## 2 Related Works  
Most of the primary shadow compensation principles for cloud shadows and ground object shadows are similar. The image mosaic principle is often used for cloud shadow removal. However, when cloud shadows occur in high-resolution images, the typical shadow compensation methods can restore the shaded information. The shadows in high-resolution images are the primary concern of this study.  
The effects of automatic shadow compensation methods depend on the capability of the compensation principles and the accuracy of the relevant parameters. Among the image enhancement principles, LCC has been shown to be more productive with fewer parameters, utilizing the target mean and variance as well as an intensity coefficient. LCC is widely used in automatic shadow compensation studies [24; 25]. [PERSON] et al. [26] used LCC to compensate for the shadow area by combining the mean and variance in the shadow and non-shadow areas with a certain compensation coefficient. The target mean and variance were obtained from the non-shadow areas; however, they applied a certain coefficient value for all the shadow regions, and their method cannot adjust based on the shadow difference. [PERSON] et al. [27] detected shadows and segmented images into regions; and the shadow restoration was carried out for each region based on the degree of correspondence between the shadow and neighboring non-shadow regions and the LCC principle. [PERSON] et al. [28] applied the LCC method to compensate for those cloud shadows which cannot be removed by image mosaic; and referring to compensation model methods, the model parameters have a vital effect on the compensation results. [PERSON] et al. [29] designed a cubic polynomial nonlinear compensation model and adopted the Inner-Outer Outline Profile Line (IOCPL) matching method to adaptively compensate for the shaded information. The IOPLs were obtained for the boundary lines of shadows; and shadow removal was then performed according to the homogeneous sections through IOPL similarity matching to provide model parameters. [PERSON] et al. [30] implemented adaptive compensation for shadows and utilized the least-squares method to determine the parameters of the brightness correction model based on the simulated shadow cast model.  
In summary, the critical principle for automatic shadow compensation is the automatic calculation of the compensation parameter value. An efficient compensation model and a reasonable parameter calculation strategy are both essential in performing accurate shadow removal. To fill this need, our method strengthened our model's capability and designed an efficient parameter calculation strategy to improve its shadow compensation. The main highlights of our work can be summed up as follows:  
1. By taking full advantage of Wallis filter with adjustable coefficients for contrast and brightness enhancement as well as the useful LCC model in shadow compensation, we propose a compensation model by introducing two useful intensity and stretching coefficients based on Wallis filtering and LCC model. The capability of enhancing the contrast and brightness is strengthened significantly. Then it can be applied to shadow compensation more effectively.
2. Customize the shadow compensation model for the pixels in each shadow region by automatic parameter calculation and a compensation combination strategy. First, the compensation parameters are calculated using automatic feature points selection and matching for each shadow area. Then, the local window information of every pixel is considered by the combination strategy. Then, the adaptive compensation model is implemented so that they are suitable to recover the shaded information more flexibly and evenly.