## 4 Results and Evaluation
### Statistical Analysis  
#### 4.2.1 Reflectance Analysis  
To further investigate the overall reflectance change for different slopes and aspects after topographic correction, we took band 4 for instance and demonstrated the reflectance intensity distribution of each sub-scene outlined in Figure 2 with polar-coordinate plots (Figure 3). The upper row is for the original spring TM sub-scene and its correction results by different methods; the lower row is for the autumn TM sub-scene and its corresponding correction results. It is evident that sun-facing slopes (aspect angles ranging from about 49\({}^{\circ}\) to about 229\({}^{\circ}\)) reveal higher reflectance values than sun-averted slopes before topographic correction, though the land cover types are quite uniformly distributed in terms of slopes and aspects (as can be seen in Figure 2). This phenomenon, if not being dealt with, is expected to interfere with the subsequent application of images.  
Figure 2: TM scenes before and after topographic correction (composite of band 5, 4 and 3 in red, green and blue), the upper half part is for the autumn scene, and the lower for the spring scene. (**A**) is autumn scene before correction; (**B**) after correction by the proposed model; (**a1**) is illumination condition map for “sub-scene a”; (**a2**) is enlarged window for “sub-scene a”; (**a3–a5**) are “sub-scene a” corrected by Sandmeier model, Li model and model proposed, respectively; (**C**) is spring scene before correction; (**D**) after correction by the proposed model; (**b1**) is illumination condition map for “sub-scene b”; (**b2**) is enlarged window for “sub-scene b”; and (**b3–b5**) are “sub-scene b” corrected by Sandmeier model, Li model and the proposed model, respectively.  
After topographic correction by Sandmeier model, reflectance in sun-averted slopes is strongly enhanced, and the reflectance values tend to be more uniformly distributed than before. However, some points in sun-averted slopes (with relatively large slope angles) show inharmonious large values, especially for the spring sub-scene (Figure 3b). This may be explained by the over-correction of faintly illuminated pixels. Li model and model proposed achieved very similar results (Figure 3c _vs._ Figure 3d, Figure 3g _vs._ Figure 3h). They all further reduced the reflectance differences between sun-facing and sun-averted slopes, and made the reflectance distribution more uniform compared with Sandmeier model. Minor differences between results from Li model and model proposed are not directly noticeable. Thus, subtractions between them were done and demonstrated in Figure 4. Nevertheless, Figure 4 only suggests that differences exist. Whether proposed model outperforms Li model need further quantitative investigation.  
Figure 3: The reflectance intensity distribution of band 4 from different topographic correction methods for different slope (denoted by the radius) and aspect angles (**a**–**h**). The upper row is the for spring TM sub-scene and its correction results from different methods; the lower row is for the autumn TM sub-scene and its correction results from different methods, therein, first column for the original images, second column for the correction results by Sandmeier model, third column for the correction results by Li model, forth column for the correction results by the model proposed, respectively.