method to speed up lut-based crop canopy parameter ...
METHOD TO SPEED UP LUT-BASED CROP CANOPY PARAMETER MAPPING Yingying Dong1,2,3,4, Jinkai Zhang1,2, Zhijie Wang1,2, Karl Staenz1,2, Craig Coburn1,2, Wei Xu1,2, Xiaodong Yang3, Jihua Wang4 1. Alberta Terrestrial Imaging Center, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada; 2. Department of Geography, University of Lethbridge, Lethbridge, Alberta T1K 3M4, Canada; 3. Beijing Research Center for Information Technology in Agriculture, Beijing Academy of Agriculture and Forestry Sciences, Beijing 100097, P. R. China; 4. Beijing Research Center for Agricultural Standards and Testing, Beijing Academy of Agriculture and Forestry Sciences, Beijing 100097, P. R. China; ABSTRACT Estimation of canopy biophysical and biochemical parameters using remote sensing data is important for regional crop-growth condition monitoring and yield assessment. The inversion of the radiative transfer model PROSAIL based on the look-up table (LUT) approach is widely used for this purpose, taking remotely sensed reflectance as input. For the LUT-based parameter mapping, the main part is searching for the optimal solution from a large LUT. Due to the computational complexity of the sorting algorithm and size of the LUT for the solution search, a substantial amount of time is normally needed for estimation. In order to speed up the mapping of parameters using remote sensing observations, a faster method is developed for searching the LUT by introducing a binary search algorithm. The results of the experiments based on SPOT-5 imagery show that the proposed method can increase the mapping speed by about 70 times compared to the sorting algorithm. Index Terms— Parameter mapping, PROSAIL model, look-up table (LUT), binary search 1. INTRODUCTION Estimation of crop canopy parameters using remote sensing observations plays a significant role in regional crop-growth monitoring and yield evaluation [1, 2, 3, 4]. The PROSAIL radiative transfer model, which combines the leaf optical model PROSPECT and canopy reflectance model SAIL, is widely used to simulate vegetation canopy reflectance under various biochemical and biophysical conditions [5]. The PROSPECT model simulates leaf reflectance and transmittance features with pigment contents, equivalent water thickness, leaf mass per unit leaf area, and structure coefficient of vegetation as input [6]. By passing the outputs of the PROSPECT model together with canopy parameters,
978-1-4799-5775-0/14/$31.00 ©2014 IEEE
soil parameters, and view and illumination parameters into the SAIL model, spectrodirectional canopy reflectance in the wavelength range from 400 to 2500 nm can then be simulated [7]. Both sub-models are relatively simple and need only a limited number of input parameters. On the premise of obtaining crop canopy reflectance, different canopy parameters, such as pigment concentration and leaf area index (LAI), can be retrieved by inverting the PROSAIL model. The look-up table (LUT) approach as one of the simplest techniques to invert these kind of models has been widely used for mapping canopy biophysical and biochemical parameters based on remotely sensed agricultural data [8, 9, 10]. The key point of LUT-based inversion of the PROSAIL model for crop canopy parameters estimation is to search for the optimal solution from the simulated LUTs based on the similarity between measured and simulated reflectances. Using the root mean square error (RMSE) between measured and simulated reflectances as the evaluating index, the computational complexity of finding records (spectra) with minimum RMSE values based on the sorting algorithm is O(Nlog(N)), in which N is the number of records in the LUT [11, 12]. A large LUT is normally required to ensure a satisfactory accuracy of the retrieved parameters [13]. Accordingly, it will take more and more searching time as the size of the LUT increases to meet the crop canopy biochemical and biophysical parameters mapping requirements. In order to fulfill the needs of quickly mapping crop canopy parameters using remotely sensed data, a faster data search method is proposed in this study. For this purpose, a binary search algorithm with computational complexity of O(log(N)) is introduced for finding the closest simulated canopy reflectance to the measured one within the LUT [14, 15]. This can effectively reduce computation time of solution searching compared to the sorting algorithm. With the new proposed method, numerical experiments based on 10-m SPOT-5 imagery were selected for crop canopy parameters estimation.
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IGARSS 2014
2. MATERIALS AND METHODS 2.1. Study area and data The study area is situated in Lethbridge in the southern part of Alberta (49°32′N, 112°48′W), Canada. The main crop types in this region are wheat, durum, canola, and pea. A SPOT-5 multispectral image covering this experimental area was acquired on July 23, 2012. Its sensor has 10-m spatial resolution and four bands in the green (500 to 590 nm), red (610 to 680 nm), near infrared (780 to 890 nm), and shortwave infrared (1580 to 1750 nm). The study area and the satellite image are shown in Fig.1. 2.2. Look-up table LUT-based inversion of the PROSAIL model includes the following steps. Firstly, a large number of input variable combinations of the PROSAIL model are randomly generated and used in the forward calculation of the model for canopy spectral reflectance simulation. The minimum and maximum ranges for each input variable of the PROSAIL model need to be specified in this step. Afterwards, the canopy biochemical and biophysical variables are retrieved using the PROSAIL model in the inverse mode. This consists in finding within the LUT the closest simulated reflectance spectrum to the measured one in the remotely sensed imagery. The corresponding set of input variables of the PROSAIL model will then be chosen as the desired solution. The RMSE is normally used as the error criterion to measure the distance between measured and simulated reflectance. 2.3. Searching method The new proposed faster algorithm for solution searching consists of the following steps: (1) splitting the entire reflectance LUT into M smaller LUTs (where M is the number of spectral bands of the remote sensor for data processing); (2) sorting each of these LUTs based on the reflectance values; (3) using a binary search algorithm to find multiple candidate records and using the union of these candidate records selected from the single-band LUTs as a new smaller LUT (set to 10,000) to perform the final search; and (4) calculating the RMSE between the measured reflectance and the simulated reflectance in the new smaller LUT and sorting these RMSE values to find the minimum ones (set to 100) to calculate the median of input variables as the optimal solution. With this new faster method, the computational complexity as O(log(N)) is introduced, which then significantly reduces the amount of the computation time, especially when the volume of the LUT and remote sensing data for processing is large.
Fig.1. Location of the experimental area in Lethbridge, Alberta, Canada.
3. ANALYSIS AND RESULTS The new proposed approach was tested using SPOT-5 multispectral imagery. Firstly, a total number of 500,000 random combinations of eight input variables (i.e., pigment concentration, water content, dry matter content, leaf mesophyll structure, LAI, leaf angle distribution, hotspot size, and soil reflectance scale factor) of the PROSAIL model were generated. One 1-nm spectral resolution reflectance LUT was then generated using the PROSAIL model in forward mode. Secondly, the whole LUT was resampled to the spectral response functions of SPOT-5. Thirdly, the proposed faster sorting / search algorithm was used for crop canopy parameter mapping. The data were first atmospherically corrected to surface reflectance using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH). The dimension of the SPOT-5 image is 944 pixels × 2137 lines × 4 bands which was processed with the new method. This led to a run time of 4930.7s. This is considerable faster than existing sorting algorithms. The crop canopy parameters mapping results from the new approach are shown in Fig.2 for pigment concentration and LAI as examples. In order to compare the exact run time of the new proposed method with the sorting algorithm, an image subset (200 pixels × 200 lines × 4 bands) was selected, which covers the area located in the left bottom of the whole experimental area. While the traditional searching, which directly operates on the large LUT with 500,000 records, took around 5826.1s, the proposed method only required 79.7s. Accordingly, the new proposed algorithm actually shortens the canopy parameters mapping
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Fig.3. Histograms of the differences between estimated parameters extracted with the sorting and binary searching algorithms.
time by a factor of about 70. Similar numerical results using the two kinds of data searching algorithms were observed as shown in the histograms of Fig.3 for pigment concentration and LAI. However, small differences existed due to the size of the new smaller LUT used in the proposed method. When the size of the new LUT is set equal to the entire one, the two searching algorithms achieved the same parameter estimation results at the expense of time. As the new LUT size decreases, the differences between the two searching algorithms estimations will increase. In this study, the new smaller LUT size of 10,000 was found to be acceptable for parameter mapping requirements. 4. CONCLUSION AND DISCUSSION
Fig.2. Estimation examples of crop canopy parameters based on SPOT-5 image using the new proposed method.
Considering the large amount of calculations and long computation time of using existing LUT sorting algorithms, a new faster method for solution finding was proposed. In the new method, a binary algorithm was integrated into the searching data process. Theoretical analysis and numerical experiments fully confirmed the new method, not only effectively reducing the calculation time of canopy parameter estimation, but also revealing identical results as the currently existing search methods. However, the number of records required to be extracted from each of the M canopy reflectance LUTs to ensure reasonable mapping accuracy needs to be further investigated.
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5. ACKNOWLEDGEMENTS This study was supported by NSERC CREATE Advanced Methods, Education and Training in Hyperspectral Science and Technology (AMETHYST) program, Tecterra Inc. and the University of Lethbridge. The SPOT-5 data provided by Blackbridge Geomatics are acknowledged. 6. REFERENCES [1] S. L. Liang, “Recent developments in estimating land surface biogeophysical variables from optical remote sensing,” Progress in Physical Geography, 31(5), pp. 501-516, 2007. [2] R. Gebbers, D. Ehlert, and R. Adamek, “Rapid mapping of the leaf area index in agricultural crops,” Agronomy Journal, 103(5), pp. 1532-1541, 2011. [3] Y. Y. Dong, J. H. Wang, C. J. Li, G. J. Yang, Q. Wang, F. Liu, J. L. Zhao, H. F. Wang, and W. J. Huang, “Comparison and analysis of data assimilation algorithms for predicting the leaf area index of crop canopies,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 6(1), pp. 188201, 2013. [4] F Yang, J. L. Sun, H. L. Fang, Z. F. Yao, J. H. Zhang, Y. Q. Zhu, K. S. Song, Z. M. Wang, and M. G. Hu, “Comparison of different methods for corn LAI estimation over northeastern China,” International Journal of Applied Earth Observation and Geoinformation, 18, pp. 462-471, 2012. [5] S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. ZarcoTejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: A review of use for vegetation characterization,” Remote Sensing of Environment, 113, pp. 56-66, 2009. [6] S. Jacquemoud and F. Baret, “PROSPECT: a model of leaf optical properties spectra,” Remote Sensing of Environment, 34(2), pp. 75-91, 1990.
[7] W. Verhoef, “Light scattering by leaf layers with application to canopy reflectance modeling: the SAIL model,” Remote Sensing of Environment, 16(2), pp. 125-141, 1984. [8] M. Weiss, F. Baret, R. B. Myneni, A. Pragnere, and Y. Knyazikhin, “Investigation of a model inversion technique to estimate canopy biophysical variables from spectral and directional reflectance data,” Agronomie, 20(1), pp. 3-22, 2000. [9] P. C. Doraiswamy, T. R. Sinclair, S. Hollinger, B. Akhmedov, A. Stern, and J. Prueger, “Application of MODIS derived parameters for regional crop yield assessment,” Remote Sensing of Environment, 97(2), pp. 192-202, 2005. [10] S. B. Duan, Z. L. Li, H. Wu, B. H. Tang, L. L. Ma, E. Y. Zhao, and C. R. Li, “Inversion of the PROSAIL model to estimate leaf area index of maize, potato, and sunflower fields from unmanned aerial vehicle hyperspectral data,” International Journal of Applied Earth Observation and Geoinformation, 26, pp. 12-20, 2014. [11] D. E. Kauth, The Art of Computer Programming: Volume 3/Sorting and Searching, Addison-Wesley, Reading, MA, 1973. [12] S. A. Soenen, D. R. Peddle, C. A. Coburn, R. J. Hall, and F. G. Hall, “Canopy reflectance model inversion in multiple forward mode: forest structural information retrieval from solution set distributions,” Photogrammetric Engineering and Remote Sensing, 75(1), pp. 361-374, 2009. [13] R. Darvishzadeh, A. A. Matkan, and A. D. Ahangar, “Inversion of a radiative transfer model for estimation of rice canopy chlorophyll content using a lookup-table approach,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5(4), pp. 1222-1230, 2012. [14] E. W. Weisstein, Binary Search, MathWorld-A wolfram web resource. [15] T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to algorithms, MIT Press and McGraw-Hill, USA, 1990.
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978-1-4799-5775-0/14/$31.00 ©2014 IEEE
soil parameters, and view and illumination parameters into the SAIL model, spectrodirectional canopy reflectance in the wavelength range from 400 to 2500 nm can then be simulated [7]. Both sub-models are relatively simple and need only a limited number of input parameters. On the premise of obtaining crop canopy reflectance, different canopy parameters, such as pigment concentration and leaf area index (LAI), can be retrieved by inverting the PROSAIL model. The look-up table (LUT) approach as one of the simplest techniques to invert these kind of models has been widely used for mapping canopy biophysical and biochemical parameters based on remotely sensed agricultural data [8, 9, 10]. The key point of LUT-based inversion of the PROSAIL model for crop canopy parameters estimation is to search for the optimal solution from the simulated LUTs based on the similarity between measured and simulated reflectances. Using the root mean square error (RMSE) between measured and simulated reflectances as the evaluating index, the computational complexity of finding records (spectra) with minimum RMSE values based on the sorting algorithm is O(Nlog(N)), in which N is the number of records in the LUT [11, 12]. A large LUT is normally required to ensure a satisfactory accuracy of the retrieved parameters [13]. Accordingly, it will take more and more searching time as the size of the LUT increases to meet the crop canopy biochemical and biophysical parameters mapping requirements. In order to fulfill the needs of quickly mapping crop canopy parameters using remotely sensed data, a faster data search method is proposed in this study. For this purpose, a binary search algorithm with computational complexity of O(log(N)) is introduced for finding the closest simulated canopy reflectance to the measured one within the LUT [14, 15]. This can effectively reduce computation time of solution searching compared to the sorting algorithm. With the new proposed method, numerical experiments based on 10-m SPOT-5 imagery were selected for crop canopy parameters estimation.
2078
IGARSS 2014
2. MATERIALS AND METHODS 2.1. Study area and data The study area is situated in Lethbridge in the southern part of Alberta (49°32′N, 112°48′W), Canada. The main crop types in this region are wheat, durum, canola, and pea. A SPOT-5 multispectral image covering this experimental area was acquired on July 23, 2012. Its sensor has 10-m spatial resolution and four bands in the green (500 to 590 nm), red (610 to 680 nm), near infrared (780 to 890 nm), and shortwave infrared (1580 to 1750 nm). The study area and the satellite image are shown in Fig.1. 2.2. Look-up table LUT-based inversion of the PROSAIL model includes the following steps. Firstly, a large number of input variable combinations of the PROSAIL model are randomly generated and used in the forward calculation of the model for canopy spectral reflectance simulation. The minimum and maximum ranges for each input variable of the PROSAIL model need to be specified in this step. Afterwards, the canopy biochemical and biophysical variables are retrieved using the PROSAIL model in the inverse mode. This consists in finding within the LUT the closest simulated reflectance spectrum to the measured one in the remotely sensed imagery. The corresponding set of input variables of the PROSAIL model will then be chosen as the desired solution. The RMSE is normally used as the error criterion to measure the distance between measured and simulated reflectance. 2.3. Searching method The new proposed faster algorithm for solution searching consists of the following steps: (1) splitting the entire reflectance LUT into M smaller LUTs (where M is the number of spectral bands of the remote sensor for data processing); (2) sorting each of these LUTs based on the reflectance values; (3) using a binary search algorithm to find multiple candidate records and using the union of these candidate records selected from the single-band LUTs as a new smaller LUT (set to 10,000) to perform the final search; and (4) calculating the RMSE between the measured reflectance and the simulated reflectance in the new smaller LUT and sorting these RMSE values to find the minimum ones (set to 100) to calculate the median of input variables as the optimal solution. With this new faster method, the computational complexity as O(log(N)) is introduced, which then significantly reduces the amount of the computation time, especially when the volume of the LUT and remote sensing data for processing is large.
Fig.1. Location of the experimental area in Lethbridge, Alberta, Canada.
3. ANALYSIS AND RESULTS The new proposed approach was tested using SPOT-5 multispectral imagery. Firstly, a total number of 500,000 random combinations of eight input variables (i.e., pigment concentration, water content, dry matter content, leaf mesophyll structure, LAI, leaf angle distribution, hotspot size, and soil reflectance scale factor) of the PROSAIL model were generated. One 1-nm spectral resolution reflectance LUT was then generated using the PROSAIL model in forward mode. Secondly, the whole LUT was resampled to the spectral response functions of SPOT-5. Thirdly, the proposed faster sorting / search algorithm was used for crop canopy parameter mapping. The data were first atmospherically corrected to surface reflectance using the Fast Line-of-sight Atmospheric Analysis of Spectral Hypercubes (FLAASH). The dimension of the SPOT-5 image is 944 pixels × 2137 lines × 4 bands which was processed with the new method. This led to a run time of 4930.7s. This is considerable faster than existing sorting algorithms. The crop canopy parameters mapping results from the new approach are shown in Fig.2 for pigment concentration and LAI as examples. In order to compare the exact run time of the new proposed method with the sorting algorithm, an image subset (200 pixels × 200 lines × 4 bands) was selected, which covers the area located in the left bottom of the whole experimental area. While the traditional searching, which directly operates on the large LUT with 500,000 records, took around 5826.1s, the proposed method only required 79.7s. Accordingly, the new proposed algorithm actually shortens the canopy parameters mapping
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Fig.3. Histograms of the differences between estimated parameters extracted with the sorting and binary searching algorithms.
time by a factor of about 70. Similar numerical results using the two kinds of data searching algorithms were observed as shown in the histograms of Fig.3 for pigment concentration and LAI. However, small differences existed due to the size of the new smaller LUT used in the proposed method. When the size of the new LUT is set equal to the entire one, the two searching algorithms achieved the same parameter estimation results at the expense of time. As the new LUT size decreases, the differences between the two searching algorithms estimations will increase. In this study, the new smaller LUT size of 10,000 was found to be acceptable for parameter mapping requirements. 4. CONCLUSION AND DISCUSSION
Fig.2. Estimation examples of crop canopy parameters based on SPOT-5 image using the new proposed method.
Considering the large amount of calculations and long computation time of using existing LUT sorting algorithms, a new faster method for solution finding was proposed. In the new method, a binary algorithm was integrated into the searching data process. Theoretical analysis and numerical experiments fully confirmed the new method, not only effectively reducing the calculation time of canopy parameter estimation, but also revealing identical results as the currently existing search methods. However, the number of records required to be extracted from each of the M canopy reflectance LUTs to ensure reasonable mapping accuracy needs to be further investigated.
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5. ACKNOWLEDGEMENTS This study was supported by NSERC CREATE Advanced Methods, Education and Training in Hyperspectral Science and Technology (AMETHYST) program, Tecterra Inc. and the University of Lethbridge. The SPOT-5 data provided by Blackbridge Geomatics are acknowledged. 6. REFERENCES [1] S. L. Liang, “Recent developments in estimating land surface biogeophysical variables from optical remote sensing,” Progress in Physical Geography, 31(5), pp. 501-516, 2007. [2] R. Gebbers, D. Ehlert, and R. Adamek, “Rapid mapping of the leaf area index in agricultural crops,” Agronomy Journal, 103(5), pp. 1532-1541, 2011. [3] Y. Y. Dong, J. H. Wang, C. J. Li, G. J. Yang, Q. Wang, F. Liu, J. L. Zhao, H. F. Wang, and W. J. Huang, “Comparison and analysis of data assimilation algorithms for predicting the leaf area index of crop canopies,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 6(1), pp. 188201, 2013. [4] F Yang, J. L. Sun, H. L. Fang, Z. F. Yao, J. H. Zhang, Y. Q. Zhu, K. S. Song, Z. M. Wang, and M. G. Hu, “Comparison of different methods for corn LAI estimation over northeastern China,” International Journal of Applied Earth Observation and Geoinformation, 18, pp. 462-471, 2012. [5] S. Jacquemoud, W. Verhoef, F. Baret, C. Bacour, P. J. ZarcoTejada, G. P. Asner, C. Francois, and S. L. Ustin, “PROSPECT plus SAIL models: A review of use for vegetation characterization,” Remote Sensing of Environment, 113, pp. 56-66, 2009. [6] S. Jacquemoud and F. Baret, “PROSPECT: a model of leaf optical properties spectra,” Remote Sensing of Environment, 34(2), pp. 75-91, 1990.
[7] W. Verhoef, “Light scattering by leaf layers with application to canopy reflectance modeling: the SAIL model,” Remote Sensing of Environment, 16(2), pp. 125-141, 1984. [8] M. Weiss, F. Baret, R. B. Myneni, A. Pragnere, and Y. Knyazikhin, “Investigation of a model inversion technique to estimate canopy biophysical variables from spectral and directional reflectance data,” Agronomie, 20(1), pp. 3-22, 2000. [9] P. C. Doraiswamy, T. R. Sinclair, S. Hollinger, B. Akhmedov, A. Stern, and J. Prueger, “Application of MODIS derived parameters for regional crop yield assessment,” Remote Sensing of Environment, 97(2), pp. 192-202, 2005. [10] S. B. Duan, Z. L. Li, H. Wu, B. H. Tang, L. L. Ma, E. Y. Zhao, and C. R. Li, “Inversion of the PROSAIL model to estimate leaf area index of maize, potato, and sunflower fields from unmanned aerial vehicle hyperspectral data,” International Journal of Applied Earth Observation and Geoinformation, 26, pp. 12-20, 2014. [11] D. E. Kauth, The Art of Computer Programming: Volume 3/Sorting and Searching, Addison-Wesley, Reading, MA, 1973. [12] S. A. Soenen, D. R. Peddle, C. A. Coburn, R. J. Hall, and F. G. Hall, “Canopy reflectance model inversion in multiple forward mode: forest structural information retrieval from solution set distributions,” Photogrammetric Engineering and Remote Sensing, 75(1), pp. 361-374, 2009. [13] R. Darvishzadeh, A. A. Matkan, and A. D. Ahangar, “Inversion of a radiative transfer model for estimation of rice canopy chlorophyll content using a lookup-table approach,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 5(4), pp. 1222-1230, 2012. [14] E. W. Weisstein, Binary Search, MathWorld-A wolfram web resource. [15] T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to algorithms, MIT Press and McGraw-Hill, USA, 1990.
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