Topographic Correction Method for High Spatial Resolution Remote Sensing Data in Mountainous Area
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摘要: 山区地形复杂，遥感影像地形效应明显，易造成"同物异谱"、"同谱异物"现象，增大了遥感地质填图的难度.但前人对适用于复杂地形条件下地质填图的地形校正模型讨论较少，特别是校正高空间分辨率遥感影像时多缺少对应高精度数字高程模型，校正结果易受地形异常影响.在Richter"山区"校正模型基础上引入地形抹平模型，提出"Smoothed山区"校正方法，并与另14种地形校正模型在GF-1、GF-2、SPOT6山区影像上进行对比实验.结果显示，"Smoothed山区"校正模型在山区高空间分辨率遥感影像的校正效果明显优于其他模型，校正结果地形效应减弱，影像信息丰富不失真，并且直接获取地表反射率数据，可为进一步的遥感蚀变提取等工作提供基础数据.该模型适用于复杂地形山区的遥感地质填图.Abstract: With complex terrain and steep slopes, sharp orographic effect occurs in mountainous areas which obviously increases the difficulty of remote sensing geological mapping by the phenomenon of "different bodies with same spectrums" or "same body with different spectrums". Although several Topographic correction (TOC) methods have been proposed and applied to vegetationcovered area and snowfield successfully in the last decades, there is little discussion on topographic correction models for geological mapping under complex topographic conditions, which have totally different application environment since the uncovered geological bodies of mountainous areas have bigger spatial variability. Especially in the correction of high spatial resolution remote sensing images, the corresponding high-precision Digital Elevation Model (DEM) is often absent, and the correction results are vulnerable to topographic anomalies. This paper proposes a "Smoothed Mountains" correction method, which combines Richter "Mountains" correction model with terrain smoothing model. GF-1, GF-2 and SPOT6 mountain images obtained by this model have been compared with those by other 14 terrain correction models. The results show that the stability and correction effect of the "Smoothed Mountains" correction model are obviously better than other models. The correction images show that the terrain effect is weakened, and the image information is rich and undistorted. Moreover, the surface reflectance data can be obtained directly, which provides basic data for further remote sensing alteration extraction. Therefore, the "Smoothed Mountains" model could be a practical and feasible TOC model in remote sensing geological mapping over steep mountain terrain.
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图 1 实验区1坡度直方图(a)与地形抹平后坡度直方图(b)
Fig. 1. Histogram of study surface slope (a) and histogram of surface slope by smoothed terrain in study area 1 (b)
图 3 地形校正前实验区1 GF-1 3(R), 2(G)1(B)波段组合影像(a)、实验区1地理位置示意图(b)及地形阴影图(c)
Fig. 3. Composite of GF-1 bands 3, 2 and 1in study area 1(before topographic correction) (a), Geographical location sketch map of study area (b), Topographic hill-shade map (c).
图 4 地形校正前实验区2 GF-2 3(R), 2(G)1(B)波段组合影像(a)、实验区3 SPOT63(R), 2(G)1(B)波段组合影像(b)、实验区2与实验区3地理位置示意图(c)、及地形阴影图(d, e)
Fig. 4. Composite of GF-2 bands 3, 2 and 1 in study area 2 (before topographic correction) (a), Composite of SPOT6 bands 3, 2 and 1 in study area 1 (before topographic correction) (b), Geographical location sketch map of study area-2 and area-3 (c), Topographic hill-shade map (d, e)
图 5 实验区1地形校正前后影像对比[GF-1 3(R), 2(G), 1(B)1%线性拉伸]
Fig. 5. Original and corrected images in study area 1 with different topographic correction models
图 6 实验区2地形校正前后影像对比[GF-2 3(R), 2(G), 1(B)线性1%拉伸]
Fig. 6. Original and corrected images in study area 2 with different topographic correction models
图 7 实验区3地形校正前后影像对比[SPOT6 3(R), 2(G), 1(B)1%线性拉伸]
Fig. 7. Original and corrected images in study area 3 with different topographic correction models
图 8 实验区1地形校正后GF-1各波段辐射度与cosis 的回归斜率和相关系数(a、c)、地形校正后GF-1各波段辐射度四分位距减少量(b, d)
Fig. 8. Slope and correlation coefficient of regression between cosis and the radiance of each spectral band of GF-1 after topographic correction in study area-1(a, c); Intraclass IQR reduction of each spectral band of GF-1 after topographic correction in study area-1(b, d)
图 9 实验区2地形校正后GF-2各波段辐射度与cosis 的回归斜率和相关系数(a、c)、地形校正后GF-1各波段辐射度四分位距减少量(b, d)
Fig. 9. Slope and correlation coefficient of regression between cosis and the radiance of each spectral band of GF-2 after topographic correction in study area-2(a, c); Intraclass IQR reduction of each spectral band of GF-1 after topographic correction in study area-2(b, d)
图 10 实验区3地形校正后SPOT6各波段辐射度与cosis 的回归斜率和相关系数(a、c)、地形校正后SPOT6各波段辐射度四分位距减少量(b, d)
Fig. 10. Slope and correlation coefficient of regression between cosis and the radiance of each spectral band of SPOT6 after topographic correction in study area-3(a, c); Intraclass IQR reduction of each spectral band of SPOT6 after topographic correction in study area-3(b, d)
图 11 实验区1内4个岩体地形校正后GF-1各波段辐射度与cosis 的回归斜率和相关系数
Fig. 11. Slope and correlation coefficient of regression between cosis and the radiance of each spectral band of GF-1 after topographic correctionfor the 4 rocks in study area-1
图 13 实验区1内4个岩体地形校正后GF-1各波段辐射度与cosis 的回归斜率和相关系数(a、b、c、d)、地形校正后GF-1各波段辐射度四分位距减少量(e、f、g、h)
Fig. 13. Slope and correlation coefficient of regression between cosis and the radiance of each spectral band of GF-1 after topographic correction Image for the4 rocks in study area-1 (a, b, c, d); Intraclass IQR reduction of each spectral band of GF-1 after topographic correction for the 4 rocks in study area-1 (e, f, g, h)
图 12 实验区1内4个岩体地形校正后GF-1各波段辐射度四分位距减少量
Fig. 12. Intraclass IQR reduction of each spectral band of GF-1 after topographic correction for the 4 rocks in study area-1
图 14 实验区1“Smoothed山区”校正前后影像对比
Fig. 14. Image of the study area 1 before and after "Smooth Mountains" correction models
表 1 地形校正模型及其算法表达式
Table 1. algorithm Expressions of topographic correction methods
校正模型 算法公式 参考文献 校正模型 算法公式 参考文献 Teillet-回归 $ {L}_{\text{corr}, \mathtt{λ }}={{L}_{\lambda }}-a\cdot \text{cos}{{i}_{s}}-b+\overline{{{L}_{\mathtt{λ }}}}$ Teillet et al.(1982) Cosine ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}\frac{\text{cos}{{\theta }_{z}}}{\text{cos}{{i}_{s}}}$ Teillet et al.(1982) C ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}\frac{{cos}{{\theta }_{z}}+{{C}_{\mathtt{λ }}}}{\text{cos}{{i}_{s}}+{{C}_{\mathtt{λ }}}}$ Teillet et al.(1982) SCOS ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}\frac{\text{cos}{{\theta }_{z}}}{\text{cos}i{{'}_{s}}}$ 姜亢等(2014) sCC3 ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}\frac{{cos}{{\theta }_{z}}+{{C}_{\mathtt{λ }}}}{\text{cos}i{{'}_{s}}+{{C}_{\mathtt{λ }}}}$ Riano et al.(2003) Minnaert ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}\frac{\text{cos}\alpha }{\text{co}{{\text{s}}^{\text{k}}}{{i}_{\text{s}}}\cdot \text{co}{{\text{s}}^{\text{k}}}\alpha }$ Smith et al.(1980) SCS-C ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\mathtt{λ }}}\frac{{cos}{{\theta }_{z}}cos\mathtt{α}+{{C}_{\mathtt{λ }}}}{\text{cos}{{i}_{s}}+{{C}_{\mathtt{λ }}}}$ Scott et al. (2005) Minnaert-SCS ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}\frac{\text{co}{{\text{s}}^{\text{k}}}{{\theta }_{z}}\text{cos}\alpha }{\text{co}{{\text{s}}^{\text{k}}}{{i}_{s}}}$ Vincini et al.(2002) Smoothed Gamma ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\mathtt{λ }}}\frac{{cos}{{\theta }_{z}}+\text{cos}{{\theta }_{v}}}{\text{cos}i{{'}_{s}}+\text{cos}i{{'}_{v}}}$ 本文 二阶段校正 1步:${{L}_{\text{first}}}={{L}_{\lambda }}+{{L}_{\lambda }}\left(\frac{{{\mu }_{k}}-{{X}_{ij}}}{{{\mu }_{k}}} \right)$；2步:${{L}_{\text{corr, }\mathtt{λ }}}={{L}_{\lambda }}+{{L}_{\lambda }}\left(\frac{{{\mu }_{k}}-{{X}_{ij}}}{{{\mu }_{k}}} \right)\begin{array}{*{35}{l}} {{C}_{\text{2sn}}} \\ \end{array}$ Civco(1989) 坡度匹配 1步:${{L}_{\text{first}}}={{L}_{\lambda }}+\left({{L}_{\text{max}, \mathtt{λ }}}-{{L}_{\text{min}, \mathtt{λ }}} \right)\left(\frac{{{\mu }_{w}}-{{X}_{ij}}}{{{\mu }_{w}}} \right)$; 2步:${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\lambda }}+\left({{L}_{\text{max}, \mathtt{λ }}}-{{L}_{\text{min}, \mathtt{λ }}} \right)\left(\frac{{{\mu }_{w}}-{{X}_{ij}}}{{{\mu }_{w}}} \right){{C}_{2\text{sm}}}$ Nichol et al. (2006) 3因子+C ${{L}_{\text{corr}, \mathtt{λ }}}={{L}_{\mathtt{λ }}}\left\{ \frac{\text{cos}{{\theta }_{z}}+\frac{1-T\left(\lambda, \theta \right)}{2T\left(\lambda, \theta \right)}+{{C}_{\mathtt{λ }}}}{\left(1+\left(1-{{V}_{\text{sky}}}\left(x, y \right) \right)\mathtt{ρ}_{\text{terrain}}^{\left(i-1 \right)} \right)\left\{ \Phi \left(x, y \right)\text{cos}{{i}_{\text{s}}}+\frac{1-T\left(\lambda, \theta \right)}{2}\left[ \text{cos}{{i}_{s}}+\left(1/T\left(\lambda, \theta \right)-\text{cos}{{\theta }_{z}} \right){{V}_{\text{sky}}}\left(x, y \right) \right]+{{C}_{\mathtt{λ }}} \right\}} \right\}$ Zhang and Gao(2011), 张伟阁等(2015) 考虑地表BRDF校正 $ {{\mathtt{ρ}}_{\text{corr}, \mathtt{λ }}}=\frac{\pi \cdot\left[L_{\lambda}-L_\text{p}\right] / \tau_\text{u p}}{\mathtt{ɸ}(x, y) \frac{\left(E_\text{d i r}+E_\text{d i l} \tau_\text{d o m n}\right) \cos i_{s}}{\cos \theta_{s}} \frac{\Omega\left(i_{s}, i_{v}, \varphi\right)}{\Omega\left(\theta_{s}, \theta_{v}, \varphi\right)}+\frac{\left[E_\text{dif}\left(1-\mathtt{ɸ}(x, y)(x, y) \tau_\text{d o w n}\right) V_\text{s ky}(x, y)+E_\text{iter}^{(i)}\right]}{\pi \Omega\left(\theta_{s}, \theta_{v}, \varphi\right)} \int_{0}^{2 \pi} \int_{0}^{\pi / 2} \Omega\left(i_{s}, i_{v}, \varphi\right) \text{d} \Omega_{i}}$ 闻建光等(2007); 蒋璐媛等(2015) “山区”校正 ${{\mathtt{ρ}}_{\text{corr}, \mathtt{λ }}}=\frac{\mathtt{π}\left[ {{\text{d}}^{2}}{{L}_{\lambda }}-{{L}_{\text{min}, \mathtt{λ }}} \right]}{{{\mathtt{τ }}_{\text{up}}}\left\{ \Phi \left(x, y \right){{E}_{\text{dir}}}\text{cos}{{i}_{s}}+{{E}_{\text{dif}}}\left[ \Phi \left(x, y \right){{\mathtt{τ }}_{\text{down}}}\frac{\text{cos}{{i}_{s}}}{\text{cos}{{\theta }_{z}}}+\left(1-\Phi \left(x, y \right){{\mathtt{τ }}_{\text{down}}} \right){{V}_{\text{sky}}}\left(x, y \right) \right]+E_{\text{iter}}^{\left(i \right)} \right\}} $ Richter(1998); 宋丽瑶等(2017) 
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