Airborne hyperspectral imaging for estimating ... - Semantic Scholar
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Airborne hyperspectral imaging for estimating acorn yield based on the PLS B-matrix calibration technique Zhong Yao a , Kenshi Sakai a,⁎, Xujun Ye b , Tetsuya Akita c , Yuko Iwabuchi a , Yoshinobu Hoshino a a
Institute of Symbiotic Science and Technology, Department of Ecoregion Science, Faculty of Agriculture, Tokyo University of Agriculture and Technology, Tokyo 183-8509, Japan b College of Life Science, Zhejiang University, Hanzhou, China c Faculty of Environment and Information Sciences, Yokohama National University, 79-7, Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan
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Article history:
Alternate bearing of acorn is a well-marked yield variability phenomenon in forest
Received 17 October 2007
production. In Japan, this phenomenon is also related to wildlife management (e.g. of
Received in revised form
animals such as wild pigs, that rely on acorn as their major feed source). Effective
15 February 2008
management of animals dependent on acorn will require accurate estimation of acorn yield
Accepted 7 March 2008
at an early stage. In this paper, we proposed a way to estimate acorn yield from the canopy reflectance values of individual trees. Using an Airborne Imaging Spectrometer for
Keywords:
Application (AISA) Eagle System, hyperspectral images in 72 visible and near-infrared
Hyperspectral imagery
wavelengths (407–898 nm) were acquired over an acorn forest in Japan 10 times over three
Yield estimation
consecutive years (2003–2005) during the early acorn growing season. The canopy spectral
Partial least squares analysis
reflectance values for individual trees at each wavelength were extracted from the images,
B-matrix
and important wavelengths were determined as estimating factors by the B-matrix
Canopy feature
technique based on partial least squares (PLS) analysis. Yield-estimating models were
Acorn
then developed by multiple linear regression (MLR). Three models obtained from images acquired on June 27 in 2003, July 13 in 2004 and June 21 in 2005 estimated acorn yield well in comparison with ground truth, indicating that the procedure has considerable potential. The study also demonstrated the B-matrix technique based on PLS analysis to be reliable and efficient in identifying important wavelengths for determining suitable estimating factors that best contribute to the estimation model. © 2008 Elsevier B.V. All rights reserved.
1.
Introduction
Forest seeds, such as acorn, are very important as a major food source for a diverse assemblage of wildlife including birds and wild pigs. In Japan, fluctuations in acorn production affect the migration of wild pigs, which may have destructive effects on farms and even the living environment of local residents. This phenomenon, also termed alternate bearing, has long been an
attractive subject in ecology. A widely quoted model, known as resource budget model (RBM), was proposed to describe a deterministic process of internal resources as a result of photosynthesis and energy depletion due to flower and fruit production (Isagi et al., 1997). Sakai et al. (2007) detected chaos in a citrus orchard and showed the evidence of deterministic chaos behind the alternate bearing in citrus production. Therefore, we could use some properties of trees themselves, such as the
⁎ Corresponding author. Tel.:+81 42 367 5755. E-mail address: [email protected] (K. Sakai). 1574-9541/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoinf.2008.03.001
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canopy structural features, to obtain and map the potential yield information for alternate bearing management. In recent years, remote sensing has been used as a powerful tool to identify and map factors influencing plant growth, population status and yield. Previous studies suggested that remote sensing data could be used to map vegetation types (Belluco et al., 2006), estimate tree canopy cover (Carreiras et al., 2006), detect environmental stresses (Sepulcre-Cantó et al., 2006), and assist agricultural procedures (Lelong et al., 1998; Yadav et al., 2002; Tao et al., 2005; Mo et al., 2005; Noh et al., 2006; Prasad et al., 2006). Hyperspectral imagery, one of the most important advances in remote sensing, has higher spectral resolution for each pixel than multispectral data, so it can provide significant improvements in the quality of spectral information on vegetation properties (Lee et al., 2004; Ye et al., 2006; Chambers et al., 2007). Akita et al. (2006) applied airborne multispectral reflectance of acorn canopies together with tree size, cross-sectional area at breast height and canopy area to estimate acorn yield. However, a significant relationship between yield and multispectral reflectance values was obtained in only one season (2003) among three (2003, 2004 and 2005). Accordingly, it was not considered worthwhile developing models for estimating acorn yield from multispectral data. Ye et al. (2006) developed a model (with a neural network algorithm) for estimating citrus yield from airborne hyperspectral reflectance of canopies in an orchard, and a best-fit model for the testing dataset was identified (R2 = 0.8134). Hence, there is a potential for using airborne hyperspectral data to estimate citrus yield. Moreover, a study by Zhao et al. (2007) indicated that hyperspectral remotely sensed data provided more alternative red-NIR bands compared to multispectral data and, therefore, may provide greater flexibility in predicting LAI (leaf area index) and CCD (canopy chlorophyll density). Ye et al. (2008a,b) used hyperspectral imagery to estimate fruit yield in citrus, and found that the models based on TBVI (two-band vegetation index)
calculated for 823 nm (NIR)and 728 nm (red edge) wavelengths had a reasonable prediction accuracy (R2 = 0.5795). Our research was conducted as part of a project set up to determine the capability of hyperspectral imagery for investigating spatial variation in acorn production. Here, we focus on the potential for developing estimation models for acorn yield from hyperspectral imagery data.
2.
Materials and methods
2.1.
Study area
This research was conducted in an experimental acorn forest located at the Field Science Education Research Center affiliated with Tokyo University of Agriculture and Technology, Hachioji City in Japan (139°23′, 35°38′)(Fig. 1(a)), with the area of approximately 0.65 km2.This area has a temperate climate, with an annual mean minimum temperature of 9.4 °C and annual precipitation of 1303.3 mm in 2003; corresponding, data for 2004 were 10.1 °C and 1570.4 mm (in October under the influence of Typhoons 22 and 23) and 8.6 °C and 998.3 mm for 2005. Quercus serrata, a deciduous broad-leafed tree, is a common dominant in secondary forest in the region. Its acorn production is very important for local wild pig behavior. Twenty-two tree specimens were used for samples in this study (Fig. 1(a)).
2.2.
Hyperspectral data
An Airborne Imaging Spectrometer for Applications (AISA) Eagle system (Pasco Co. Ltd., Tokyo, Japan) was used to obtain hyperspectral images over the study area in 3 consecutive years (2003, 2004 and 2005), with 10 flights during the early growing season (April 10, May 22, June 5 and June 27 in 2003, May 25, June 18 and July 13 in 2004, May 26, June 21 and July 21 in 2005). Images were collected with 1.5 ⁎ 1.5 m spatial resolution, 72 channels (from 407 to 898 nm) and 6.3 nm spectral
Fig. 1 – (a) Acorn forest at the Field Science Education Research Center, Hachioji City, Japan (polygons in blue indicate 22 sample trees). (b) Example of the canopy spectral reflectance data for 22 sample trees from the hyperspectral imagery. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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resolution, and were taken at an altitude of approximately 1000 m above ground during cloud-free periods in the daytime. Hyperspectral data were processed to at-sensor radiance using calibration coefficients determined in the laboratory by SPECIM (Spectral Imaging Ltd., Oulu, Finland). The onboard Fiber Optic Downwelling Irradiance System (FODIS) was used to transform at-sensor radiance to surface reflectance. The images were atmospherically calibrated using the modified flat field method. Spectra of a sample field were obtained using a spectrophotometer during the flight of AISA Eagle on each date, which were then used for atmospheric calibration. The distortion/geometry of images was corrected for aircraft movements (yaw, pitch and roll) using onboard Global Positioning System/Inertial Navigation System (GPS/INS) data. The images were then rectified to Universal Transverse Mercator (UTM) geographic coordinates. Further rectification was performed using a reference map while keeping the estimated root mean square error (RMSE) at less than 0.5 pixel. The final corrected images were imported into ERDAS IMAGINE software (ERDAS IMAGINE 8.6), and individual tree canopies were manually identified by drawing a polygon over the image objects that corresponded to respective trees on the ground. The locations for individual sample trees were determined by the Handy Global Positioning System, and the polygon-shaped canopies were identified by the field-pictures.
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Using the embedded hyperspectral data extraction procedures in the software, the mean reflectance values of each canopy at each wavelength for each season were abstracted and were used as original hyperspectral data for model development (Fig. 1b).
2.3.
Acorn yield data
Acorn from individual trees was collected each year using conventional seed-traps, i.e. two to five seed-traps were set beneath each of 22 sample trees according to the canopy size of the samples in April and were withdrawn in December. Individual yield data (number of acorn) were then obtained as sum of acorn divided by the number of traps set. The yield (number of acorn) from individual trees for each of the years 2003–2005 was showed in Fig. 2. There was a clear left skew for all 3 years, which decreased or even damaged the efficiency of the calibration model (in the preliminary study). To avoid this problem, the original yield data were log-transformed to provide original yield information for model development.
2.4.
Estimating model based on PLS B-matrix
2.4.1.
Determination of estimating factors
One difficulty in the analysis of hyperspectral data is processing an extremely large dataset from many wavelengths. A
Fig. 2 – Yield (number of acorn) for individual trees in 3 years.
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Fig. 3 – Correlation coefficient spectra between individual wavelengths and acorn yield for each of the years 2003–2005.
multicollinearity problem is commonly found in hyperspectral data because high correlations may exist between many wavelengths, particularly those that are neighbours (Broge and Leblanc, 2001). When the number of predictor variables is larger than the number of samples (72 wavelengths vs. 22 samples in this study), the large degree of collinearity and redundancy in the data may result in overfitting. Hence, a powerful multivariate data analysis technique is necessary for determining suitable estimating factors before the modelling process can begin, i.e. significant wavelengths in hyperspectral image which best contribute to yield data should be determined for further model development. In this study, the B-matrix technique was used to determine important wavelengths. B-matrix is derived from partial least squares (PLS) analysis. The PLS analysis generalizes and combines features from principal component analysis (PCA) and multiple regression (Abdi, 2003). It is one of the standard calibration methods used in many chemical applications and other fields (Ramadan et al., 2005). PLS regression attempts to find a few components that explain as much as possible of the covariance between predictor variables and response variables. Corresponding to these components, the regression weights
represented by B-matrix are created. A B-matrix can be calculated from the PLS loadings and weights: 1 B ¼ W PT W Q T where W denotes predictor-variable weights, P denotes predictorvariable loadings, and Q denotes response-variable loadings. A previous study by Min and Lee (2003) demonstrated the feasibility of predicting nitrogen content of citrus plants from important wavelengths determined by B-matrix calculated in a PLS analysis of hyperspectral data from plant leaves, i.e. the B-matrix gave the accumulated picture of the most important wavelengths. A study from Ye et al. (2008a,b) also indicated that the B-matrix method was superior to simple correlation analysis in determining the important wavelengths that were correlated with the citrus yield. In other words, wavelengths with high absolute values in B-matrix may contribute more to the calibration model, and could be considered the most important wavelengths. However, it is important to find the number of the relatively most important wavelengths as estimating factors. In this study the important wavelengths corresponding to the first few high absolute values of the B-matrix were used as
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Table 1 – Results of the best-fit models for each sampling date across 3 years Date
Factors
R2
P-value
RRMSE
R2
Training dataset 2003
2004
2005
1 2 3 4 5 6 7 8 9 10
April 10 May 22 June 5 June 27 May 25 June 18 July 13 May 26 June 21 July 21
8 8 7 7 3 6 9 7 4 7
0.976 0.667 0.746 0.696 0.434 0.595 0.470 0.661 0.719 0.575
0.000** 0.002** 0.000** 0.001** 0.027 * 0.005** 0.020* 0.004** 0.001** 0.007**
P-value
RRMSE
Validation dataset 0.156 0.577 0.504 0.551 0.752 0.637 0.728 0.582 0.530 0.652
0.503 0.414 0.353 0.599 0.160 0.085 0.443 0.114 0.403 0.200
0.015 * 0.033* 0.054* 0.005** 0.223 0.385 0.025* 0.341 0.036* 0.195
1.000 0.947 1.292 0.673 1.026 1.189 0.752 1.085 0.922 0.962
R2 and P-values were calculated using a simple linear regression model for the relationship between actual and estimated yields. Bold indicates the best-fit model for each year. * Significant at P b 0.05. ** Significant at P b 0.01.
estimating factors, called B-matrix factors hereafter, and the cross-validation method was used to determine the number of the relatively most important wavelengths.
2.4.2.
Estimating model based on MLR with B-matrix factors
Using the B-matrix factors, estimating models based on multiple linear regression (MLR) algorithms were developed, and expressed simply as: Y ¼ f ðXÞ where Y is log-transformed acorn yield, X is estimating factors, and f is a regression model function. After model development, it is necessary to evaluate its performance. The relative root mean square of error (RRMSE) was employed: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P ðyðiÞ yVðiÞÞ2 =ðn 1Þ i¼1
RRMSE ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P P 2 ðyðiÞ y Þ =ðn 1Þ i¼1
mated ith value. RRMSE is based on the root mean square of error (RMSE), and suggests (statistically) that a value of 0 indicates a perfect model performance, while a value of 1 indicates the model performs no better than the straightforward use of the mean actual values (Sakai, 2001), i.e. the smaller the RRMSE, the better the model performance. It is a dimensionless index, allowing comparison among different model responses. Before model development, both hyperspectral data and yield data (log-transformed) were normalized using the following function: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u 1 X P ðxðiÞ x Þ2 yðiÞ ¼ ðxðiÞ x Þ=t n 1 i¼1 P
where x(i) is ith original data, y(i) is the standardized value of the x(i), x¯ is the mean of the original dataset, and n is the number of data samples. The standardized data then have means of 0 and standard deviations of 1.
2.4.3.
where n is the number of data samples, y(i) is the actual ith value, Y¯ is the average of the actual values, y′(i) is the esti-
Cross-validation procedure
In order to determine the number of the relatively most important wavelengths as well as avoiding the overfitting problem, we
Fig. 4 – Performance of the best model among 2003 models (both in log-transformed yield).
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Fig. 5 – Performance of the best model among 2004 models (both in log-transformed yield).
employed a cross-validation procedure to test the consistency of the models developed. To this end, the whole dataset was separated into two subsets by picking out alternate samples. Data samples with odd numbers were used as the training subset to develop the estimating models, while the evennumbered data samples were used as the validation subset to test the efficiency of the developed models. Data analysis was performed in a MATLAB environment. The code used for PLS was from the n-way Toolbox 2.11 for use with MATLAB (Andersson and Bro, 2000), and other statistical analyses were carried out based on codes from the Statistics Toolbox in MATLAB.
3.
Results
3.1. Correlation coefficient between individual wavelengths and acorn yield Fig. 3 shows the correlation coefficient spectra between the canopy reflectance at each wavelength and acorn yield for
each of the years 2003–2005. Individual wavelengths were found to be weakly correlated with the acorn yield (the largest correlation coefficient was 0.467), indicating that some single wavelength was inadequate for model development. Therefore, we applied the B-matrix technique to identify some important wavelengths that could explain most of the covariance between the canopy reflectance and acorn yield.
3.2.
Best-fit estimating models
We identified the best-fit model for each of the 10 sampling times across 3 years (Table 1). Among these 10 relative best-fit models, those for May 22 and June 27 in 2003, July 13 in 2004 and June 21 in 2005 performed in a consistent satisfactory way for estimation of yield both for the training and validation datasets (all R2 N 0.4, P b 0.05 and RRMSE b 1). Figs. 4–6 illustrated the performance of the best model for each year. The best model among 2003 models performed very well both for the training dataset (R2 = 0.696, P = 0.001, RRMSE = 0.551) and for the validation dataset (R2 = 0.599, P = 0.005, RRMSE = 0.673), as shown in Fig. 4, where the best-
Fig. 6 – Performance of the best model among 2005 models (both in log-transformed yield).
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fit line both for the training and validation dataset coincided very well to the line for y = x. The best model among 2004 models did not perform as well for either the training dataset (R2 = 0.470, P = 0.020, RRMSE = 0.728) or the validation dataset (R2 = 0.443, P = 0.025, RRMSE = 0.752), as shown in Fig. 5, where the data-points are relatively dispersed, though the best-fit line still coincided perfectly with the line for y = x for the training and validation datasets indicating desirable performance. The best model among 2005 models performed very well for the training dataset (R2 = 0.719, P = 0.001, RRMSE = 0.673) as shown in Fig. 6, where the best-fit line coincided perfectly with the line for y = x. For the validation dataset the values of statistical parameters (R2 = 0.403, P = 0.036, RRMSE = 0.922) were desirable, but the best-fit line did not coincide well with the line for y = x. Thus, the rank order of model performance by year was 2003 N 2004 N 2005. All of these models for the years 2003–2005 showed desirable performance in that they indicated capability for estimating acorn yield from airborne hyperspectral data.
4.
Discussions
4.1.
B-matrix factors for the estimating models
The number of estimating factors corresponding to important wavelengths (a representation of the amount of variation in the original data) mainly affects the accuracy of the models. Normally, a high number of estimating factors in a model lead to better explanation of variation in the original data (higher R2). However, high numbers of estimating factors increases the risk of multicollinearity and redundancy. As showed in Table 1, those three best models for each of the years 2003–2005 (in bold) had different estimating factors, indicating that the power of selected important wavelengths for explaining the covariance between the canopy spectral reflectance and acorn yield were different among seasons, which may reflect the temporal dynamics in acorn production. In other words, the cross-validation approach was fundamental for applying the PLS B-matrix technique to determine the number of estimating factors.
4.2.
The problem of overfitting
In Table 1, the R2 values for the training datasets were all N0.4, all P b 0.03 and all RRMSE were b0.8, indicating powerfully fits for the training datasets. In contrast, the R2 values for the validation datasets were all smaller than those for training datasets, with some P N 0.05, and some RRMSE N 1, indicating generally poor fits (some models were considered unsatisfactory). The inconsistent model performances between the training and validation datasets were mainly due to an overfitting problem in the model development procedure for the training dataset (arising from the number of estimating factors). The overfitting problem can be tested for and overcome by a cross-validation procedure. We separated the whole dataset into two subsets (training and validation datasets). Thus a satisfactory estimating model was determined by the performance of models for both training and validation datasets.
4.3.
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Selecting a suitable season for image acquisition
Identification of a suitable season for acquiring images was essential for developing and selecting estimating models. Among the best-fit models developed with the 2003 data, that for June 27 performed best (R2 = 0.599, RRMSE = 0.673 for validation data). In 2004, the best-fit model for July 13 data performed best (R2 = 0.443, RRMSE = 0.752 for validation data); among 2005 best-fit models, that developed for June 21 data performed best (R2 = 0.403, RRMSE = 0.922 for validation data). Additionally, the best-fit model for May 22, 2003 showed desirable performance (R2 = 0.414, RRMSE = 0.947 for validation data).
5.
Conclusions
We demonstrated the potential and utility of estimating acorn yield from airborne hyperspectral imagery data. We extracted the canopy reflectance value at each wavelength from 407– 898 nm for 22 sample trees. The B-matrix technique based on PLS analysis was used to determine the estimating factors because of the high multicollinearity in the original hyperspectral data. Multiple linear regression was employed to develop calibration models, and a cross-validation procedure was then employed for model validation. Conclusions are as follows: (1) Three best-fit models, obtained on June 27 in 2003, July 13 in 2004 and June 21 in 2005, showed good performance in acorn yield estimation both for the training and validation datasets, with R2 N 0.4, P b 0.05 and RRMSE b 1, indicating the capability for estimating acorn yield from airborne hyperspectral data. (2) B-matrix on PLS analysis was demonstrated to be a reliable and efficient method to identify important wavelengths for determining a suitable number of estimating factors that best contributed to the estimating models. And the cross-validation approach was fundamental for applying this technique to determine the number of estimating factors (with respect to multicollinearity and redundancy). (3) The forest we studied consists mostly of Q. serrata. However, in mixed forest, trees grow together with overlapping canopies, which makes it difficult to get an accurate spectral map for individual trees. Therefore, the higher spatial resolution of hyperspectral imagery as well as relevant sophisticated feature selective technologies is essential to obtain the information for individual sample trees.
Acknowledgments This research was supported by the Japan Society for the Promotion of Science (JSPS) grant-in-aid for scientific research project (No.14360148). We express our appreciation to Dr. Bhuweneshwar P. Sah and Mr. Suhama of Pasco Co. LTD., Japan for the acquisition of the hyperspectral images.
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a v a i l a b l e a t w w w. s c i e n c e d i r e c t . c o m
w w w. e l s e v i e r. c o m / l o c a t e / e c o l i n f
Airborne hyperspectral imaging for estimating acorn yield based on the PLS B-matrix calibration technique Zhong Yao a , Kenshi Sakai a,⁎, Xujun Ye b , Tetsuya Akita c , Yuko Iwabuchi a , Yoshinobu Hoshino a a
Institute of Symbiotic Science and Technology, Department of Ecoregion Science, Faculty of Agriculture, Tokyo University of Agriculture and Technology, Tokyo 183-8509, Japan b College of Life Science, Zhejiang University, Hanzhou, China c Faculty of Environment and Information Sciences, Yokohama National University, 79-7, Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa 240-8501, Japan
AR TIC LE I N FO
ABS TR ACT
Article history:
Alternate bearing of acorn is a well-marked yield variability phenomenon in forest
Received 17 October 2007
production. In Japan, this phenomenon is also related to wildlife management (e.g. of
Received in revised form
animals such as wild pigs, that rely on acorn as their major feed source). Effective
15 February 2008
management of animals dependent on acorn will require accurate estimation of acorn yield
Accepted 7 March 2008
at an early stage. In this paper, we proposed a way to estimate acorn yield from the canopy reflectance values of individual trees. Using an Airborne Imaging Spectrometer for
Keywords:
Application (AISA) Eagle System, hyperspectral images in 72 visible and near-infrared
Hyperspectral imagery
wavelengths (407–898 nm) were acquired over an acorn forest in Japan 10 times over three
Yield estimation
consecutive years (2003–2005) during the early acorn growing season. The canopy spectral
Partial least squares analysis
reflectance values for individual trees at each wavelength were extracted from the images,
B-matrix
and important wavelengths were determined as estimating factors by the B-matrix
Canopy feature
technique based on partial least squares (PLS) analysis. Yield-estimating models were
Acorn
then developed by multiple linear regression (MLR). Three models obtained from images acquired on June 27 in 2003, July 13 in 2004 and June 21 in 2005 estimated acorn yield well in comparison with ground truth, indicating that the procedure has considerable potential. The study also demonstrated the B-matrix technique based on PLS analysis to be reliable and efficient in identifying important wavelengths for determining suitable estimating factors that best contribute to the estimation model. © 2008 Elsevier B.V. All rights reserved.
1.
Introduction
Forest seeds, such as acorn, are very important as a major food source for a diverse assemblage of wildlife including birds and wild pigs. In Japan, fluctuations in acorn production affect the migration of wild pigs, which may have destructive effects on farms and even the living environment of local residents. This phenomenon, also termed alternate bearing, has long been an
attractive subject in ecology. A widely quoted model, known as resource budget model (RBM), was proposed to describe a deterministic process of internal resources as a result of photosynthesis and energy depletion due to flower and fruit production (Isagi et al., 1997). Sakai et al. (2007) detected chaos in a citrus orchard and showed the evidence of deterministic chaos behind the alternate bearing in citrus production. Therefore, we could use some properties of trees themselves, such as the
⁎ Corresponding author. Tel.:+81 42 367 5755. E-mail address: [email protected] (K. Sakai). 1574-9541/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ecoinf.2008.03.001
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canopy structural features, to obtain and map the potential yield information for alternate bearing management. In recent years, remote sensing has been used as a powerful tool to identify and map factors influencing plant growth, population status and yield. Previous studies suggested that remote sensing data could be used to map vegetation types (Belluco et al., 2006), estimate tree canopy cover (Carreiras et al., 2006), detect environmental stresses (Sepulcre-Cantó et al., 2006), and assist agricultural procedures (Lelong et al., 1998; Yadav et al., 2002; Tao et al., 2005; Mo et al., 2005; Noh et al., 2006; Prasad et al., 2006). Hyperspectral imagery, one of the most important advances in remote sensing, has higher spectral resolution for each pixel than multispectral data, so it can provide significant improvements in the quality of spectral information on vegetation properties (Lee et al., 2004; Ye et al., 2006; Chambers et al., 2007). Akita et al. (2006) applied airborne multispectral reflectance of acorn canopies together with tree size, cross-sectional area at breast height and canopy area to estimate acorn yield. However, a significant relationship between yield and multispectral reflectance values was obtained in only one season (2003) among three (2003, 2004 and 2005). Accordingly, it was not considered worthwhile developing models for estimating acorn yield from multispectral data. Ye et al. (2006) developed a model (with a neural network algorithm) for estimating citrus yield from airborne hyperspectral reflectance of canopies in an orchard, and a best-fit model for the testing dataset was identified (R2 = 0.8134). Hence, there is a potential for using airborne hyperspectral data to estimate citrus yield. Moreover, a study by Zhao et al. (2007) indicated that hyperspectral remotely sensed data provided more alternative red-NIR bands compared to multispectral data and, therefore, may provide greater flexibility in predicting LAI (leaf area index) and CCD (canopy chlorophyll density). Ye et al. (2008a,b) used hyperspectral imagery to estimate fruit yield in citrus, and found that the models based on TBVI (two-band vegetation index)
calculated for 823 nm (NIR)and 728 nm (red edge) wavelengths had a reasonable prediction accuracy (R2 = 0.5795). Our research was conducted as part of a project set up to determine the capability of hyperspectral imagery for investigating spatial variation in acorn production. Here, we focus on the potential for developing estimation models for acorn yield from hyperspectral imagery data.
2.
Materials and methods
2.1.
Study area
This research was conducted in an experimental acorn forest located at the Field Science Education Research Center affiliated with Tokyo University of Agriculture and Technology, Hachioji City in Japan (139°23′, 35°38′)(Fig. 1(a)), with the area of approximately 0.65 km2.This area has a temperate climate, with an annual mean minimum temperature of 9.4 °C and annual precipitation of 1303.3 mm in 2003; corresponding, data for 2004 were 10.1 °C and 1570.4 mm (in October under the influence of Typhoons 22 and 23) and 8.6 °C and 998.3 mm for 2005. Quercus serrata, a deciduous broad-leafed tree, is a common dominant in secondary forest in the region. Its acorn production is very important for local wild pig behavior. Twenty-two tree specimens were used for samples in this study (Fig. 1(a)).
2.2.
Hyperspectral data
An Airborne Imaging Spectrometer for Applications (AISA) Eagle system (Pasco Co. Ltd., Tokyo, Japan) was used to obtain hyperspectral images over the study area in 3 consecutive years (2003, 2004 and 2005), with 10 flights during the early growing season (April 10, May 22, June 5 and June 27 in 2003, May 25, June 18 and July 13 in 2004, May 26, June 21 and July 21 in 2005). Images were collected with 1.5 ⁎ 1.5 m spatial resolution, 72 channels (from 407 to 898 nm) and 6.3 nm spectral
Fig. 1 – (a) Acorn forest at the Field Science Education Research Center, Hachioji City, Japan (polygons in blue indicate 22 sample trees). (b) Example of the canopy spectral reflectance data for 22 sample trees from the hyperspectral imagery. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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resolution, and were taken at an altitude of approximately 1000 m above ground during cloud-free periods in the daytime. Hyperspectral data were processed to at-sensor radiance using calibration coefficients determined in the laboratory by SPECIM (Spectral Imaging Ltd., Oulu, Finland). The onboard Fiber Optic Downwelling Irradiance System (FODIS) was used to transform at-sensor radiance to surface reflectance. The images were atmospherically calibrated using the modified flat field method. Spectra of a sample field were obtained using a spectrophotometer during the flight of AISA Eagle on each date, which were then used for atmospheric calibration. The distortion/geometry of images was corrected for aircraft movements (yaw, pitch and roll) using onboard Global Positioning System/Inertial Navigation System (GPS/INS) data. The images were then rectified to Universal Transverse Mercator (UTM) geographic coordinates. Further rectification was performed using a reference map while keeping the estimated root mean square error (RMSE) at less than 0.5 pixel. The final corrected images were imported into ERDAS IMAGINE software (ERDAS IMAGINE 8.6), and individual tree canopies were manually identified by drawing a polygon over the image objects that corresponded to respective trees on the ground. The locations for individual sample trees were determined by the Handy Global Positioning System, and the polygon-shaped canopies were identified by the field-pictures.
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Using the embedded hyperspectral data extraction procedures in the software, the mean reflectance values of each canopy at each wavelength for each season were abstracted and were used as original hyperspectral data for model development (Fig. 1b).
2.3.
Acorn yield data
Acorn from individual trees was collected each year using conventional seed-traps, i.e. two to five seed-traps were set beneath each of 22 sample trees according to the canopy size of the samples in April and were withdrawn in December. Individual yield data (number of acorn) were then obtained as sum of acorn divided by the number of traps set. The yield (number of acorn) from individual trees for each of the years 2003–2005 was showed in Fig. 2. There was a clear left skew for all 3 years, which decreased or even damaged the efficiency of the calibration model (in the preliminary study). To avoid this problem, the original yield data were log-transformed to provide original yield information for model development.
2.4.
Estimating model based on PLS B-matrix
2.4.1.
Determination of estimating factors
One difficulty in the analysis of hyperspectral data is processing an extremely large dataset from many wavelengths. A
Fig. 2 – Yield (number of acorn) for individual trees in 3 years.
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Fig. 3 – Correlation coefficient spectra between individual wavelengths and acorn yield for each of the years 2003–2005.
multicollinearity problem is commonly found in hyperspectral data because high correlations may exist between many wavelengths, particularly those that are neighbours (Broge and Leblanc, 2001). When the number of predictor variables is larger than the number of samples (72 wavelengths vs. 22 samples in this study), the large degree of collinearity and redundancy in the data may result in overfitting. Hence, a powerful multivariate data analysis technique is necessary for determining suitable estimating factors before the modelling process can begin, i.e. significant wavelengths in hyperspectral image which best contribute to yield data should be determined for further model development. In this study, the B-matrix technique was used to determine important wavelengths. B-matrix is derived from partial least squares (PLS) analysis. The PLS analysis generalizes and combines features from principal component analysis (PCA) and multiple regression (Abdi, 2003). It is one of the standard calibration methods used in many chemical applications and other fields (Ramadan et al., 2005). PLS regression attempts to find a few components that explain as much as possible of the covariance between predictor variables and response variables. Corresponding to these components, the regression weights
represented by B-matrix are created. A B-matrix can be calculated from the PLS loadings and weights: 1 B ¼ W PT W Q T where W denotes predictor-variable weights, P denotes predictorvariable loadings, and Q denotes response-variable loadings. A previous study by Min and Lee (2003) demonstrated the feasibility of predicting nitrogen content of citrus plants from important wavelengths determined by B-matrix calculated in a PLS analysis of hyperspectral data from plant leaves, i.e. the B-matrix gave the accumulated picture of the most important wavelengths. A study from Ye et al. (2008a,b) also indicated that the B-matrix method was superior to simple correlation analysis in determining the important wavelengths that were correlated with the citrus yield. In other words, wavelengths with high absolute values in B-matrix may contribute more to the calibration model, and could be considered the most important wavelengths. However, it is important to find the number of the relatively most important wavelengths as estimating factors. In this study the important wavelengths corresponding to the first few high absolute values of the B-matrix were used as
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Table 1 – Results of the best-fit models for each sampling date across 3 years Date
Factors
R2
P-value
RRMSE
R2
Training dataset 2003
2004
2005
1 2 3 4 5 6 7 8 9 10
April 10 May 22 June 5 June 27 May 25 June 18 July 13 May 26 June 21 July 21
8 8 7 7 3 6 9 7 4 7
0.976 0.667 0.746 0.696 0.434 0.595 0.470 0.661 0.719 0.575
0.000** 0.002** 0.000** 0.001** 0.027 * 0.005** 0.020* 0.004** 0.001** 0.007**
P-value
RRMSE
Validation dataset 0.156 0.577 0.504 0.551 0.752 0.637 0.728 0.582 0.530 0.652
0.503 0.414 0.353 0.599 0.160 0.085 0.443 0.114 0.403 0.200
0.015 * 0.033* 0.054* 0.005** 0.223 0.385 0.025* 0.341 0.036* 0.195
1.000 0.947 1.292 0.673 1.026 1.189 0.752 1.085 0.922 0.962
R2 and P-values were calculated using a simple linear regression model for the relationship between actual and estimated yields. Bold indicates the best-fit model for each year. * Significant at P b 0.05. ** Significant at P b 0.01.
estimating factors, called B-matrix factors hereafter, and the cross-validation method was used to determine the number of the relatively most important wavelengths.
2.4.2.
Estimating model based on MLR with B-matrix factors
Using the B-matrix factors, estimating models based on multiple linear regression (MLR) algorithms were developed, and expressed simply as: Y ¼ f ðXÞ where Y is log-transformed acorn yield, X is estimating factors, and f is a regression model function. After model development, it is necessary to evaluate its performance. The relative root mean square of error (RRMSE) was employed: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P ðyðiÞ yVðiÞÞ2 =ðn 1Þ i¼1
RRMSE ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P P 2 ðyðiÞ y Þ =ðn 1Þ i¼1
mated ith value. RRMSE is based on the root mean square of error (RMSE), and suggests (statistically) that a value of 0 indicates a perfect model performance, while a value of 1 indicates the model performs no better than the straightforward use of the mean actual values (Sakai, 2001), i.e. the smaller the RRMSE, the better the model performance. It is a dimensionless index, allowing comparison among different model responses. Before model development, both hyperspectral data and yield data (log-transformed) were normalized using the following function: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u 1 X P ðxðiÞ x Þ2 yðiÞ ¼ ðxðiÞ x Þ=t n 1 i¼1 P
where x(i) is ith original data, y(i) is the standardized value of the x(i), x¯ is the mean of the original dataset, and n is the number of data samples. The standardized data then have means of 0 and standard deviations of 1.
2.4.3.
where n is the number of data samples, y(i) is the actual ith value, Y¯ is the average of the actual values, y′(i) is the esti-
Cross-validation procedure
In order to determine the number of the relatively most important wavelengths as well as avoiding the overfitting problem, we
Fig. 4 – Performance of the best model among 2003 models (both in log-transformed yield).
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Fig. 5 – Performance of the best model among 2004 models (both in log-transformed yield).
employed a cross-validation procedure to test the consistency of the models developed. To this end, the whole dataset was separated into two subsets by picking out alternate samples. Data samples with odd numbers were used as the training subset to develop the estimating models, while the evennumbered data samples were used as the validation subset to test the efficiency of the developed models. Data analysis was performed in a MATLAB environment. The code used for PLS was from the n-way Toolbox 2.11 for use with MATLAB (Andersson and Bro, 2000), and other statistical analyses were carried out based on codes from the Statistics Toolbox in MATLAB.
3.
Results
3.1. Correlation coefficient between individual wavelengths and acorn yield Fig. 3 shows the correlation coefficient spectra between the canopy reflectance at each wavelength and acorn yield for
each of the years 2003–2005. Individual wavelengths were found to be weakly correlated with the acorn yield (the largest correlation coefficient was 0.467), indicating that some single wavelength was inadequate for model development. Therefore, we applied the B-matrix technique to identify some important wavelengths that could explain most of the covariance between the canopy reflectance and acorn yield.
3.2.
Best-fit estimating models
We identified the best-fit model for each of the 10 sampling times across 3 years (Table 1). Among these 10 relative best-fit models, those for May 22 and June 27 in 2003, July 13 in 2004 and June 21 in 2005 performed in a consistent satisfactory way for estimation of yield both for the training and validation datasets (all R2 N 0.4, P b 0.05 and RRMSE b 1). Figs. 4–6 illustrated the performance of the best model for each year. The best model among 2003 models performed very well both for the training dataset (R2 = 0.696, P = 0.001, RRMSE = 0.551) and for the validation dataset (R2 = 0.599, P = 0.005, RRMSE = 0.673), as shown in Fig. 4, where the best-
Fig. 6 – Performance of the best model among 2005 models (both in log-transformed yield).
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fit line both for the training and validation dataset coincided very well to the line for y = x. The best model among 2004 models did not perform as well for either the training dataset (R2 = 0.470, P = 0.020, RRMSE = 0.728) or the validation dataset (R2 = 0.443, P = 0.025, RRMSE = 0.752), as shown in Fig. 5, where the data-points are relatively dispersed, though the best-fit line still coincided perfectly with the line for y = x for the training and validation datasets indicating desirable performance. The best model among 2005 models performed very well for the training dataset (R2 = 0.719, P = 0.001, RRMSE = 0.673) as shown in Fig. 6, where the best-fit line coincided perfectly with the line for y = x. For the validation dataset the values of statistical parameters (R2 = 0.403, P = 0.036, RRMSE = 0.922) were desirable, but the best-fit line did not coincide well with the line for y = x. Thus, the rank order of model performance by year was 2003 N 2004 N 2005. All of these models for the years 2003–2005 showed desirable performance in that they indicated capability for estimating acorn yield from airborne hyperspectral data.
4.
Discussions
4.1.
B-matrix factors for the estimating models
The number of estimating factors corresponding to important wavelengths (a representation of the amount of variation in the original data) mainly affects the accuracy of the models. Normally, a high number of estimating factors in a model lead to better explanation of variation in the original data (higher R2). However, high numbers of estimating factors increases the risk of multicollinearity and redundancy. As showed in Table 1, those three best models for each of the years 2003–2005 (in bold) had different estimating factors, indicating that the power of selected important wavelengths for explaining the covariance between the canopy spectral reflectance and acorn yield were different among seasons, which may reflect the temporal dynamics in acorn production. In other words, the cross-validation approach was fundamental for applying the PLS B-matrix technique to determine the number of estimating factors.
4.2.
The problem of overfitting
In Table 1, the R2 values for the training datasets were all N0.4, all P b 0.03 and all RRMSE were b0.8, indicating powerfully fits for the training datasets. In contrast, the R2 values for the validation datasets were all smaller than those for training datasets, with some P N 0.05, and some RRMSE N 1, indicating generally poor fits (some models were considered unsatisfactory). The inconsistent model performances between the training and validation datasets were mainly due to an overfitting problem in the model development procedure for the training dataset (arising from the number of estimating factors). The overfitting problem can be tested for and overcome by a cross-validation procedure. We separated the whole dataset into two subsets (training and validation datasets). Thus a satisfactory estimating model was determined by the performance of models for both training and validation datasets.
4.3.
243
Selecting a suitable season for image acquisition
Identification of a suitable season for acquiring images was essential for developing and selecting estimating models. Among the best-fit models developed with the 2003 data, that for June 27 performed best (R2 = 0.599, RRMSE = 0.673 for validation data). In 2004, the best-fit model for July 13 data performed best (R2 = 0.443, RRMSE = 0.752 for validation data); among 2005 best-fit models, that developed for June 21 data performed best (R2 = 0.403, RRMSE = 0.922 for validation data). Additionally, the best-fit model for May 22, 2003 showed desirable performance (R2 = 0.414, RRMSE = 0.947 for validation data).
5.
Conclusions
We demonstrated the potential and utility of estimating acorn yield from airborne hyperspectral imagery data. We extracted the canopy reflectance value at each wavelength from 407– 898 nm for 22 sample trees. The B-matrix technique based on PLS analysis was used to determine the estimating factors because of the high multicollinearity in the original hyperspectral data. Multiple linear regression was employed to develop calibration models, and a cross-validation procedure was then employed for model validation. Conclusions are as follows: (1) Three best-fit models, obtained on June 27 in 2003, July 13 in 2004 and June 21 in 2005, showed good performance in acorn yield estimation both for the training and validation datasets, with R2 N 0.4, P b 0.05 and RRMSE b 1, indicating the capability for estimating acorn yield from airborne hyperspectral data. (2) B-matrix on PLS analysis was demonstrated to be a reliable and efficient method to identify important wavelengths for determining a suitable number of estimating factors that best contributed to the estimating models. And the cross-validation approach was fundamental for applying this technique to determine the number of estimating factors (with respect to multicollinearity and redundancy). (3) The forest we studied consists mostly of Q. serrata. However, in mixed forest, trees grow together with overlapping canopies, which makes it difficult to get an accurate spectral map for individual trees. Therefore, the higher spatial resolution of hyperspectral imagery as well as relevant sophisticated feature selective technologies is essential to obtain the information for individual sample trees.
Acknowledgments This research was supported by the Japan Society for the Promotion of Science (JSPS) grant-in-aid for scientific research project (No.14360148). We express our appreciation to Dr. Bhuweneshwar P. Sah and Mr. Suhama of Pasco Co. LTD., Japan for the acquisition of the hyperspectral images.
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