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Hyperspectral Feature Extraction Based On The Reference Spectral Background Removal Method Hengqian Zhao, Student Member, IEEE, Lifu Zhang, Senior Member, IEEE, Xia Zhang, Jia Liu, Taixia Wu, and Shudong Wang
Abstract—In spectral analysis, diagnostic absorption features can indicate the existence of specific materials. Absorption parameters such as absorption center, absorption width, and absorption depth can be used in not only identification and quantitative analysis of minerals, but also in retrieval of surface physical properties. Continuum removal (CR) is commonly used to extract absorption features. However, for a band range containing more than one absorption contribution factors, the feature extracted by CR could be a result of comprehensive effect of different factors. In this paper, a new spectral feature extraction method named reference spectral background removal (RSBR) is proposed. Given the reference spectral background, RSBR can eliminate the influence of unwanted contribution factor, and extract the absorption feature of target contribution factor. Using RSBR, the basic absorption feature parameters including the absorption center, absorption width, and absorption depth are extracted. The results are compared with those obtained from the CR. It is shown that RSBR can effectively extract pure absorption features of target material, while more accurate absorption parameters can also be achieved. Index Terms—Diagnostic absorption feature, hyperspectral remote sensing, mineralogy, reference spectral background removal (RSBR).
I. I NTRODUCTION
R
EFLECTANCE spectroscopy is the study of light as a function of wavelength that has been reflected from a solid, liquid, or gas, and has been used as a quantitative tool for many years [1]. Many materials, especially minerals, exhibit absorption bands that are diagnostic of specific types and composition [2], [3]. These spectral features can indicate the Manuscript received November 16, 2014; revised December 31, 2014; accepted January 28, 2015. Date of publication March 19, 2015; date of current version July 30, 2015. This work was supported in part by the National Natural Science Foundation of China under Grant 41371362, Grant 41272364, Grant 41371359, and Grant 41202234, and in part by the High Resolution Earth Observing-Water Application Demonstration Program of China under Grant 08-Y30B07-9001-13/15-01. (Corresponding author: Lifu Zhang.) H. Zhao is with the State Key Laboratory Of Remote Sensing Sciences, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China, and also with the University of Chinese Academy of Sciences, Beijing 100101, China (e-mail:
[email protected]). L. Zhang, X. Zhang, J. Liu, T. Wu, and S. Wang are with the State Key Laboratory Of Remote Sensing Sciences, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100101, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTARS.2015.2401052
existence of specific materials. This is the foundation of composition identification using hyperspectral remote sensing [4], [5]. Even, small changes in chemistry affect the waveform, position, and strength of absorption features. Diagnostic absorption features can be described by a series of spectral absorption parameters, such as the band position, depth, width, symmetry, and area. Based on these parameters, both qualitative and quantitative information can be extracted [3]. Among these parameters, the band position, the depth of the absorption feature, and the full width at half-maximum (FWHM) are the most commonly used spectral parameters in mineral analysis [6]. The absorption band position has been shown to be an effective method to distinguish different kinds of minerals [7]. To make an informed judgment about surface composition, an accurate knowledge of the wavelength of certain absorption features is required. The width of absorption is a function of the composition, the absorption band position, and the partitioning of ions [8]. The depth of absorption is relative to the abundance and the grain size of the material [9]. As the measured strength of absorption features is linked in part to the relative proportions of minerals on the surface, the strength of absorption features could be used to interpret the contents of specific elements or mineral species on the surface [10]–[13]. Besides, some factors in the environment have influence on the absorption feature, such as leaf water, and soil moisture [14], [15] By building the statistical relationships between the absorption parameters and environmental stress factors, the influence of these factors can be estimated or removed from remote sensing image. In order to correctly calculate the above absorption parameters, absorption feature should be extracted from the original reflectance spectrum first. The most commonly used method to extract absorption feature is CR. The continuum is a background spectrum based on which the absorption features are superimposed, and could be expressed as a mathematical function of nonselective absorption and scattering as well as broad wavelength selective absorptions [16], [17]. The spectral properties defining the continuum are partially controlled by the physical properties of the surface (particle size, roughness, and texture) and the chemical composition of the material [1]. Because of complexity, it is not appropriate to achieve the continuum directly based on all the properties of scattering, and only simulation of the continuum based on the reflectance spectrum is available [10]. Usually, the continuum is a hull fitted over the top of the spectrum, and the
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ZHAO et al.: HYPERSPECTRAL FEATURE EXTRACTION BASED ON THE RSBR METHOD
continuum-removed spectrum is achieved by dividing the continuum into the original spectrum [18]. Through CR, the pure absorption features caused by transmitted radiation could be extracted. CR can distinguish subtle spectral details, eliminate sloping effects, and achieve better positional information on absorption features [3]. Furthermore, CR can greatly eliminate the effects of topography and illumination on the spectral intensity and depth of absorption features [19]. In geological research, CR has been widely used in mineral abundance mapping on the Earth [20], Moon [21], [22], Mars [23], etc. CR has also various applications in ecological and vegetation research, including determination of leaf biochemistry concentrations [24], [25], estimation of urban vegetation abundance [26], and discrimination of vegetation types [27]. According to previous studies, the wavelengths of the minimum reflectance points for absorption features vary nonlinearly with composition [28], [29]. This indicates that for a band range containing more than one absorption contribution factors, the absorption center position shifts under the comprehensive mixing effect of these factors. To extract accurate band position of specific absorption factor, the effects of the interfering factor must be excluded first. However, for mixing spectrum, CR cannot extract pure absorption feature of particular material directly. In other words, the absorption feature extracted by CR could be a mixture of overlapped absorption features. Under this situation, an algorithm to extract pure absorption feature of the target absorption contribution factor is needed. In this paper, a new method named reference spectral background removal (RSBR) is proposed. First, a spectral fitting method is created to simulate the background curve containing the absorption features of unwanted components. Then the whole work flow of RSBR is introduced and performed on experimental data. Later on, basic absorption-feature parameters including the absorption center, absorption width, absorption depth, and spectral waveform are extracted and compared using both CR and RSBR methods. Finally, a discussion of the findings and a summary of the study are presented.
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The transmission of energy through different materials or separated into different absorption processes can be modeled using the mean optical path length (MOPL) n (3) ki di I = I0 exp − i=1
where for a multimineral surface in an intimate mixture, ki is the absorption coefficient of the ith material with MOPL di . Additionally, ki may represent the equivalent absorption coefficient for a particular absorption factor whose equivalent MOPL is di . Similarly, di = 2mi Di .
(4)
For mixtures of uniform particle-size distributions, the particle diameter of different materials or factors is the same, so di is only related to mi . If it is assumed that, for a mixture of uniform distributions of particle sizes, the mean number of particles encountered by photons is the same, then mi is proportional to the fraction of the ith material in the mixture, indicating that di is proportional to the fraction. If the first-order Fresnel reflection from crystal surfaces is excluded, then n r(λ) = I/Io = exp − ki di (5) i=1
where λ represents wavelength and r(λ) is the reflectance spectrum of the mixture. If we define the reflectance spectrum of the absorption feature of interest as rinterest (λ), then rinterest λ = exp(−k1 d1 )
(6)
where k1 and d1 are the absorption coefficient and MOPL of this absorption factor, respectively. In this way, all the other absorption factors that form the continuum spectra can be expressed as n−1 rc (λ) = exp − ki di . (7) i=2
II. M ETHODOLOGY A. Physical Model of Background Removal Spectral absorption has two components: the background and the individual features [18]. Usually, the continuum can be considered as the background and individual features are superimposed onto it. When radiation is transmitted through solid particles, absorption bands in reflectance spectra obey the Beer–Lambert’s law [30] I = I0 e−kd
(1)
where IO is the initial intensity, I is the attenuated intensity, k is the absorption coefficient, and d is the optical path length. If m is the mean number of particles encountered by photons in the surface, then d = 2 mD where D is the radius of the particles of the surface.
(2)
Usually, the absorption coefficient and MOPL are not available, so rinterest (λ) cannot be calculated directly from (6). If rc (λ)is available, we could get rinterest (λ) through the CR method, which can be expressed as rinterest (λ) = r(λ)/rc (λ).
(8)
As shown above, if the spectrum is in reflectance, the removal of a continuum should be done as a division [31]. In (6), k1 is a constant value, and d1 is proportional to the fraction of the component. To ensure that the band depth calculated from the continuum removed spectrum correlates linearly with the fraction of the component of interest, it is necessary to perform a natural log operation on the reflectance spectrum. If we perform a log operation on r(λ) and rc (λ), then N(λ) = −
n i=1
ki di
(9)
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and
of the background component, while no such method could be found in contemporary scientific literature. As we all know, the reflectance spectrum is located in a two-dimensional (2-D) Cartesian coordinate system, with wavelength on the x-axis, reflectance value along y-axis, and the point of intersection of two axes as the origin. By shifting spectrum of the background component in y-axis, we can only make it meet with the mixing spectrum at one end, but at the other end, they may be still separated. To solve this problem, we come up with the idea of scaling and rotation of the spectral curve, which can be more easily done in polar coordinate system. So, we developed a new background curve simulation method based on coordinate transformations. This method could transform the background spectrum to be coincident with the mixing spectrum at two ends, while keeping its spectral waveform unchanged. Here, we define rB (λ) as the reflectance spectrum of background component, and rT (λ) as that of target component, which are shown in Fig. 1(a). The process of the background curve simulation method is as follows: a) Calculating the gap between the reflectance values of the left starting points and shifting of the background spectrum in y-axis to make the left starting points coincide
Nc (λ) = −
n−1
ki di
(10)
i=2
where N stands for the natural log reflectance. Then, the natural log reflectance of interest can be expressed as Ninterest (λ) = N(λ) − Nc (λ) = −k1 d1 .
(11)
As stated above, k1 is a constant value, and d1 is proportional to the fraction of the component. From Ninterest (λ), we can calculate the band depth, which is linearly related to the composite fraction of interest, enabling quantitative analysis. B. A Spectral Fitting Method to Achieve the Background Curve Diagnostic absorption features are unique to particular materials and it is very important to focus on them in mineral analysis [32]. When dealing with specific absorption features, selection of an appropriate wavelength range should be done first [18]. Here, we define the band range of particular absorption feature to be in-between the two shoulders nearby the absorption center. In remainder of this paper, all the background removal operations are performed within specific band ranges. The core of CR could be seen as to retrieve the energy that is lost when light transmit through the inner portion of the particles. Simply stated, the progress of CR could be divided into three steps: 1) selecting the inflection points as nodes from the reflectance spectrum; 2) simulating the continuum between the selected nodes based on linear function or quadratic function; 3) removing the continuum from the reflectance spectrum to achieve the CR spectrum. The band range selection part stated above is equivalent to step 1), which defines the starting and ending nodes for the background curve. The core of RSBR locates in step 2), in which RSBR simulates the background curve based on the reference spectrum of background component in the sample, which has physical meaning. In this way, we could extract the pure absorption feature of target material through the step 3), without the interference of unwanted components. The background curve is the spectrum on which the target absorption feature is imposed. Different from the continuum, it should not only contain the nontransmitted component energy, but should also contain information of the transmitted component energy of unwanted materials. For a pure mineral, the background curve is only related to one kind of material. Under this situation, the continuum could effectively act as the background curve. For mineral mixtures, in contrast, the spectrum of the mixture is a mixing result of the components [33], [34]. Under this situation, the absorption features extracted using CR could be a mixture of the absorption features, although the nontransmitted component radiation could be excluded. If we build the background curve based on the spectra of background components, then through step 3), the pure absorption feature of target component could be extracted. A method is needed to simulate the background curve between the starting and ending nodes based on the waveform
δ = rT (λS ) − rB (λS ) r B (λ) = rB (λ) + δ
(12) (13)
where δ is the gap between the starting points of the two spectra, λS is the starting wavelength of the absorp (λ) is the spectrum after shifting [shown tion feature, rB in Fig. 1(b)]. Through step a), the starting point of the background component meets with that of the target component. b) Translating the origin of the coordinate to PS (λS , rT (λS )) x = x − λS y = y − rT (λS ).
(14) (15)
The result is shown in Fig. 1(c). c) Transforming the Cartesian coordinate system to a polar coordinate system, with the coincident left end point as the origin, and the direction of x-axis as pole axis θ = arctan2(y , x )
ρ = hypot(x , y )
(16) (17)
where θ is the polar angle, ρ is the polar radius, “arctan2” is the function for four quadrant inverse tangent of codistributed array in MATLAB software, and ‘hypot’ is the function for robust computation of square root of sum of squares for co-distributed array in MATLAB software. d) Calculating the scaling factor and rotating factor for the background spectrum: α = ρ(P1 )/ρ(P2 ) β = θ(P1 ) − θ(P2 )
(18) (19)
where α is the scaling factor, β is the rotating factor, P1 is the right end point of target spectrum, P2 is the right end point of the background spectrum.
ZHAO et al.: HYPERSPECTRAL FEATURE EXTRACTION BASED ON THE RSBR METHOD
Fig. 1. Flowchart of background curve simulation. (a) Original spectra. (b) Spectra after step a). (c) Spectra after step b). (d) Final simulations results.
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Fig. 2. Original and fitted reflectance spectra. The value in the bracket is the right end point value in y-axis.
e) Rescaling and rotating every point of the background spectrum ρ Bi = αρBi ,
θ
Bi
= θBi + β,
i = 1, . . . , n
(20)
i = 1, . . . n
(21)
where θBi is the polar angle of the ith point of the background spectrum after rotation, and ρBi is the polar radius of the ith point of the rescaled background spectrum. After step e)
ρ(P 2 ) = ρ(P2 )α = ρ(P1 ) θ(P
2)
= θ(P2 ) + β = θ(P1 )
(22) (23)
so through the process of rescaling and rotation, the right end point of the background spectrum meets with that of the target spectrum. f) Transforming the polar coordinate system back to the original Cartesian coordinate system x = ρ cos(θ)
(24)
y = ρ sin(θ).
(25)
To make sure that the wavelengths remain accurate after the above processing steps, spline interpolation is carried out before the next step. g) Translating the origin of the coordinate back to the original origin x = x + λ S y = y + rT (λS ).
(26) (27)
Besides, in order to meet the requirement that the background curve should have value no less than that of target spectrum at each wavelength, we assign the value of background curve which is smaller than that of the target spectrum to be the same as the target spectrum’s value. The final results of background curve simulation are shown in Fig. 1(d).
Fig. 3. Continuum removed spectra of the original and fitted spectra. The value in the bracket is the reflectance value of the right end point before CR.
To verify the effects of the above spectral fitting method, a test was performed on the spectrum of a mixture (50% plaster and 50% allochite), which is shown as a dotted line in Fig. 2. In the background curve simulation method after step b), the only initial parameter is the target value of the right end point in y-axis. Through the spectral fitting process, the test data can be transformed to the spectrum with any right end reflectance in y-axis. To cover most of the situations, we set the target value of the right end point to range from 5% to 95%, and then perform the above coordinate transformation method on the original spectrum (the spectrum of plaster) individually to make its right end point meet the target value requirement, which is shown in Fig. 2 in different colors. To present the spectral waveform better, the continuum removed spectra of the original and fitted spectra were created and are shown in Fig. 3. The results show
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that the spectral waveform was well preserved after the spectral fitting process, and the absorption feature was generally the same between the original and fitted spectrum, with the only difference being in the absorption depth. This result laid a solid foundation for the RSBR. C. RSBR Process Based on the spectral fitting method introduced in Section IIA, we could simulate the background curve for the target spectra, but that just gets part of the job done. In this section, the whole work flow of RSBR is introduced in detail. 1) Target Feature Definition: In strong absorption bands, the transmitted component of reflected light plays a dominant role in the measured spectral characteristics [10]. To achieve better performance in quantitative analysis, the absorption feature of interest should be diagnostic of specific category of materials. In this study, the band range of the spectral feature starts and ends at the shoulder of the absorption valley of laboratory measured spectra. In practical applications, it could also be determined from the spectra of spectral library. 2) Background Spectra Definition: Based on background knowledge of the research area, a largely covered background component should be selected, which has influence on the precise retrieval of the target feature. The reference background spectra can be achieved either by field/laboratory measurement or from spectral library. Subset the spectra to have the same band range as the target feature. 3) Natural Log Operation: As stated in Section II-A, when radiation is transmitted through solid particles, absorption bands in reflectance spectra obey the Beer–Lambert’s law. To ensure that the absorption depth calculated from the background removed spectrum correlates linearly with the fraction of the component of interest, it is necessary to perform a natural log operation on the reflectance spectrum. But this is not an essential step for RSBR. When the scenario contains minerals, such as vegetation, water, etc., log operation may no longer be appropriate. Under this situation, this step can be omitted. 4) Spectral Fitting: Obtaining the background curve for the target component and the mixing spectra as the procedure described in Section II-B1. 5) Background Removal Operation: Removing the background curve by subtraction to create the background removed spectrum of the mixing spectrum and the target component. For bands where the background curve is below the mixing spectrum or the target component, the background curve value should be modified to be the same as the target spectral value, which means that at these bands the value of the background removed spectrum will be zero. In this way, the values of the background removed spectrum are set to be no more than zero. The process of RSBR is shown in Fig. 4. After finishing steps 1) to 5), individual features are extracted while the background information is eliminated. Based on the natural log spectrum, accurate absorption parameters including the absorption center, absorption width, and absorption depth could be calculated. It is without doubt that noises can cause large influence on the accurate extraction of absorption parameters, such as absorption center, and absorption depth. Generally, there can be four
Fig. 4. Flowchart of RSBR.
Fig. 5. Schematic diagrams of different conditions relating to noises. (a) Both without noises. (b) Background spectra has noises. (c) Target spectra has noises. (d) Both with noises.
conditions for background removal when noises are to be considered: 1) they are both of high quality; 2) the background curve is with strong noises while the target curve is not; 3) the target curve is with strong noises while the background curve is not; and 4) they both have strong noises. The schematic diagrams of these four conditions are shown in Fig. 5. For condition 1), the noise is not a problem at all. For condition 2) and 3), the spectra with strong noises should be denoised or smoothed first. For condition 4), the situation can be quite complicated, because the sources of noises can be different for the target spectra and the background spectra, and the solving
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TABLE I C OMPOSITION OF M INERAL M IXTURES
Fig. 6. Natural log reflectance spectra of the full band range.
strategies can be different from time to time. However, the noise problem can be quite complex, and is not the theme of this paper. But it should be considered carefully when the data quality has significant effects on the results of RSBR. It will be further discussed in future research.
III. DATA P ROCESSING A. Acquisition of Experimental Data In the experiment, plaster and allochite samples were crushed into a powder, and a set of mixtures of different proportions were made, with accurate measurements taken using an electronic balance and graduated cylinder. As the absorption depth of absorption features has complex relationship with temperature and particle size [35], we make sure that the samples have the same particle size and temperature to avoid these effects. The mineral mixture scheme is shown in Table I. A SVC HR-1024 Hand-held Spectrometer covering the UV, visible, and NIR wavelengths from 350 to 2500 nm was used to measure the in situ reflectance with a 25◦ field of view at a distance of 1 m above the species. The spectral reflectance was calculated as the ratio of measured radiance to the radiance from a white standard reference panel. The spectral reflectance data were obtained between 9:00 P.M. and 12:00 P.M., under dark conditions. To facilitate the subsequent derivation, the original reflectance spectra were resampled to 1-nm intervals. The natural log reflectance spectrum is shown in Fig. 6. Plaster is a typical sulfate mineral with formula CaSO4 · 2H2 O. Plaster has three consecutive water absorption features at 1449, 1490, and 1535 nm, a diagnostic sulfate absorption feature at 1750 nm, and a very strong water absorption feature at 1950 nm. Allochite is a calcium silicate with formula Ca2 Fe3+ Al2 O · OH · Si2 O7 · SiO4 . It has an absorption feature at 2256 nm and a strong diagnostic absorption feature at 2335–2342 nm.
Fig. 7. Natural log reflectance spectra (1670–1828 nm).
B. Background Removal Process As an example, the diagnostic absorption of plaster at 1750 nm is chosen for processing, and the band range is between 1670 nm and 1828 nm. The allochite spectrum is treated as the background in this case. The natural log reflectance spectrum within the band range is shown in Fig. 7. From Fig. 7, we can see that allochite does not have a strong absorption feature in this band range, but some weak features can still be recognized. Based on these weak features, the background curve of the plaster will be formed through the spectral fitting procedure. The background spectra after the spectral fitting procedure are shown in Fig. 8. From Fig. 8, it is clear that every mixing spectrum has a different background curve, but they all share similar spectral waveforms with allochite. Then, the background curve is subtracted from the spectrum, creating the background removed spectrum (Fig. 9). When the target feature is not predefined, RSBR can also be performed on the spectra of the full band range. The demarcation points of band ranges of RSBR are the same as those of CR, which are the inflection points of the derivative spectra. The background removed spectra of RSBR and CR are shown in Figs. 10 and 11 individually. Through comparison,
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Fig. 8. Background spectra of RSBR and natural log reflectance spectra (1670– 1828 nm).
Fig. 11. Background removed spectra of CR of the full band range.
C. Experiments on Hyperspectral Image Data
Fig. 9. Background removed spectra of RSBR (1670–1828 nm).
The experimental hyperspectral image is the AVIRIS Cuprite data set, obtained over the Cuprite mining region in Nevada, USA. A pixel subset from the 1997 reflectance data set is selected, and pruned to contain only 50 spectral bands in the range, since this wavelength range allows for better discrimination of mineral signatures. An image of the region (2.16 µm) and the regions of interest (ROIs) for alunite and kaolinite are shown in Fig. 12(a). The reflectance data and the ROI file are available from the Exelis website (http://www.exelisvis.com). Alunite and kaolinite are both widely spread in the Cuprite region. They have a lot of overlapping distributions, and the mean spectra of their ROIs are very similar [shown in Fig. 13(a)]. Even after CR, it is still hard to separate one from the other [shown in Fig. 13(b)]. If we set alunite as the target component and kaolinite as the background component, then RSBR can be performed on the data set to extract the pure absorption features of alunite. From RSBR spectra, alunite and kaolinite can be easily distinguished [shown in Fig. 13(c)]. We also added the alunite classification map extracted from [32] to make a comparison [shown in Fig. 12(b)]. The presence of alunite can be roughly estimated from the absorption depth map of 2.16 µm. It is clear that both the maps of CR and RSBR [shown in Fig. 12(c) and (d)] agree well with the classification map, but the map of CR overestimate the presence of alunite due to the presence of kaolinite, while the map of RSBR estimate the presence of alunite more accurately. However, there are some white dots in Fig. 12(d), which can be either potential alunitization information or noises. More experiments need to be done to fully investigate the causes.
Fig. 10. Background removed spectra of RSBR of the full band range.
IV. R ESULTS AND D ISCUSSION it is obvious that RSBR can effectively eliminate the influence of the background material, while the absorption features extracted CR are mixing results of Plater’s features and allochite’s. In the next section, the absorption parameters are calculated based on the background removed spectrum (1670– 1828 nm) obtained by both CR and RSBR, and accuracy is evaluated. Also, in order to fully validate the effects of RSBR, more absorption features will be processed.
A. Evaluation of Band-Center Extraction The absorption center is the band that has a local minimum value in the absorption band range. To compare the absorption center estimation, we chose the absorption feature near 1750 nm and calculated the absorption center of the original spectrum, the natural log reflectance spectrum, the CR spectrum, and the RSBR spectrum. The results are listed in Table II.
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Fig. 12. (a) Cuprite image (2.16 µm) and the ROIs for alunite and kaolinite. (b) Classification map of the alunite endmember, extracted from Fig. 9(b) in [32], which is a classification color map of the Cuprite data set obtained by the tetracorder software. (c) Absorption depth map of 2.16 µm obtained from CR. (d) Absorption depth map of 2.16 µm obtained from RSBR.
Fig. 13. Mean spectra of ROIs for alunite and kaolinite. (a) Original image. (b) CR. (c) RSBR.
From Fig. 7, we know that allochite does not have individual absorption features in this band range, and the reflectance keeps increasing with wavelength. Therefore, it is not surprising that for samples with a high proportion of allochite, the absorption center is located at 1670 nm, which is the first band in this band range. It is noticeable that the absorption centers of the original and natural log reflectance spectra are the same. This indicates that the natural log operation has no effect on the absorption center, which can be explained as that the log operation does not change the monotonic property. The CR process can basically extract a precise absorption center position, but the result is not very stable, as it shifts from 1749 to 1748 nm several times. RSBR achieved completely uniform results, which showed that the absorption feature of interest was well extracted.
To fully illustrate the advantage of the RSBR for overlapping features, we picked the water absorption feature around 1535 nm as another example. To its right, allochite also has weak water absorption. The absorption center detected from CR continuum removed spectrum [shown in Fig. 14(a)] shifts to shorter wavelengths as the fraction of plaster decreases. However, in the case of RSBR background removed spectrum [shown in Fig. 14(b)], the absorption center remains highly stable, even when the abundance of plaster is as low as 5%. The absorption center results are listed in Table III. Due to the elimination of slope effects, the absorption center of both CR and RSBR moves to longer wavelengths. Compared with CR, RSBR can better eliminate the effects of the overlapping absorption feature and extract purer absorption features of
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TABLE II A BSORPTION C ENTER P OSITIONS (1670–1828 NM )
Fig. 14. Background removed spectra (1520–1669 nm). (a) CR. (b) RSBR. TABLE III A BSORPTION C ENTER P OSITIONS (1520–1669 NM )
TABLE IV A BSORPTION W IDTH OF THE A BSORPTION F EATURE (U NITS : NM ) (1670–1828 NM )
as the abundance changes. The width of the absorption band is determined by a complex function of the composition of the sample, and it does not vary significantly as a function of modal abundance [8]. For spectral mixtures, the absorption width does vary in some extent with the abundance of absorbers, because adding a mixture component in the sample will change the proportion of MOPL at the bands of absorption features, thus changing the width of the feature. However, if the absorption feature could be purely extracted without the influence of the adding component, then the absorption width should not vary with the abundance anymore, because the width of the feature extracted is only related to the absorber itself. The true value of absorption width is hard to achieve, but the absorption character caused by specific factors should have a relatively consistent absorption width. In this sense, RSBR extract purer absorption width of the absorption feature we are interested in, which is obviously shown from the results. C. Evaluation of Absorption Depth Extraction According to the statement of Clark, the absorption depth D from the continuum removed reflectance spectrum rCR is defined as D = 1 − rCR (λc )
interest. In general, better absorption center position information could be retrieved by using RSBR.
B. Evaluation of Absorption Width Extraction The FWHM is considered the bandwidth in this paper. The absorption width of the natural log spectrum of CR and RSBR are listed in Table IV. As Table IV shows, the absorption widths of the CR spectra increase with the abundance of plaster, whereas for the RSBR spectra, the absorption widths remain relatively stable
(28)
where λc is the absorption center. For the natural log spectrum, the absorption depth Dlog should be Dlog = −N (λc )
(29)
where N is the natural log reflectance spectrum. The absorption centers are used according to the calculation results in Table II. The extracted absorption depth is shown in Table V. As expected, a higher proportion of plaster in the mixture and stronger absorption features result in deeper absorption. As explained in Section II-A, the absorption depth here is linearly
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TABLE V D EPTH OF A BSORPTION F EATURE (1670–1828 NM )
Fig. 15. Scatter plot of predicted abundance and reference abundance.
TABLE VI A PPROXIMATED A BUNDANCES OF P LASTER
Fig. 16. Normalized background removed spectrum (1670–1828 nm). (a) CR. (b) RSBR.
D. Evaluation of Spectral-Waveform Extraction
related to the abundance of plaster. We set the depth of pure plaster as a standard and divided the depth of the mixture by that figure. The result was the approximated abundance of plaster in the mixture. The calculation results for CR and RSBR are shown in Table VI and Fig. 15. The root-mean-square error (RMSE) and chi square (R2 ) are calculated to allow quantitative evaluation of the model’s precision. From the results, we can see that RSBR can estimate the abundance of compositions in the mixture to an RMSE of ± 5%. From the results above, we can see that RSBR has a higher precision than CR. The reasons may be as follows: as RSBR takes spectral mixing effects into consideration, RSBR absorption center is more accurate than CR absorption center, and band strength extracted by RSBR is purely related to the endmember of interest. Hence, it is not surprising that the RSBR could achieve better performance in quantitative analysis.
As described above, the new background removal process can be very effective in quantitative analysis for minerals. In this section, its effects on the extraction of spectral waveform will be tested. Spectral angle matching (SAM) is a commonly used method in spectral-waveform matching that is very helpful in mineral species identification [36]. Before we carry out the SAM calculation, absorption depth normalization will be performed. 1) Absorption Depth Normalization: The abundance of the absorber composition has strong influence on the absorption depth of absorption features, but it was not expected to have big influence on the spectral waveform. Absorption depth normalization can effectively reduce the topographic, atmospheric, and abundance effects [35]. The normalized background removed spectrum Nnormal is calculated by dividing the absorption depth Dlog into the background removed spectrum Ncr , which can be expressed as Nnormal = −Ncr /Dlog .
(30)
The normalized background removed spectra are shown in Fig. 16. Comparing with Fig. 8, we can see that variations in Nnormal with wavelength could describe the waveform of the absorption feature without the interference of abundance effects. Additionally, the normalized spectra obtained by using RSBR have more consistent spectral waveform than those by CR.
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TABLE VII SAD S B ETWEEN P LASTER S PECTRUM AND THE M IXING S PECTRUM (1670–1828 NM )
Fig. 17. Background removed spectrum (2138–2273 nm). (a) CR. (b) RSBR. TABLE VIII SAD S B ETWEEN THE A LLOCHITE S PECTRUM AND THE M IXING S PECTRUM (1670–1828 NM )
2) Results of Spectral Angle Distance: Spectral angle distance (SAD) is a key parameter that measures the spectral similarity between two spectra [36]. SAD can be expressed as ⎛ ⎞ nb
ti ri ⎜ ⎟ ⎟ i=1 −1 ⎜ (31) α = cos ⎜ 1 1 ⎟ ⎝
⎠ nb n 2 2
b 2 2 ti ri i=1
i=1
where t is the test spectrum, r is the reference spectrum, and nb is the number of bands. The SADs between each mixing spectrum and plaster’s spectrum were calculated, and the results are shown in Table VII. Smaller value of spectral angle could indicate more similar spectral waveform. In this sense, the RSBR results are much better than those of CR, especially when the abundance of plaster was relatively low. This indicates that RSBR could more effectively eliminate background information and strengthen the spectral waveform of interest, which is very helpful in identifying minerals. To further discuss the effects of the RSBR on overlapping feature extraction, another example using the absorption feature of allochite will be shown. In this case, allochite is the target component and plaster is the background material. Around the band range of allochite’s 2256 nm feature, plaster also has some invalid features that could cause severe interference in the continuum removed spectrum of CR. As shown in Fig. 17(a), the absorption centers are totally misplaced in some cases, and no consistent features can be found. However, in the RSBR background removed spectra [Fig. 17(b)], the effects of plaster’s invalid features are eliminated, and the diagnostic absorption feature of allochite is clear. The spectral angles between the normalized background removed spectra of the mixture and that of allochite are listed in Table VIII. Again, RSBR achieved much better results. This result strongly suggests that for the mixing spectral cases, RSBR could improve the identification accuracy of minerals. If a threshold for the minimum spectral
angle is set, then the existence of a specific absorption feature or composition in a pixel of a particular mineral is identifiable. V. C ONCLUSION Usually, a typical absorption feature does not only refer to a specific kind of mineral, but can also refer to a category of minerals or materials. In geological remote sensing, diagnostic absorption features play an important role in detection of alteration minerals. To retrieve pure absorption feature of interest, the background curve should be simulated first before removal is performed. In this paper, a new spectral fitting method is presented to obtain the background curve, and a novel background removal method named RSBR is given. Background curve is the base line on which the feature of interest is imposed, and the continuum can be considered as a simple circumstance of background curve when background interference is not considered. RSBR retains the advantages of CR, such as enhancing subtle spectral features and eliminating the effects of slopes, topography, and illumination. Besides, RSBR can retrieve pure absorption features without the influence of overlapping or invalid features. The experimental results suggest that: 1) RSBR can extract accurate absorption centers and absorption widths from mixing spectrum, independent of the variation in abundance. 2) Absorption depths calculated from the RSBR spectra are strongly linearly correlated to the fractions of the component of interest. 3) The spectral waveform of the specific absorption
ZHAO et al.: HYPERSPECTRAL FEATURE EXTRACTION BASED ON THE RSBR METHOD
factor can be well extracted by RSBR, and by using spectral matching methods, such as SAM, the mineral composition can be identified. Based on diagnostic absorption features, RSBR can identify the existence of specific category of materials and estimate the fraction excluding interference from other components in the sample. Different from CR, the selection of the background spectra is a unique feature of RSBR. It gives much more choices for the simulation of background, and much broader imagination space. However, comparing with CR, it may indeed add some extra cost for the background curve simulation. As a widely used and successful algorithm, CR still has its own scope of application. But when CR cannot achieve good performance, for instance, when the background material has overlapping feature with the target component, and they are intimately mixed together, RSBR can be the best solution for the identification and quantitative analysis of the target component. In a sense, RSBR can be applied as an object detection approach. Besides, depending on the selection of the background curve, different features can be extracted by RSBR. So, RSBR also has great potential in imaging enhancement processing. However, in this research, only binary mixtures are involved. When dealing with hyperspectral image, the circumstances will be much more complicated, such as multiendmembers and noises. For the multiendmember problem, RSBR has its own limitation, but when the fraction ratio of the background materials is available, whether through field experiment or empirical formula, the background curve can be achieved by linear mixing of the background endmembers. Besides, noises are indeed unavoidable in hyperspectral images, and they can have severe influence on the precise extraction of absorption feature parameters, especially for band depth and band center. To evaluate noises’ influence on the accuracy of RSBR, we already carried out abundant experiments, both on simulated data and hyperspectral images, and a complete set of processing solution can be given. This research will be presented in a future paper. RSBR can not only be applied when the components are known, but can also be utilized to eliminate the effects of a wide range of existing background material, such as vegetation and soil„ and extract the absorption feature of potential target (altered minerals). RSBR is clearly an effective tool in mineral spectral analysis and is going to be applied in core mining and outer space exploration soon. Besides, this method can be applied not only in mineral analysis, but also can be applied in much wider areas. In vegetation or environmental research, RSBR also has great potential for estimation of the leaf area index (LAI), accurate vegetation classification, water quality check among others, where absorption feature analysis plays important roles.
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Hengqian Zhao received the B.S. degree in geographic information system from China University of Mining and Technology, Xuzhou, China, in 2010. He is currently pursuing the Ph.D. degree in cartography and geographical information systems at the Laboratory of Hyperspectral Remote Sensing Applications, Institute of Remote Sensing and Digital Earth (RADI), Chinese Academy of Sciences, Beijing, China. His research interests include hyperspectral absorption feature analysis, spectral unmixing, and quantitative analysis of minerals.
Lifu Zhang (S’04–M’05–SM’14) received the B.E. degree from the Department of Airborne Photogrammetry and Remote Sensing, Wuhan Technical University of Surveying and Mapping (WTUSM), Wuhan, China, in 1992, the M.E. degree from the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, WTUSM, in 2000, and the Ph.D. degree from the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan, China, in 2005, all in photogrammetry and remote sensing. He was a Visiting Researcher with the Department of Information and Computer Sciences, Nara Women’s University, Nara, Japan, from 2003 to 2004, a Postdoctoral Researcher with the Institute of Remote Sensing and Geographic Information System, School of Earth and Space Sciences, Peking University, Beijing, China, from 2005 to 2007, and an Advanced Visiting Researcher with the Earth Science and Resource Engineering, Commonwealth Scientific and Industrial Research Organization (CSIRO), Sydney, Australia, in 2011. He is currently a Fulltime Professor and the Dean of the Hyperspectral Remote Sensing Division, Institute of Remote Sensing and Digital Earth (RADI), Chinese Academy of Sciences (CAS), Beijing, China. His research interests include hyperspectral remote sensing, imaging spectrometer system development, and its applications. Dr. Zhang is a member of SPIE and the Academy of Space Science of China and is also a Committeeman of Chinese National Committee of the International Society for Digital Earth (CNISDE), a Vice Chairman of Hyperspectral Earth Observation Committee (HEOC) of CNISDE, and a Standing Committeeman of the Expert Committee of China Association of Remote Sensing Applications.
Xia Zhang received the B.E. degree in agricultural meteorology from Nanjing Institute of Meteorology, Nanjing, China, in 1995, the M.E. degree in remote sensing and geography information system, Beijing Normal University, Beijing, China, in 1998, and the Ph.D. degree in cartography and geography information system, Institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing, China, in 2005. She is currently a Fulltime Professor with the Institute of Remote Sensing and Digital Earth (RADI), Chinese Academy of Sciences (CAS). Her research interests include vegetation biochemical and biophysical parameters retrieval, land cover classification, and quantitative retrieval of the deep-space minerals based on hyperspectral remote sensing data.
Jia Liu received the B.E. degree in software engineering from Beihang University, Beijing, China, in 2006, and the Ph.D. degree in solid earth physics from the Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China, in 2012. Currently, she is an Assistant Research Fellow with the Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, since 2012. Her research interests include hyperspectral remote sensing application and recognition and classification.
Taixia Wu received the B.Ag. degree in forestry remote sensing from Nanjing Forestry University, Nanjing, China, in 1999, the M.S. degree in cartography and GIS from the College of Urban and Environmental Sciences, Northeast Normal University, Changchun, China, in 2006, and the Ph.D. degree in remote sensing from Peking University, Beijing, China, in 2010. He is currently an Associate Research Fellow with the Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China, since 2010. His research interests include polarization and hyperspectral remote sensing.
Shudong Wang received the Ph.D. degree in cartography and GIS from the State Key Laboratory of Remote Sensing, Institute of Remote Sensing and Digital Earth, Normal University, Beijing, China, in 2007 He is currently an Associate Research Fellow with the Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China, since 2013. His research interests include optical remote sensing intelligent observation and its application in ecological and environment field.
