Spectral Domain Noise Suppression in Dual-Sensor ... - Springer Link
Spectral Domain Noise Suppression in Dual-Sensor Hyperspectral Imagery Using Gaussian Processes Arman Melkumyan and Richard J. Murphy Australian Centre for Field Robotics, Rose Street Building J04 The University of Sydney, NSW, Australia, 2006 [email protected], [email protected]
Abstract. The use of hyperspectral data is limited, in part, by increased spectral noise, particularly at the extremes of the wavelength ranges sensed by scanners. We apply Gaussian Processes (GPs) as a preprocessing step prior to extracting mineralogical information from the image using automated feature extraction. GPs are a probabilistic machine learning technique that we use for suppressing noise in the spectral domain. The results demonstrate that this approach leads to large reductions in the amount of noise, leading to major improvements in our ability to automatically quantify the abundance of iron and clay minerals in hyperspectral data acquired from vertical mine faces. Keywords: Hyperspectral, Gaussian Processes, Machine Learning, Feature Extraction, Absorption Feature, Iron minerals.
1 Introduction Technological and methodological developments over the past 25 years have enabled remote identification, quantification and mapping of geological and biological materials on the Earth’s surface using hyperspectral imagery. Hyperspectral imagery is most commonly acquired from airborne platforms. Continuing improvements in sensor technology have, however, enabled imagery to be acquired, cost-effectively, from field-based platforms for several applications including mapping of geology and mineraology [1]. Hyperspectral sensors typically measure reflected electromagnetic radiation in 10s to 100s of discrete, contiguous bands between 400 nm and 2500 nm. Hyperspectral data enables absorption features, diagnostic of many biogeochemical materials, to be measured in a semi-continuous spectrum, enabling identification rather than mere separation of components [2] and [3]. Hyperspectral bands are narrow (< 6nm), and are often noisy in the spectral domain. Technological constraints mean that hyperspectral data are collected using different sensors to sample the Visible Near-InfraRed (VNIR; 400 – 1000 nm) and Short-Wave Infra-Red (SWIR; 1000 nm – 2500 nm) parts of the spectrum. Decreasing solar irradiance towards longer wavelengths, means that SWIR data are often acquired at a coarser spatial K.W. Wong et al. (Eds.): ICONIP 2010, Part II, LNCS 6444, pp. 684–691, 2010. © Springer-Verlag Berlin Heidelberg 2010
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resolution than are VNIR, allowing light to be collected over a greater area of ground. This means that data from the VNIR and SWIR sensors have to be spatially-registered after acquisition. The separate image cubes are then merged in the spectral domain so that each image pixel describes a complete spectral signature between 400 nm and 2500 nm. Merging of these data presents problems for their subsequent analyses: 1) decreasing sensitivity of the sensors causes increasing noise towards the extremes of the VNIR spectrum (< 480 nm; > 960 nm); 2) the reflectance at long-wavelength terminus of the VNIR spectrum may not exactly match that of the short-wavelength terminus of the SWIR data, causing abrupt positive or negative changes in reflectance at this join; 3) the spectral join is located in the same part of the spectrum as a diagnostic absorption feature associated with iron minerals (Fig. 1), making the quantification of this feature difficult. We propose a method based on Gaussian processes (GPs) [4] for suppressing noise in the spectrum at all wavelengths, with the primary objective of smoothing the spectrum across the wavelengths at, or close to, the junction of the data acquired by the two different sensors. This is a fully automated GP-based machine learning algorithm which uses the squared exponential covariance function [4] to learn the data provided by the sensors and suppress noise. Once spectral noise has been suppressed for each of the sensors, the algorithm compensates for the possible reflectance mismatch at the termini of VNIR and SWIR spectra, thus providing a single smoothed curve for all the wavelengths of interest. The smoothed spectral curve is then used to parameterize absorption features in the spectrum.
2 Materials and Methods 2.1 Hyperspectral Data Hyperspectral imagery was acquired from a vertical mine face in an open-pit iron ore mine in Hamersley Province, Western Australia. Scanning VNIR and SWIR sensors (Specim, Finland) were mounted adjacently on a rotating stage. A reflectance panel (~ 99% Spectralon ®) was placed within the field of view of the sensors. Data at each band, in each sensor, were corrected for dark current and converted to reflectance using pixel values over the calibration panel [5]. Data from the sensors were spatially-registered using multiple ground control points and merged into a single data-cube comprising 390 bands (400 – 2334 nm). 2.2 Gaussian Processes for Machine Learning This section provides a brief introduction to GPs. Consider the supervised learning problem with a training set D = ( xi , yi ) , i = 1: N , consisting of N input points xi and the corresponding outputs yi . The objective is to compute the predictive distribution f ( x∗ ) at a new test point x ∗ . The GP model uses a covariance function to place a
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multivariate Gaussian distribution over the space of function variables f ( x) mapping input to output spaces. This multivariate Gaussian distribution is then conditioned on the observed training dataset, resulting in a new predictive distribution for the points x ∗ : p ( f∗ | X ∗ , X , y ) = N ( μ∗ , Σ∗ ) where μ∗ is the predicted mean and Σ∗ is the predicted covariance. During the learning stage GP model determines the hyper-parameters of the covariance function from the training dataset. In a Bayesian framework this can be performed by maximizing the log of the marginal likelihood (lml). The lml incorporates both data fit and complexity penalty to avoid possible overfitting of the dataset. This is a non-convex optimization task which can be performed using the gradient descent techniques with multiple starting points. For further information on GPs and detailed mathematical derivations refer to [4]. VNIR
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Fig. 1. Reflectance spectra of Goethite from individual image pixels. The spectral regions sensed by the VNIR and SWIR sensors are shown (dotted vertical lines).
2.3 Absorption Feature Extraction and Parameterization To determine if Gaussian smoothing improved outcomes of spectral analysis, we compared the results from an Automated Feature Extraction (AFE) technique applied to the original and GP-smoothed image data. AFE automatically identifies absorption features and describes them in terms of a small number of parameters including, wavelength position, depth and width [6]. In the case of minerals, wavelength position is indicative of mineral type, depth is indicative of the mineral abundance and width is indicative of both type and abundance. The basic concept of AFE is shown in Fig. 2 using a reflectance spectrum of goethite, acquired using a non-imaging field spectrometer (ASD, Boulder, Co.). In comparison to imaging spectrometers, field spectrometers produce relatively noisefree spectra (cf. Fig. 2a, Fig. 1). Several absorption associated with Fe3+ are evident
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(Fig. 2a). The first stage of AFE is to remove the spectral continuum by dividing the spectrum by its upper convex hull (dotted line, Fig. 2a), at each wavelength. The resulting hull-quotients spectrum places all absorptions on the same plane of reference (Fig. 2b) [7]. The second stage identifies the wavelength position of the centre of an absorption feature and its shoulders (where the spectrum reaches unity); from these the other parameters are calculated. This is repeated for all absorptions in the spectrum.
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Fig. 2. Library spectrum of goethite: a) reflectance (solid line) showing 3 absorptions due to ferric iron (Fe3+). The continuum is fitted over spectral maxima (gray dashed line). Data near 1400 nm and 1900 nm are not shown as they are affected by atmospheric water vapour. b) hullquotients spectrum. The parameters (wavelength position, depth and width), derived from each absorption feature are indicated. The spectral region used to process the image data is indicated (solid black line).
Hyperspectral imagery from vertical mine faces can be used to determine their mineralogical composition and to separate ore from waste materials. Ore-bearing rocks have strong absorptions between 500 – 1300 nm. Some waste materials, mainly shale, can be distinguished by an absorption feature at 2208 nm caused by the clay mineral kaolinite. Parameterization of these absorption features using AFE enables ore to be separated from waste. Noise in image spectra strongly impacts all stages of AFE, making the determination of feature parameters inaccurate and imprecise.
3 Results 3.1 Effects on Image Spectra Individual pixel spectra from areas of goethite and shale were extracted from the original and GP-smoothed images (Fig. 3). The original image spectra show large variations in reflectance caused by noise (Fig. 3, top panel). GP smoothing produces a seamless spectrum which is similar to the library spectrum acquired by the field spectrometer (cf. Fig. 3a, Fig. 2a). The hull-quotients spectra (lower panel) from GPsmoothed data are continuous and AFE now becomes straightforward.
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Fig. 3. Reflectance (top) and hull-quotients (bottom) spectra from individual image pixels; a) goethite, b) shale. Original (circles) and GP-smoothed (solid line) spectra show large differences. The parameters of the strongest absorption feature are shown in the bottom graphs: wavelength position (λ); depth (D) and width (W).
3.2 Effects on Parameter Images GP smoothing of the image in spectral domain had no effect on the spatial domain. There were, however, major spatial improvements in the parameter images derived from GP-smoothed data. Mapping in the field indicated that the mine face was made up of distinct geological zones (Fig. 4). An image of the depth parameter derived from the original image (Fig. 5a) shows greater depth, in zones 3 – 6, of the iron absorption at ~ 950-1000 nm. Some iron is present in the zones 1 & 2. There are no consistent changes in the depth of the feature among zones 3-6, indicating, incorrectly, that no single zone has more iron than another. The image of depth derived from the GP-smoothed image (Fig. 5b) showed an improved distinction between the ore and waste zones and zone 5 was correctly delimited from adjacent zones based on its iron content. Shales are distinguished by the presence of the ~2208 nm absorption due to kaolinite. The depth parameter of this feature, derived from the original image (Fig. 6a), showed increased amounts of kaolinite in zone 1 and, in particular, zone 2 but incorrectly quantified kaolinite in zones 3-6. In the less-noisy depth image, derived from GP-smoothed data (Fig. 6b), ore zones (3-6) are now accurately distinguished from the shales (1&2) and there is improved discrimination of linear variations in kaolinite in zone 2.
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Fig. 4. Image of a mine face showing geological boundaries: 1) shale with moderate kaolinite; 2) manganiferous shale with abundant kaolinite; 3) mixed shale and goethite; 4) goethite; 5) martite-goethite; 6) martite and chert. Zones 1 & 2 are waste. Zones 3-6 are ore-bearing rocks, zone 5 being particularly abundant in iron.
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Fig. 5a. Depth parameter from the original image, for the deepest absorption feature. Pixel brightness in all images is proportional to the depth of the absorption feature. 6
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Fig. 5b. Depth parameter generated from the GP-smoothed image, for the deepest absorption feature. Zone 5, particularly iron-rich, is now distinguished.
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Fig. 6a. Depth parameter generated from original image, for the deepest absorption feature between 2000 nm and 2500 nm.
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Fig. 6b. Depth parameter generated from the GP-smoothed image, for the deepest absorption feature in the spectrum between 2000 nm and 2500 nm.
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Fig. 7. Scatterplots of pixel values for each parameter, derived from the original and GPsmoothed data, superimposed with average parameter values for 5 rock types derived from the spectral library (large symbols). The minimum and maximum of values for each parameter derived from the library are indicated by straight lines.
3.3 Comparison of Parameters from the Image and Spectral Library The images of wavelength position, depth and width were compared with the same parameters derived from a spectral library of 5 rock types found at the mine site (Fig. 7). The depth parameter from the GP-smoothed data had most values within the minimum and maximum values of the library spectra. Greater than 50% of pixels in the original image had values much greater than the maximal depth derived from the library spectra. The average depth of the absorption derived from library spectra, fell within the range of the values measured from the image. This was not true for depth derived from original image, where the depth parameter for one rock type - manganiferous shale (◊) was below the limits defined by the pixel values for the original, but not the GPsmoothed data. Similarly, most pixel values for the width parameter derived from the GP-smoothed data fell within the limits of the library spectra but many from the original image fell below the minimal library limit. The majority of pixel values representing wavelength position derived from the GP-smoothed data, were within the limits derived from the library spectra, but were incorrectly partitioned into 2 discrete groups when derived from the original image. This is entirely due to spectral noise.
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4 Conclusions Noise in the spectral domain can have a deleterious impact on many techniques used to analyse hyperspectral imagery. The GP-smoothing method presented here greatly improved the discrimination and quantification of minerals in hyperspectral imagery of a vertical mine face. Used as a preprocessing step to AFE, the GP method enabled areas of abundant iron within the ore zones to be discriminated which were not distinguished in the original data. After application of GP-smoothing, absorptions indicative of kaolinite could be parameterized with high-specificity, enabling the separation of ore from waste materials and improving interpretation of the structure of the mine face. Further work is currently underway to improve results by incorporating spatial information.
Acknowledgments This work has been supported by the Rio Tinto Centre for Mine Automation and the ARC Centre of Excellence programme, funded by the Australian Research Council (ARC) and the New South Wales State Government.
References 1. Herrala, R., Okkonen, J., Hyvärinen, T., Aikio, M., Lammasniemi, J.: Imaging Spectrometer for Process Industry Applications. In: European Symposium on Optics for Productivity in Manufacturing Optical Measurements and Sensors for the Process Industries, pp. 33–40. SPIE (1994) 2. Vane, G., Goetz, A.F.H.: Terrestrial Imaging Spectroscopy. Remote Sens. Environ. 24, 1– 29 (1988) 3. Clark, R.N., Kind, T.V.V., Klejwa, M., Swayze, G.A.: High Resolution Reflectance Spectroscopy of Minerals. J. Geophys. Res. 95, 1265–12680 (1990) 4. Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006) 5. Murphy, R.J., Underwood, A.J., Pinkerton, M.H.: Quantitative Imaging to Measure Photosynthetic Biomass on an Intertidal Rock Platform. Mar. Ecol. Prog. Ser. 312, 45–55 (2006) 6. Kruse, F.A.: Use of Imaging Spectrometer Data to Map Minerals Associated with Hydrothermally Altered Rocks in the Northern Grapevine Mountains, Nevada, and California. Remote Sens. Environ. 24, 31–51 (1988) 7. Clark, R.N., Roush, T.L.: Reflectance Spectroscopy: Quantitative Analysis Techniques for Remote Sensing Applications. J. Geophys. Res. 89, 6329–6340 (1984)
Abstract. The use of hyperspectral data is limited, in part, by increased spectral noise, particularly at the extremes of the wavelength ranges sensed by scanners. We apply Gaussian Processes (GPs) as a preprocessing step prior to extracting mineralogical information from the image using automated feature extraction. GPs are a probabilistic machine learning technique that we use for suppressing noise in the spectral domain. The results demonstrate that this approach leads to large reductions in the amount of noise, leading to major improvements in our ability to automatically quantify the abundance of iron and clay minerals in hyperspectral data acquired from vertical mine faces. Keywords: Hyperspectral, Gaussian Processes, Machine Learning, Feature Extraction, Absorption Feature, Iron minerals.
1 Introduction Technological and methodological developments over the past 25 years have enabled remote identification, quantification and mapping of geological and biological materials on the Earth’s surface using hyperspectral imagery. Hyperspectral imagery is most commonly acquired from airborne platforms. Continuing improvements in sensor technology have, however, enabled imagery to be acquired, cost-effectively, from field-based platforms for several applications including mapping of geology and mineraology [1]. Hyperspectral sensors typically measure reflected electromagnetic radiation in 10s to 100s of discrete, contiguous bands between 400 nm and 2500 nm. Hyperspectral data enables absorption features, diagnostic of many biogeochemical materials, to be measured in a semi-continuous spectrum, enabling identification rather than mere separation of components [2] and [3]. Hyperspectral bands are narrow (< 6nm), and are often noisy in the spectral domain. Technological constraints mean that hyperspectral data are collected using different sensors to sample the Visible Near-InfraRed (VNIR; 400 – 1000 nm) and Short-Wave Infra-Red (SWIR; 1000 nm – 2500 nm) parts of the spectrum. Decreasing solar irradiance towards longer wavelengths, means that SWIR data are often acquired at a coarser spatial K.W. Wong et al. (Eds.): ICONIP 2010, Part II, LNCS 6444, pp. 684–691, 2010. © Springer-Verlag Berlin Heidelberg 2010
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resolution than are VNIR, allowing light to be collected over a greater area of ground. This means that data from the VNIR and SWIR sensors have to be spatially-registered after acquisition. The separate image cubes are then merged in the spectral domain so that each image pixel describes a complete spectral signature between 400 nm and 2500 nm. Merging of these data presents problems for their subsequent analyses: 1) decreasing sensitivity of the sensors causes increasing noise towards the extremes of the VNIR spectrum (< 480 nm; > 960 nm); 2) the reflectance at long-wavelength terminus of the VNIR spectrum may not exactly match that of the short-wavelength terminus of the SWIR data, causing abrupt positive or negative changes in reflectance at this join; 3) the spectral join is located in the same part of the spectrum as a diagnostic absorption feature associated with iron minerals (Fig. 1), making the quantification of this feature difficult. We propose a method based on Gaussian processes (GPs) [4] for suppressing noise in the spectrum at all wavelengths, with the primary objective of smoothing the spectrum across the wavelengths at, or close to, the junction of the data acquired by the two different sensors. This is a fully automated GP-based machine learning algorithm which uses the squared exponential covariance function [4] to learn the data provided by the sensors and suppress noise. Once spectral noise has been suppressed for each of the sensors, the algorithm compensates for the possible reflectance mismatch at the termini of VNIR and SWIR spectra, thus providing a single smoothed curve for all the wavelengths of interest. The smoothed spectral curve is then used to parameterize absorption features in the spectrum.
2 Materials and Methods 2.1 Hyperspectral Data Hyperspectral imagery was acquired from a vertical mine face in an open-pit iron ore mine in Hamersley Province, Western Australia. Scanning VNIR and SWIR sensors (Specim, Finland) were mounted adjacently on a rotating stage. A reflectance panel (~ 99% Spectralon ®) was placed within the field of view of the sensors. Data at each band, in each sensor, were corrected for dark current and converted to reflectance using pixel values over the calibration panel [5]. Data from the sensors were spatially-registered using multiple ground control points and merged into a single data-cube comprising 390 bands (400 – 2334 nm). 2.2 Gaussian Processes for Machine Learning This section provides a brief introduction to GPs. Consider the supervised learning problem with a training set D = ( xi , yi ) , i = 1: N , consisting of N input points xi and the corresponding outputs yi . The objective is to compute the predictive distribution f ( x∗ ) at a new test point x ∗ . The GP model uses a covariance function to place a
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multivariate Gaussian distribution over the space of function variables f ( x) mapping input to output spaces. This multivariate Gaussian distribution is then conditioned on the observed training dataset, resulting in a new predictive distribution for the points x ∗ : p ( f∗ | X ∗ , X , y ) = N ( μ∗ , Σ∗ ) where μ∗ is the predicted mean and Σ∗ is the predicted covariance. During the learning stage GP model determines the hyper-parameters of the covariance function from the training dataset. In a Bayesian framework this can be performed by maximizing the log of the marginal likelihood (lml). The lml incorporates both data fit and complexity penalty to avoid possible overfitting of the dataset. This is a non-convex optimization task which can be performed using the gradient descent techniques with multiple starting points. For further information on GPs and detailed mathematical derivations refer to [4]. VNIR
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Fig. 1. Reflectance spectra of Goethite from individual image pixels. The spectral regions sensed by the VNIR and SWIR sensors are shown (dotted vertical lines).
2.3 Absorption Feature Extraction and Parameterization To determine if Gaussian smoothing improved outcomes of spectral analysis, we compared the results from an Automated Feature Extraction (AFE) technique applied to the original and GP-smoothed image data. AFE automatically identifies absorption features and describes them in terms of a small number of parameters including, wavelength position, depth and width [6]. In the case of minerals, wavelength position is indicative of mineral type, depth is indicative of the mineral abundance and width is indicative of both type and abundance. The basic concept of AFE is shown in Fig. 2 using a reflectance spectrum of goethite, acquired using a non-imaging field spectrometer (ASD, Boulder, Co.). In comparison to imaging spectrometers, field spectrometers produce relatively noisefree spectra (cf. Fig. 2a, Fig. 1). Several absorption associated with Fe3+ are evident
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(Fig. 2a). The first stage of AFE is to remove the spectral continuum by dividing the spectrum by its upper convex hull (dotted line, Fig. 2a), at each wavelength. The resulting hull-quotients spectrum places all absorptions on the same plane of reference (Fig. 2b) [7]. The second stage identifies the wavelength position of the centre of an absorption feature and its shoulders (where the spectrum reaches unity); from these the other parameters are calculated. This is repeated for all absorptions in the spectrum.
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Fig. 2. Library spectrum of goethite: a) reflectance (solid line) showing 3 absorptions due to ferric iron (Fe3+). The continuum is fitted over spectral maxima (gray dashed line). Data near 1400 nm and 1900 nm are not shown as they are affected by atmospheric water vapour. b) hullquotients spectrum. The parameters (wavelength position, depth and width), derived from each absorption feature are indicated. The spectral region used to process the image data is indicated (solid black line).
Hyperspectral imagery from vertical mine faces can be used to determine their mineralogical composition and to separate ore from waste materials. Ore-bearing rocks have strong absorptions between 500 – 1300 nm. Some waste materials, mainly shale, can be distinguished by an absorption feature at 2208 nm caused by the clay mineral kaolinite. Parameterization of these absorption features using AFE enables ore to be separated from waste. Noise in image spectra strongly impacts all stages of AFE, making the determination of feature parameters inaccurate and imprecise.
3 Results 3.1 Effects on Image Spectra Individual pixel spectra from areas of goethite and shale were extracted from the original and GP-smoothed images (Fig. 3). The original image spectra show large variations in reflectance caused by noise (Fig. 3, top panel). GP smoothing produces a seamless spectrum which is similar to the library spectrum acquired by the field spectrometer (cf. Fig. 3a, Fig. 2a). The hull-quotients spectra (lower panel) from GPsmoothed data are continuous and AFE now becomes straightforward.
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Fig. 3. Reflectance (top) and hull-quotients (bottom) spectra from individual image pixels; a) goethite, b) shale. Original (circles) and GP-smoothed (solid line) spectra show large differences. The parameters of the strongest absorption feature are shown in the bottom graphs: wavelength position (λ); depth (D) and width (W).
3.2 Effects on Parameter Images GP smoothing of the image in spectral domain had no effect on the spatial domain. There were, however, major spatial improvements in the parameter images derived from GP-smoothed data. Mapping in the field indicated that the mine face was made up of distinct geological zones (Fig. 4). An image of the depth parameter derived from the original image (Fig. 5a) shows greater depth, in zones 3 – 6, of the iron absorption at ~ 950-1000 nm. Some iron is present in the zones 1 & 2. There are no consistent changes in the depth of the feature among zones 3-6, indicating, incorrectly, that no single zone has more iron than another. The image of depth derived from the GP-smoothed image (Fig. 5b) showed an improved distinction between the ore and waste zones and zone 5 was correctly delimited from adjacent zones based on its iron content. Shales are distinguished by the presence of the ~2208 nm absorption due to kaolinite. The depth parameter of this feature, derived from the original image (Fig. 6a), showed increased amounts of kaolinite in zone 1 and, in particular, zone 2 but incorrectly quantified kaolinite in zones 3-6. In the less-noisy depth image, derived from GP-smoothed data (Fig. 6b), ore zones (3-6) are now accurately distinguished from the shales (1&2) and there is improved discrimination of linear variations in kaolinite in zone 2.
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Fig. 4. Image of a mine face showing geological boundaries: 1) shale with moderate kaolinite; 2) manganiferous shale with abundant kaolinite; 3) mixed shale and goethite; 4) goethite; 5) martite-goethite; 6) martite and chert. Zones 1 & 2 are waste. Zones 3-6 are ore-bearing rocks, zone 5 being particularly abundant in iron.
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Fig. 5a. Depth parameter from the original image, for the deepest absorption feature. Pixel brightness in all images is proportional to the depth of the absorption feature. 6
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Fig. 5b. Depth parameter generated from the GP-smoothed image, for the deepest absorption feature. Zone 5, particularly iron-rich, is now distinguished.
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Fig. 6a. Depth parameter generated from original image, for the deepest absorption feature between 2000 nm and 2500 nm.
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Fig. 6b. Depth parameter generated from the GP-smoothed image, for the deepest absorption feature in the spectrum between 2000 nm and 2500 nm.
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Fig. 7. Scatterplots of pixel values for each parameter, derived from the original and GPsmoothed data, superimposed with average parameter values for 5 rock types derived from the spectral library (large symbols). The minimum and maximum of values for each parameter derived from the library are indicated by straight lines.
3.3 Comparison of Parameters from the Image and Spectral Library The images of wavelength position, depth and width were compared with the same parameters derived from a spectral library of 5 rock types found at the mine site (Fig. 7). The depth parameter from the GP-smoothed data had most values within the minimum and maximum values of the library spectra. Greater than 50% of pixels in the original image had values much greater than the maximal depth derived from the library spectra. The average depth of the absorption derived from library spectra, fell within the range of the values measured from the image. This was not true for depth derived from original image, where the depth parameter for one rock type - manganiferous shale (◊) was below the limits defined by the pixel values for the original, but not the GPsmoothed data. Similarly, most pixel values for the width parameter derived from the GP-smoothed data fell within the limits of the library spectra but many from the original image fell below the minimal library limit. The majority of pixel values representing wavelength position derived from the GP-smoothed data, were within the limits derived from the library spectra, but were incorrectly partitioned into 2 discrete groups when derived from the original image. This is entirely due to spectral noise.
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4 Conclusions Noise in the spectral domain can have a deleterious impact on many techniques used to analyse hyperspectral imagery. The GP-smoothing method presented here greatly improved the discrimination and quantification of minerals in hyperspectral imagery of a vertical mine face. Used as a preprocessing step to AFE, the GP method enabled areas of abundant iron within the ore zones to be discriminated which were not distinguished in the original data. After application of GP-smoothing, absorptions indicative of kaolinite could be parameterized with high-specificity, enabling the separation of ore from waste materials and improving interpretation of the structure of the mine face. Further work is currently underway to improve results by incorporating spatial information.
Acknowledgments This work has been supported by the Rio Tinto Centre for Mine Automation and the ARC Centre of Excellence programme, funded by the Australian Research Council (ARC) and the New South Wales State Government.
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