3.1.

Concept and Procedures

Since the K&P method is sensitive to inaccuracies from radiometric calibration and/or atmospheric correction, we propose its modified version as described below.

First, the HS- and the MS-images in an overlapping area are accurately co-registered between them and converted to surface reflectance images by atmospheric correction, respectively. Mineral discrimination is then performed with the HS-image using a general procedure like (1) data compression by the minimum noise fraction (MNF) conversion,¹⁷ (2) extraction of spectrally pure pixels by the pixel purity index (PPI) analysis,¹⁸ (3) extraction of endmember pixels by a $n$-dimensional scatter plotting,¹⁸ and (4) determination of minerals corresponding to each endmember through a comparison between the endmember spectra and the library spectra. This procedure links HS-based endmember spectra and mineral labels in the overlapping area. Next, the MS-based endmember spectra are taken from surface reflectance spectra of the MS-pixels at the same positions with the HS-pixels selected as the HS-based endmembers in the overlapping area. This means that MS-based endmember spectra are linked to mineral labels via HS-based endmember spectra in the overlapping area. Finally, mineral discrimination is performed for the MS-image over the overlapping and the nonoverlapping areas using the MS-based endmember spectra obtained above, assuming that the MS-based endmember spectra can be applied not only to the overlapping area but also to the nonoverlapping area. Figure 1 shows the flowchart of the proposed method.

Fig. 1

Flowchart of the proposed method.

Though the K&P method uses the extracted HS-based endmember spectra in calculating the MS-based endmember spectra, the proposed method calculates the MS-based endmember spectra from surface reflectance spectra of the MS-pixels at the same positions with the HS-pixels selected as the HS-based endmembers in the overlapping area. Since the MS-based endmember spectra are determined based on the MS-image itself, spectral inconsistency between the HS- and the MS-surface reflectance images will not produce an error in mineral mapping by the SAM method with the MS-image and the MS-based endmember spectra, unlike the K&P method.

3.2.

Necessity of Accurate Co-registration

In the proposed method, co-registration between the HS- and the MS-images should be accurately performed, because the MS-based endmembers are derived from the MS-pixels corresponding to the HS-pixels selected as the HS-based endmembers. If co-registration is inaccurate, the proposed method will perform less well, as demonstrated in Sec. 5.4. Therefore, accurate image-to-image matching between the HS- and the MS-images should be applied after system geometric correction of each image. Though various matching methods are available,¹⁹ its simplest method is probably to match the positions of the two images visually by parallel translation in integer pixels using an appropriate feature point, if geometric distortion is small in each image after system geometric correction.

If the whole of the overlapping area cannot be co-registered with enough accuracy by single operation, co-registration can be performed for each subarea divided from the whole area.

3.3.

Details of Mineral Mapping with MS-Based Endmember Spectra

Several methods are available for mineral mapping with the MS-based endmember spectra. In the proposed method, we employed the SAM method for this purpose. The SAM method determines the spectral similarity between two spectra by calculating the angle between the two spectra, treating them as vectors in a space with dimensionality equal to the number of bands,¹⁶ where the cosine similarity calculated from the angle is often used instead of the angle. In the proposed method, each MS-pixel is assigned to the MS-based endmember that the cosine similarity against that pixel is highest among all the MS-based endmembers and then classified to the mineral corresponding to the assigned MS-based endmember.

In practice, the highest or near-highest cosine similarity can be often found in two or more minerals. In addition, some minerals will often show a lower cosine similarity against a target pixel than other minerals due to spectral distortion even if that mineral is present at that pixel location. The proposed method, therefore, employs a thresholding approach for solving these problems. In this approach, the threshold of the cosine similarity ($C_k$) is determined for each mineral $k$ in the overlapping area as follows:

The basic concept of this procedure is to find $C_k$ giving an acceptable producer’s accuracy for mineral $k$ and to recalculate $C_k$ by relaxing the condition of the producer’s accuracy if its user’s accuracy is not acceptable. Thus the threshold of the cosine similarity is determined for each mineral in the overlapping area, and all minerals that exceed each threshold are selected as candidate minerals for each pixel in the overlapping area.

If two or more minerals remain as candidates for an MS-pixel, the mineral with the highest cosine similarity is basically assigned to that pixel. However, sometimes this mineral is not dominant in that pixel. If such case is observed through comparison between the HS- and the MS-mineral maps, the second or subsequent highest mineral in the cosine similarity can be selected instead of the highest mineral for getting higher consistency between the HS- and the MS-mineral maps. As a result, the MS-based mineral map obtained will become more consistent with the HS-based mineral map.

4.1.

Study Areas

In this paper, AVIRIS and ASTER images acquired around Cuprite and Goldfield, Nevada, USA, were used for validation of the proposed method. Figure 2 shows the locations of these study areas. These areas are covered by various minerals including silicate minerals such as kaolinite and muscovite, sulfate minerals such as alunite, and carbonate minerals such as calcite.^20–23 Small amounts of buddingtonite are also seen in the east side of Highway 95 (shown by “A” in Fig. 3) in the Cuprite study area (referred to as the eastern part of Cuprite).

Fig. 2

Locations of the Cuprite and the Goldfield study areas, Nevada, USA. The photos were taken by the authors.

Fig. 3

Mineral maps derived (a) from the AVIRIS image by the traditional way, and from the AST_07XT image (b) by the K&P method and (c) by the proposed method (blue, kaolinite; red, alunite; pink, muscovite; green, calcite; and yellow, buddingtonite).

4.2.

Mineral Mapping Using the AVIRIS Image

The AVIRIS image used was acquired over the study areas on September 20, 2006, with a ground resolution of 15.7 m (flight name: f060920t01p00r05). The wavelength region used is from 1967 to 2496 nm, because this spectral region allows identification of some important minerals,¹⁵ and also because we compare the results with the published papers on the K&P method.^14,15 First, the image was atmospherically corrected by the FLAASH module on the ENVI software,²⁴ and then converted to the surface reflectance image. Then mineral mapping was performed with this image by the MNF conversion, the PPI analysis, the endmember extraction, and the SAM method implemented in the ENVI software. This processing is referred to as the traditional way from now on.

The result of mineral mapping is displayed by Fig. 3(a), where kaolinite, alunite, muscovite, calcite, and buddingtonite are shown in blue, red, pink, green, and yellow, respectively. This color assignment is used for the following figures in this paper. Unclassified pixels are displayed by the grayscale image of AVIRIS band 171 (1976 nm), and this way is also applied to (a) in Figs. 4Fig. 5–6. Figure 3 shows that the eastern part of Cuprite has annularly distributed alunite with surrounding kaolinite, and small amounts of buddingtonite, and the western part of Cuprite (shown by “B” in Fig. 3) has alunite surrounded by kaolinite, muscovite, and calcite. The Goldfield area located in the north of Cuprite is shown to be dominated by muscovite with surrounding kaolinite and alunite. These classification results are visually consistent with previously published studies.^22,23

Fig. 4

Mineral maps derived (a) from the AVIRIS image by the traditional way, and from the ASTER simulation image (b) by the K&P method and (c) by the proposed method (blue, kaolinite; red, alunite; pink, muscovite; green, calcite; and yellow, buddingtonite).

Fig. 5

Mineral maps derived (a) from the AVIRIS image by the traditional way, and from the spectrally modified ASTER simulation image (b) by the K&P method and (c) by the proposed method (blue, kaolinite; red, alunite; pink, muscovite; green, calcite; and yellow, buddingtonite).

Fig. 6

Mineral maps derived (a) from the AVIRIS image by the traditional way, and from the shifted ASTER simulation image (b) by the K&P method and (c) by the proposed method (blue, kaolinite; red, alunite; pink, muscovite; green, calcite; and yellow, buddingtonite).

4.3.

Mineral Mapping Using the ASTER Image

The ASTER image used is the shortwave infrared (SWIR) image provided as the ASTER Surface Reflectance VNIR and Crosstalk Corrected SWIR (AST_07XT) product, acquired with a ground resolution of 30 m over the both study areas on August 15, 2006 (local granule ID: AST_07XT_00308152006183834_20180112005948_22159). Using this ASTER image and the previous AVIRIS image, mineral mapping was performed using the following procedures.

First, the AVIRIS image (15.7-m resolution) and the ASTER image (30-m resolution) were co-registered with resampling to ASTER’s pixel resolution (30 m). In this processing, both images were co-registered based on geolocation information attached to each image, and then visually adjusted by parallel translation in integer pixels using a feature point near the center line of the AVIRIS image around the Cuprite study area.

Next, the K&P and the proposed methods were applied to the pair of the AVIRIS and the ASTER images. In these methods, the Cuprite area was defined as the overlapping area of the HS- and the MS-images, and the Goldfield area was defined as the nonoverlapping area covered by only the MS-image. These definitions are used also in the following sections. The HS-image acquired over the Goldfield study area is used only for evaluating the results of the K&P and the proposed methods. In the proposed method, MS-based endmember pixels were selected from each subarea divided based on distributions of the HS-based endmembers, where subareas with a co-registration error of one or more pixels were additionally co-registered by parallel translation in integer pixels using a feature point in each subarea. The thresholding method mentioned in Sec. 3.3 was applied not only to the proposed method but also to the K&P method. In the two methods, alunite was exceptionally assigned to all pixels that alunite remained as one of candidates, resulting in higher consistency with the HS-based mineral map.

Figures 3(b) and 3(c) show the mineral maps obtained by the K&P and the proposed methods, respectively. Unclassified pixels are displayed by the grayscale image of ASTER/SWIR band 5, and this way is also applied to (b) and (c) in Figures 4 to 6. In Figs. 3(b) and 3(c), kaolinite, muscovite, and calcite have many spike-like noises caused by noises on the ASTER image. The K&P method misclassified some muscovite as kaolinite and could not detect buddingtonite, probably because of spectral inconsistency between the AVIRIS and the ASTER images, as discussed in Sec. 5.3. On the other hand, the proposed method demonstrates better agreement with the AVIRIS-based map than the K&P method. For example, the distributions of alunite and kaolinite in the eastern part of Cuprite (shown by “A” in Fig. 3) show similar patterns with the AVIRIS-based map, and buddingtonite exists in only the eastern part of Cuprite, not in the western part of Cuprite (shown by “B” in Fig. 3) and the Goldfield area. In the western part of Cuprite, alunite is surrounded by kaolinite, muscovite, and calcite, as shown in the AVIRIS-based map. In the Goldfield area, muscovite and kaolinite are correctly separated, though calcite was partly misclassified. As for a part of the western part of Cuprite, it is known that kaolinite and muscovite occur as mixtures and cannot be easily discriminated even using the AVIRIS image.^20,21

Table 1 provides the producer’s accuracy and the user’s accuracy for the K&P and the proposed methods in the Cuprite and Goldfield areas, assuming that the AVIRIS-based map represents the true distribution of minerals on the ground. In this table, a hyphen for the producer’s accuracy means that no pixel was classified as that mineral in the AVIRIS-based map, and a hyphen for the user’s accuracy means that no pixel was classified as that mineral by the K&P or the proposed methods.

Table 1

The producer’s and the user’s accuracies of the K&P and the proposed methods with the AST_07XT image in the Cuprite and the Goldfield areas for each mineral. Each value in bold face is more than 5% better than the other.

As for muscovite, the producer’s accuracy is better in the proposed method, and the user’s accuracy is better in the K&P method. As for calcite, the producer’s accuracy is much better in the proposed method, whereas the user’s accuracy is a little better in the K&P method. Buddingtonite in the Cuprite area was detected by the proposed method partly, but not by the K&P method. The producer’s accuracy and the user’s accuracy for alunite are almost same between the two methods. As for kaolinite, the producer’s accuracy is better in the K&P method, and the user’s accuracy is better in the proposed method.

5.1.

Overview

It is expected that the proposed method is less sensitive to inaccuracies from radiometric calibration and atmospheric correction than the K&P method. In order to confirm this, we evaluated the two methods using an ASTER simulation image. This image was generated by weighting the AVIRIS surface reflectance image with the response functions of ASTER’s SWIR bands (bands 4 to 9). Using the ASTER simulation image, the two methods can be evaluated without geometric or radiometric errors.

5.2.

Mineral Mapping Using the ASTER Simulation Image

The K&P and the proposed methods were applied to the AVIRIS image and the ASTER simulation image. The definitions of the overlapping and the nonoverlapping areas were same with Sec. 4.3. The thresholding of the cosine similarity with the exceptional assignment of alunite was applied to the two methods in the same way as Sec. 4.3.

Figure 4 displays the mineral maps obtained from the AVIRIS image and from the ASTER simulation image by each method, showing similar distributions of minerals between the two methods. Table 2 provides the producer’s accuracy and the user’s accuracy for each method for the Cuprite and the Goldfield areas, assuming that the AVIRIS-based map represents the true distribution of minerals on the ground. In the Cuprite area, the K&P and the proposed methods show the producer’s accuracy of about 90% for alunite and muscovite, though showing the user’s accuracy of about 50% for muscovite. As for kaolinite, the producer’s accuracy and the user’s accuracy decreased to 50% or 60% in the two methods, mainly because some of kaolinite in the western part of Cuprite (shown by “C” in Fig. 4) were misclassified as muscovite. Since kaolinite and muscovite occur as mixtures around the area “C,”^20,21 it is not easy to discriminate these minerals even by AVIRIS-based mineral mapping, so that the producer’s accuracy decreased by a small difference in the cosine similarity between kaolinite and muscovite, particularly in the proposed method. On the other hand, the both methods performed well for buddingtonite and calcite—particularly buddingtonite seen in only the eastern part of Cuprite shows the producer’s accuracy of about 80% and the user’s accuracy of about 90%. In the Goldfield area, the producer’s accuracy for calcite and buddingtonite was not calculated because they were not detected in AVIRIS-based mineral mapping, though calcite was incorrectly detected and the user’s accuracy for it is 0.0% in the two methods. Muscovite, alunite, and kaolinite were successfully discriminated by each method.

Table 2

The producer’s and the user’s accuracies of the K&P and the proposed methods with the ASTER simulation image in the Cuprite and the Goldfield areas for each mineral. Each value in bold face is more than 5% better than the other.

5.3.

Mineral Mapping Using the Spectrally Modified ASTER Simulation Image

For investigation of sensitivity of each method to spectral distortion in the MS image, the spectrally modified ASTER simulation image which was spectrally consistent with the AST_07XT image used in Sec. 4.3 for each mineral and was consistent with the AVIRIS image except for spectral bands and spectral distortion was generated as follows. First, the surface reflectance ratio of the AST_07XT-based endmember (Sec. 4.3) to the ASTER simulation-based endmember (Sec. 5.2) was calculated at each band for each mineral. Then the ratio of each band was averaged over all minerals and then multiplied to the surface reflectance of the ASTER simulation image for each band. Applying the K&P and the proposed methods to this spectrally modified ASTER simulation image, we can evaluate the influence of spectral distortion for each method.

Figure 5 shows the mineral maps obtained from the AVIRIS image and the spectrally modified ASTER simulation image by each method, and Table 3 gives the producer’s accuracy and the user’s accuracy for each case, assuming that the AVIRIS-based map represents the true distribution of minerals on the ground. The thresholding of the cosine similarity with the exceptional assignment of alunite was applied to the two methods in the same way as Sec. 4.3. As shown, the K&P method failed to classify muscovite and kaolinite correctly, as described by Kruse et al.⁶ Particularly, the producer’s accuracy for muscovite is much lower in the K&P method than in the proposed method, because muscovite and kaolinite had similar spectra due to spectral distortion and the K&P method is sensitive to such error factor. The reason why the K&P method gives higher producer’s accuracy for kaolinite than the proposed method is because the proposed method classified kaolinite as muscovite in the mixed area of them (C in Fig. 4)—actually, the user’s accuracy for kaolinite is lower in the K&P method than in the proposed method. The K&P method failed to detect buddingtonite, because the threshold used in the SAM method could not be determined for buddingtonite. Calcite and alunite show similar performance in the two methods, because the spectra of these minerals were not strongly affected by spectral distortion due to their unique shapes. As a whole, the proposed method shows more consistent results with the AVIRIS image, which indicates that the proposed method is more robust against spectral distortion than the K&P method.

Table 3

The producer’s and the user’s accuracies of the K&P and the proposed methods with the spectrally modified ASTER simulation image in the Cuprite and the Goldfield areas for each mineral. Each value in bold face is more than 5% better than the other.

5.4.

Mineral Mapping Using the Shifted ASTER Simulation Image

For investigation of sensitivity of each method to co-registration errors between the HS- and the MS-images, the ASTER simulation image was shifted by $+2\text{pixels}$ toward the right and $+2\text{pixels}$ toward the upper. This shifted ASTER simulation image is consistent with the AVIRIS image except for spectral bands and pixel positions. In calculation of the producer’s accuracy and the user’s accuracy, the shifted ASTER simulation image was shifted back to the original position of the AVIRIS image.

Figure 6 shows the mineral maps obtained from the AVIRIS image and the shifted ASTER simulation image by each method, and Table 4 gives the producer’s accuracy and the user’s accuracy for each case, assuming that the AVIRIS-based map represents the true distribution of minerals on the ground. The thresholding of the cosine similarity with the exceptional assignment of alunite was applied to the two methods in the same way as Sec. 4.3. As shown, the results by the K&P method are almost same with those for the ASTER simulation image (Sec. 5.2), supporting our prediction that the K&P method should be robust against co-registration errors in principle, though these results are dependent on homogeneity of the study areas to some extent. On the other hand, the proposed method performed well for muscovite and calcite, but less well for buddingtonite, alunite, and kaolinite in the two areas. For example, most of areas classified as kaolinite in the ASTER simulation image (Sec. 5.2) are misclassified as alunite. Also a part of areas classified as alunite and kaolinite in the Cuprite area are misclassified as buddingtonite. Thus the producer’s accuracies for buddingtonite and kaolinite reduced almost by half, and the user’s accuracy for buddingtonite is just 0.5%. The accuracies for alunite also decreased, though only the producer’s accuracy in the Goldfield area increased.

Table 4

The producer’s and the user’s accuracies of the K&P and the proposed methods with the shifted ASTER simulation image in the Cuprite and the Goldfield areas for each mineral. Each value in bold face is more than 5% better than the other.

The reason why the proposed method performed well in muscovite and calcite but less well in buddingtonite, alunite, and kaolinite is because the endmember spectra of the latter minerals are not consistent between the ASTER simulation image and the shifted one due to spatial distributions that involve widely separated exposures of small areal extent, unlike the former minerals, as shown by Fig. 7. It must, therefore, be recognized that the proposed method is sensitive to co-registration errors for minerals with such spatial distributions. In the case of the K&P method, the ASTER simulation image and the shifted one provided almost same spectra for all minerals. The spectra obtained from the shifted one by the K&P method are displayed in Fig. 7 for comparison to the spectra of the proposed method.

Fig. 7

Comparison of the endmember spectra obtained from the ASTER simulation image (no shifted) and the shifted one by the proposed method, and from the shifted one by the K&P method, for each mineral.