reference with respect to shapes and pixel values. The PBIM synthetic image is overly sharpened and contains excessive spatial details. The lower part of each subset in figure 1 contains mountain areas. The mountain areas within the MV synthetic image are slightly smoother than the reference, and they contain more spatial details than the mountain areas within the NMV image. The mountain ridges within the Price synthetic image are jagged, and the opposite sides of each ridge within the PBIM synthetic image lack contrast. The upper part of each subset within figure 1 contains field areas. Most of the towns within the NMV, MV and Price synthetic images are smooth and bright and have clear boundaries. By contrast, each town within the ARSIS synthetic image has a bright centre and a blurred edge, and each town within the PBIM synthetic image is obscure. Figures 2(d) 2(h) are subsets showing urban and suburban areas of all the 120-m synthetic TIR images. Compared with the reference image (figure 2(b)), the urban areas within the MV, NMV and ARSIS synthetic products lack spatial details and appear blurred. The NMV synthetic product contains significantly fewer anomalously bright pixels than the MV synthetic image. The PBIM synthetic image contains excessive spatial details. Most of the obvious edges present within the reference image turn jagged in the Price synthetic product, and they are eliminated within the PBIM synthetic product. The performance discrepancies of the five fusion methods are also clearly illustrated with individual features within the images. For instance, the three bright neighbouring spots on the right side of point A (figure 2(b)) within the reference image are represented as different shapes, edges and pixel values in the five synthetic products. In conclusion, the MV and NMV synthetic images are almost identical and are the closest to the reference image among all the fused images. The NMV synthetic image contains fewer anomalies and more spatial details, and appears closer to the reference than the MV synthetic product. The next best is the Price synthetic image. The ARSIS and PBIM synthetic images are of lower visual quality and have significant discrepancies from the reference. To understand the 30-m NMV synthetic image generated from the original 120-m TIR band, 30-m reflective bands 1 5 and 7, and 30-m reflective bands 1 5 and 7 raised to a power of 2, two subsets showing agricultural fields and urban areas of the NMV synthetic image are illustrated in figures 3(c) and 3(f), respectively. The enhanced patterns within the two subsets confirm that the clarity of the 120-m TIR image (figures 3(b) and 3(e)) has been significantly improved by image fusion. It is worth pointing out that the fusion quality of the NMV method varies with scene and land use. The method performs well over areas with small spectral and spatial diversities, such as field areas, but it works less effectively over areas with large variations, as in urban regions. 3.3 Statistical comparison Table 1 reports the statistics of the mean bias, correlation coefficient and standard deviation of the error of all the 120-m synthetic products. In this table, row Exp

8 A fusion method for TIR and reflective data 6465 (a) (b) (c) (d) (e) (f) (g) (h) Figure pixels 100 pixels original and synthetic images: (a) 120-m MS image; (b) 120-m TM6 image; (c) 480-m TM6 image; (d) MV fusion; (e) NMV fusion; (f) Price fusion; (g) ARSIS fusion; (h) PBIM fusion. refers to the 480-m TIR image bicubically upsampled by a factor of 4, representing the spectral distortion of the degraded TIR image with reference to real 120-m TIR data. As demonstrated in table 1, the mean bias of each synthetic TIR image is nearly zero. The mean bias of the NMV synthetic product is the highest among all the biases. The correlation coefficient of each synthetic TIR image presented in table 1 represents the correlation coefficient between the synthetic image and the 120-m reference TIR image. The MV method provides the second highest correlation, up to Such a high correlation indicates that the multivariate analysis technique used in the MV method effectively improves the spectral accuracy of the synthetic images. The NMV method supplies the highest correlation of 0.928, confirming that using non-linearly transformed reflective bands as independent variables in the multivariate analysis may further improve the fusion quality yielded by the MV method. Compared with the MV and NMV methods, the Price and ARSIS methods offer

9 6466 L. Jing and Q. Cheng (a) (b) (c) (d) (e) (f) Figure pixels 200 pixels original and synthetic images: (a) 30-m field MS image; (b) 120-m field TM6 image bicubically upsampled by a factor of 4; (c) NMV fusion; (d) 30-m urban MS image; (e) 120-m urban TM6 image bicubically upsampled by 4; (f) NMV fusion. Table 1. Quality index statistics of the synthetic TM6 images. Mean bias Correlation coefficient Standard deviation of the error MV NMV Price ARSIS Model PBIM Exp lower correlations of and 0.824, respectively, and the PBIM method yields the lowest correlation. The standard deviation of the error of each synthetic TIR image in table 1 represents the standard deviation of the difference between the synthetic image and the reference TIR image. The MV and NMV synthetic products have the lowest errors of 1.69 and 1.62, respectively. The Price synthetic product contains more error. The error of the ARSIS synthetic image is slightly higher than that of the degraded TIR image, and the error of the PBIM synthetic image is several times higher. The NMV method, based upon non-linear transform and multivariate analysis, statistically performs the best in preserving the spectral characteristics of the TIR image. The second best is found to be the MV method, which is only based upon multivariate analysis. The other methods work less effectively in reducing the spectral distortion of the synthetic products.

10 A fusion method for TIR and reflective data Discussion 4.1 Analysis of spectral distortion of each fusion method Bright pixels in reflective bands may lead to extremely bright pixels in the MV synthetic image. As more variables of reflective bands are taken into account in the NMV method, anomalously bright pixels can be effectively eliminated in the NMV synthetic image. The smooth visualization of the NMV synthetic image is primarily attributed to a bicubic upsampling approach, which is used to spatially expand the low spatial resolution TIR image. Rectangular pseudo-edges within the Price synthetic image occur in areas with high albedo contrast. In the Price fusion method, if the input TIR image and the image I TL in equation (3) are previously bicubically upsampled to match the pixel size of the input reflective band, such pseudo-edges can be effectively eliminated. The low correlation between TIR and near-ir data may make the ARSIS fusion method fail. In the ARSIS fusion using a near-ir band, the significant near-ir spectral differences between vegetation and non-vegetation are incorrectly injected into the synthetic image. For instance, for a developed area on one side of a town field boundary, its TM4 pixels are dark, its spatial details within TM4 are typically negative, and its TIR pixels are bright. By contrast, for a vegetated area on the side of the town field boundary, its TM4 pixels are bright, its spatial details within TM4 are positive, and its TIR pixels are dark. Injecting such spatial details within TM4 into TIR pixels reduces the original TIR contrast between the opposite sides of the boundary and makes the boundary more blurred, as demonstrated from the town - field boundaries within figure 1(g). Because of the TIR flux from the atmosphere and the magnitude of the Earth s surface temperature, each TIR pixel value is significant and each synthetic TIR pixel value needs be notably higher than zero. As indicated in equation (4) of the PBIM image fusion method, however, once the P tmp term is close to zero, the resulting synthetic pixel may approximate zero, as for shadow or water pixels. Assuming that a TIR image contains a constant component (c) that is related to both the TIR flux from the atmosphere and the minimum surface temperature and is free of topographic effects, equation (4) of the PBIM fusion method can be modified as follows: M TIR;f ¼ ðm TIR cþ P tmp þ c (9) P tmp;l where P tmp,l is previously bicubically upsampled to match the pixel size of the reflective image. Regarding the minimum pixel value of the TIR image as the constant component, this modified PBIM fusion method was applied to the test data used in the preceding experiment. The three quality indices, mean bias, correlation coefficient and standard deviation of the error, of the resulting synthetic TIR image are 0.00, and 2.08, respectively. The resulting synthetic image has significantly higher visual and spectral qualities than the original PBIM fused image demonstrated in figures 1(h) and 2(h) and table Multivariate regressions for the NMV and MV In the NMV image fusion method proposed in this paper, reflective bands and their non-linearly transformed versions are used as independent variables in a multivariate

11 6468 L. Jing and Q. Cheng linear regression. This is in an attempt to better explain the different components of a TIR image, including the temperature and TIR emittance of the Earth s surface, and to derive a variable to have a maximum correlation with the TIR image to be fused. In the preceding MV and NMV fusion using the degraded TIR and reflective data, the multiple correlation coefficients of the related regressions (equation (7)) are and 0.699, respectively. As expected, the resulting MV synthetic image has slightly lower quality than the resulting NMV synthetic product in visual and statistical comparisons. In the previous MV fusion, the coefficients a i for TM reflective bands 1 5 and 7 in equation (7) are 0.43, 0.13, 0.34, 0.05, 0.01 and 0.28, respectively. In the preceding NMV fusion, the coefficients a i are 1.11, 0.16, 0.41, 0.22, 0.16 and 0.27, respectively. Neither coefficient set supports an assumption that a TIR image is a linear function of multiple reflective bands with positive weights. Such a linear function expresses the albedo and topographic effects within the reflective image. Although TM bands 4 and 6 are weakly correlated, including TM4 in the multivariate regression for either of the NMV and MV fusion methods can improve the related multiple correlation coefficient and thus improve the fused TIR image. Once TM4 is removed from the regression for MV fusion, the multiple regression coefficient becomes 0.658, and the mean bias, correlation coefficient and standard deviation of the error of the resulting fused TIR image are 0.00, and 1.69, respectively. This resulting fused image has lower spectral quality than the preceding MV fused image obtained from TM reflective bands 1 5 and 7. Once TM4 is removed from the regression for NMV fusion, the related multiple regression coefficient becomes 0.692, and the mean bias, correlation coefficient and standard deviation of the error of the resulting fused TIR image are 0.17, and 1.63, respectively. This resulting fused image has lower spectral quality than the previous NMV fused image obtained from the TM reflective bands 1 5 and 7. As the exponent t in equation (8) of the NMV method increases from 0 to 0.9 and from 1.1 to 3.0 in steps of 0.1, a series of NMV synthetic products can be generated from the spatially degraded Landsat TM data described previously. Figure 4(a) illustrates the quality variations of the series in terms of the quality index correlation coefficient. As demonstrated in this figure, a correlation jump occurs as the exponent steps from 0 to 0.1, indicating that as non-linearly transformed reflective bands are used in fusion, the correlation between the resulting synthetic TIR image and the reference image increases. As the exponent keeps growing, the quality index steadily increases to a maximum with the exponent close to 2.5 and then gradually declines. Figure 4(b) illustrates the quality variations of the series of NMV synthetic products in terms of standard deviation of the error. In contrast with the preceding graph, the spectral error of the synthetic images falls as the exponent increases from 0 to 0.1, confirming that including non-linearly transformed reflective bands as independent variables in the related multivariate analysis notably reduces the spectral distortion of the synthetic images. The spectral error of the series demonstrates a clear dependence on the exponent. As the exponent increases from 0.1 to 0.9 and from 1.1 to 3.0, the error gradually declines from 1.65 to a minimum for an exponent close to 2.5, and then steadily increases. This graph, together with the prior one, shows that the NMV synthetic products keep their high spectral quality when the exponent is larger than 1.0.

12 A fusion method for TIR and reflective data 6469 Figure 4. Quality variations of the series of NMV synthetic products with the increase of the exponent: (a) correlation coefficient; (b) standard deviation of the error. 5. Conclusions Because of the weak correlation between TIR and reflective data, synthetic TIR images obtained using current fusion methods typically contain significant spectral distortion. In the image fusion method proposed in this paper, reflective data and their nonlinearly transformed versions are used as independent variables in a multivariate linear regression of TIR and reflective data. The spatial details of the original and the transformed reflective data are then injected into a low spatial resolution TIR image to synthesize a high spatial resolution image. If the transformed reflective data are ignored in the regression, a simplified version of the fusion method can be realized. The fusion method and its simplified version were tested upon Landsat TM reflective and TIR bands spatially degraded by a factor of 4, and yielded synthetic TIR images with significantly better visualization and less spectral distortion than several existing image fusion methods. This study demonstrates that multivariate analysis combined with a non-linear transform technique may facilitate improvement of fused TIR images. Acknowledgements This research was jointly supported by the National Natural Science Foundation of China (Grants and ), the Ministry of Education of China (No.

13 6470 L. Jing and Q. Cheng , No. IRT0755), and the Chinese 863 project (2006AA06Z115). We thank two anonymous referees for their constructive comments. References AIAZZI, B., ALPARONE, L., BARONTI, S. and GARZELLI, H., 2002, Context-driven fusion of high spatial and spectral resolution images based on oversampled multiresolution analysis. IEEE Transactions on Geoscience and Remote Sensing, 40, pp AIAZZI, B., ALPARONE, L., BARONTI, S. and LOTTI, F., 1997, Lossless image compression by quantization feedback in a content-driven enhanced Laplacian pyramid. IEEE Transactions on Image Processing, 6, pp AIAZZI, B.,ALPARONE, L.,BARONTI, S.andPIPPI, I., 1999, Fusion of 18 m MOMS-2P and 30 m Landsat TM multispectral data by the generalized Laplacian pyramid. ISPRS International Archives of Photogrammetry and Remote Sensing, 32, pp AIAZZI, B., BARONTI, S. and SELVA, M., 2007, Improving component substitution pansharpening through multivariate regression of MSþPan data. IEEE Transactions on Geoscience and Remote Sensing, 45, pp CHAVEZ, P.S., SLIDES, S.C. and ANDERSON, J.A., 1991, Comparison of three different methods to merge multiresolution and multispectral data: Landsat TM and SPOT panchromatic. Photogrammetric Engineering and Remote Sensing, 57, pp DAUBECHIES, I., 1988, Orthogonal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, 41, pp DUTILLEUX, P., 1989, An implementation of the algorithme à trous to compute the wavelet transform. In Wavelets: Time-Frequency Methods and Phase Space, J.-M. Combes, A. Grossman and Ph. Tchamitchian (Eds), pp (Berlin, Germany: Springer- Verlag). FLOUZAT, G., AMRAM, O., LAPORTERIE, F. and CHERCHALI, S., 2001, Multiresolution analysis and reconstruction by a morphological pyramid in the remote sensing of terrestrial surfaces. Signal Processing, 81, pp GONZÁLEZ-AUDÍCANA, M., SALETA, J.L., CATALÁN, R.G. and GARCÍA, R., 2004, Fusion of multispectral and panchromatic images using improved IHS and PCA mergers based on wavelet decomposition. IEEE Transactions on Geoscience and Remote Sensing, 42, pp HOPE, A.S., 1986, Parameterization of surface moisture availability for evapotranspiration using combined remotely sensed spectral reflectance and thermal-ir observations. PhD dissertation, University of Maryland, College Park, MD, USA. LAPORTERIE, F. and FLOUZAT, G., 2003, The morphological pyramid concept as a tool for multiresolution data fusion. Integrated Computer-aided Engineering, 10, pp LILLO-SAAVEDRA, M. and GONZALO, C., 2007, Multispectral images fusion by a joint multidirectional and multiresolution representation. International Journal of Remote Sensing, 28, pp LIU, J.G.andMOORE, J.M., 1998, Pixel block intensity modulation: adding spatial detail to TM band 6 thermal imagery. International Journal of Remote Sensing, 19, pp MALLAT, S.G., 1989, A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, pp. s MARDIA, K.V., KENT, J.T. and BIBBY, J.M. (Eds), 1979, Multivariate Analysis, pp (New York: Academic Press). MORAN, M.S., 1990, A window-based technique for combining Landsat Thematic Mapper thermal-ir data with higher-resolution multispectral data over agricultural lands. Photogrammetric Engineering and Remote Sensing, 56, pp

14 A fusion method for TIR and reflective data 6471 MUNECHIKA, C.K., WARNICK, J.S., SALVAGGIO, C. and SCHOTT, J.R., 1993, Resolution enhancement of multispectral image data to improve classification accuracy. Photogrammetric Engineering and Remote Sensing, 59, pp NENCINI, F., GARZELLI, A., BARONTI, S. and ALPARONE, L., 2007, Remote sensing image fusion using the curvelet transform. Information Fusion, 8, pp NÚÑEZ, J., OTAZU, X., FORS, O., PRADES, A., PALA, V. and ARBIOL, R., 1999, Multiresolutionbased image fusion with additive wavelet decomposition. IEEE Transactions on Geoscience and Remote Sensing, 37, pp OTAZU, X., GONZÁLEZ-AUDÍCANA, M., FORS, O. and NÚÑEZ, J., 2005, Introduction of sensor spectral response into image fusion methods. Application to wavelet-based methods. IEEE Transactions on Geoscience and Remote Sensing, 44, pp POHL, C. and VAN GENDEREN, J.L., 1998, Multisensor image fusion in remote sensing: concepts, methods and applications. International Journal of Remote Sensing, 19, pp PRICE, J.C., 1987, Combining panchromatic and multispectral imagery from dual resolution satellite instruments. Remote Sensing of Environment, 21, pp RANCHIN, T., AIAZZI, B., ALPARONE, L., BARONTI, S. and WALD, L., 2003, Image fusion the ARSIS concept and some successful implementation schemes. ISPRS Journal of Photogrammetric Engineering and Remote Sensing, 58, pp RANCHIN, T. and WALD, L., 2000, Fusion of high spatial and spectral resolution images: the ARSIS concept and its implementation. Photogrammetric Engineering and Remote Sensing, 66, pp RANCHIN, T., WALD, L. and MANGOLINI, M., 1996, The ARSIS method: a general solution for improving spatial resolution of images by means of sensor fusion. In Proceedings EARSeL Conference Fusion of Earth Data, 6 8 February, 1996, Cannes, France, pp (Nice, France: SEE Gre CA). SCHOWENGERDT, R.A., 1980, Reconstruction of multispatial, multispectral image data using spatial frequency content. Photogrammetric Engineering and Remote Sensing, 46, pp SCHOWENGERDT, R.A., 1997, Remote Sensing: Models and Methods for Image Processing, 2nd edn, pp (Orlando, FL: Academic Press). WALD, L. and BALEYNAUD, J.M., 1999, Observing air quality over the city of Nautes by the means of Landsat thermal-ir data. International Journal of Remote Sensing, 20, pp WALD, L., RANCHIN, T. and MANGOLINI, M., 1997, Fusion of satellite images of different spatial resolutions: assessing the quality of resulting images. Photogrammetric Engineering and Remote Sensing, 63, pp YOCKY, D.A., 1996, Multiresolution wavelet decomposition image merger of Landsat Thematic Mapper and SPOT panchromatic data. Photogrammetric Engineering and Remote Sensing, 62, pp