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Flexbrdf/hytools/brdf/kernels.py
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Flexbrdf/hytools/brdf/kernels.py
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# -*- coding: utf-8 -*-
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"""
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HyTools: Hyperspectral image processing library
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Copyright (C) 2021 University of Wisconsin
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Authors: Adam Chlus, Zhiwei Ye, Philip Townsend.
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, version 3 of the License.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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本模块包含计算 BRDF 散射核函数的函数。
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方程和常数可在以下论文中找到：
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Colgan, M. S., Baldeck, C. A., Feret, J. B., & Asner, G. P. (2012).
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Mapping savanna tree species at ecosystem scales using support vector machine classification
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and BRDF correction on airborne hyperspectral and LiDAR data.
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Remote Sensing, 4(11), 3462-3480.
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https://doi.org/10.3390/rs4113462
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Lucht, W., Schaaf, C. B., & Strahler, A. H. (2000).
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An algorithm for the retrieval of albedo from space using semiempirical BRDF models.
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IEEE Transactions on Geoscience and Remote sensing, 38(2), 977-998.
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https://doi.org/10.1109/36.841980
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Maignan, F., Bréon, F. M., & Lacaze, R. (2004).
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Bidirectional reflectance of Earth targets: Evaluation of analytical
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models using a large set of spaceborne measurements with emphasis on the Hot Spot.
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Remote Sensing of Environment, 90(2), 210-220.
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https://doi.org/10.1016/j.rse.2003.12.006
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Roujean, J. L., Leroy, M., & Deschamps, P. Y. (1992).
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A bidirectional reflectance model of the Earth's surface for the correction
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of remote sensing data.
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Journal of Geophysical Research: Atmospheres, 97(D18), 20455-20468.
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https://doi.org/10.1029/92JD01411
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Schlapfer, D., Richter, R., & Feingersh, T. (2015).
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Operational BRDF effects correction for wide-field-of-view optical scanners (BREFCOR).
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IEEE Transactions on Geoscience and Remote Sensing, 53(4), 1855-1864.
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https://doi.org/10.1109/TGRS.2014.2349946
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Wanner, W., Li, X., & Strahler, A. H. (1995).
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On the derivation of kernels for kernel-driven models of bidirectional reflectance.
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Journal of Geophysical Research: Atmospheres, 100(D10), 21077-21089.
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https://doi.org/10.1029/95JD02371
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Zhang, X., Jiao, Z., Dong, Y., Zhang, H., Li, Y., He, D., ... & Chang, Y. (2018).
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Potential investigation of linking PROSAIL with the ross-li BRDF model for
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vegetation characterization.
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Remote Sensing, 10(3), 437.
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https://doi.org/10.3390/rs10030437SSS
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"""
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import numpy as np
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def calc_geom_kernel(solar_az,solar_zn,sensor_az,sensor_zn,kernel,b_r=1.,h_b =2.):
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"""计算几何散射核函数。
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常数 b_r (b/r) 和 h_b (h/b) 来自 Colgan 等人 RS 2012
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替代方案包括 MODIS 规范：
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b/r : 稀疏: 1, 密集: 2.5
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h/b : 稀疏, 密集 : 2
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所有输入几何单位必须以弧度为单位。
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参数:
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solar_az (numpy.ndarray): 太阳方位角。
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solar_zn (numpy.ndarray): 太阳天顶角。
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sensor_az (numpy.ndarray): 传感器视角方位角。
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sensor_zn (numpy.ndarray): 传感器视角天顶角。
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kernel (str): Li 几何散射核类型 [li_dense,li_sparse, roujean]。
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b_r (float, 可选): 物体高度。默认为 10。
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h_b (float, 可选): 物体形状。默认为 2。
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返回:
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numpy.ndarray: 几何散射核。
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"""
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relative_az = sensor_az - solar_az
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# Eq. 37,52. Wanner et al. JGRA 1995
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solar_zn_p = np.arctan(b_r * np.tan(solar_zn))
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sensor_zn_p = np.arctan(b_r * np.tan(sensor_zn))
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# Eq 50. Wanner et al. JGRA 1995
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D = np.sqrt((np.tan(solar_zn_p)**2) + (np.tan(sensor_zn_p)**2) - 2*np.tan(solar_zn_p)*np.tan(sensor_zn_p)*np.cos(relative_az))
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# Eq 49. Wanner et al. JGRA 1995
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t_num = h_b * np.sqrt(D**2 + (np.tan(solar_zn_p)*np.tan(sensor_zn_p)*np.sin(relative_az))**2)
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t_denom = (1/np.cos(solar_zn_p)) + (1/np.cos(sensor_zn_p))
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t = np.arccos(np.clip(t_num/t_denom,-1,1))
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# Eq 33,48. Wanner et al. JGRA 1995
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O = (1/np.pi) * (t - np.sin(t)*np.cos(t)) * t_denom
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# Eq 51. Wanner et al. JGRA 1995
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cos_phase_p = np.cos(solar_zn_p)*np.cos(sensor_zn_p) + np.sin(solar_zn_p)*np.sin(sensor_zn_p)*np.cos(relative_az)
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if kernel == 'li_sparse':
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# Eq 32. Wanner et al. JGRA 1995
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k_geom = O - (1/np.cos(solar_zn_p)) - (1/np.cos(sensor_zn_p)) + .5*(1+ cos_phase_p) * (1/np.cos(sensor_zn_p))
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elif kernel == 'li_dense':
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# Eq 47. Wanner et al. JGRA 1995
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k_geom = (((1+cos_phase_p) * (1/np.cos(sensor_zn_p)))/ (t_denom - O)) - 2
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elif kernel == 'li_sparse_r':
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# Eq 39. Lucht et al. TGRS 2000
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k_geom = O - (1/np.cos(solar_zn_p)) - (1/np.cos(sensor_zn_p)) + .5*(1+ cos_phase_p) * (1/np.cos(sensor_zn_p)) * (1/np.cos(solar_zn_p))
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elif kernel == 'li_dense_r':
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# Eq 5. Zhang et al. RS 2018 <-- Find a more original reference
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k_geom = (((1+cos_phase_p) * (1/np.cos(sensor_zn_p)) * (1/np.cos(solar_zn_p)))/ (t_denom - O)) - 2
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elif kernel == 'roujean':
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# Eq 2 Roujean et al. JGR 1992
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k_geom1 = (1/(2*np.pi)) * ((np.pi - relative_az)*np.cos(relative_az)+np.sin(relative_az)) *np.tan(solar_zn)*np.tan(sensor_zn)
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k_geom2 = (1/np.pi) * (np.tan(solar_zn) + np.tan(sensor_zn) + np.sqrt(np.tan(solar_zn)**2 + np.tan(sensor_zn)**2 - 2*np.tan(solar_zn)*np.tan(sensor_zn)*np.cos(relative_az)))
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k_geom = k_geom1 - k_geom2
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else:
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print("Unrecognized kernel type: %s" % kernel)
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k_geom = None
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return k_geom
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def calc_volume_kernel(solar_az,solar_zn,sensor_az,sensor_zn,kernel):
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"""计算体积散射核函数。
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所有输入几何单位必须以弧度为单位。
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参数:
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solar_az (numpy.ndarray): 太阳方位角。
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solar_zn (numpy.ndarray): 太阳天顶角。
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sensor_az (numpy.ndarray): 传感器视角方位角。
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sensor_zn (numpy.ndarray): 传感器视角天顶角。
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kernel (str): 体积散射核类型 [ross_thick,ross_thin]。
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返回:
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numpy.ndarray: 体积散射核。
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"""
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relative_az = sensor_az - solar_az
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# Eq 2. Schlapfer et al. IEEE-TGARS 2015
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phase = np.arccos(np.cos(solar_zn)*np.cos(sensor_zn) + np.sin(solar_zn)*np.sin(sensor_zn)* np.cos(relative_az))
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if kernel == 'ross_thin':
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# Eq 13. Wanner et al. JGRA 1995
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k_vol = ((np.pi/2 - phase)*np.cos(phase) + np.sin(phase))/ (np.cos(sensor_zn)*np.cos(solar_zn)) - (np.pi/2)
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elif kernel == 'ross_thick':
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# Eq 7. Wanner et al. JGRA 1995
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k_vol = ((np.pi/2 - phase)*np.cos(phase) + np.sin(phase))/ (np.cos(sensor_zn)+np.cos(solar_zn)) - (np.pi/4)
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elif kernel in ('hotspot','roujean'):
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# Eq 8 Roujean et al. JGR 1992
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k_vol1 = (4/(3*np.pi)) * (1/(np.cos(solar_zn) + np.cos(sensor_zn)))
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k_vol2 = (((np.pi/2) - phase) * np.cos(phase) + np.sin(phase))
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k_vol = k_vol1*(k_vol2- (1/3))
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if kernel == 'hotspot':
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# Eq. 12 Maignan et al. RSE 2004
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k_vol = k_vol1* k_vol2 * (1 + (1 + (phase/np.radians(1.5)))**-1) - (1/3)
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else:
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print("Unrecognized kernel type: %s" % kernel)
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k_vol = None
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return k_vol
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