Objectives  Shadows in high-resolution remote sensing images will cause objects information loss and image quality decline, which is not beneficial for relative applications. Current shadow compensation methods often take advantage of non-shadow information around the shadow area to increase the brightness, whereas there is an unsolved problem that the contrast cannot be enhanced well enough and self-adaptively. Wallis filter principle has been used in image dodging. However, when it is used in shadow compensation, contrast improvement is not as good as other methods, leading to poor compensation results. Therefore, an improved Wallis model compensation method is proposed in this paper to enhance the brightness and contrast better to restore the shaded information.

  Methods  First, by adding compensation strength and stretch parameters, an improved Wallis model is designed. The strength parameter is positive to the brightness and contrast, and the stretch parameter is sensitive to the contrast. Therefore, the improved Wallis model is more efficient to adjust brightness and contrast. Moreover, an automatic parameters calculation strategy is further explored to customize a suitable compensation model for each shadow area. On one hand, the brightness average and deviation of the adjacent non-shadow region are calculated and used as the compensation target values. On the other hand, based on searching the same kinds of points around shadow boundaries, a series of non-shadow and shadow feature points are matched. Assumed the feature value of the non-shadow point is the approximate value of its responding shadow point, they can be used to calculate strength and stretch parameters automatically. Lastly, the brightness of each pixel in different shadow regions will be compensated by customized models to cover the shaded information self-adaptively.

  Results  In this paper, three sets of comparative experiments are set up to analyze and compare the part compensation methods algorithm, original Wallis method in three images with ordinary object shadows and cloud shadows, respectively. The differences in brightness average and gradient average between the compensated value and the non-shadow target value are used to evaluate the compensation quality. The experimental results show that: (1) Original Wallis model is useful to enhance brightness to some extent, while it is insufficient to improve contrast. As a consequence, the visual compensated results are not acceptable as the other two methods. (2) Part compensation method can improve brightness and contrast effectively. However, it cannot adjust self-adaptively according to each shadow regions condition, leading to some over-compensated and some insufficient compensation results in the same image. (3) The proposed method results indicate the best compensation quality in different shadow regions because the improved Wallis model is more pointed to improve contrast and the automatically calculated parameters values are suitable to customize the compensation model for each shadow region.

  Conclusions  Aiming at the contrast improvement of the current algorithm of automatic shadow compensation, an automatic compensation method based on an improved Wallis model is proposed in this paper. The experimental results show that the newly designed model is more effective to enhance brightness and contrast, which is useful for finding suitable parameters values. Combining with the strategy of automatic parameters calculation, its customized model can adaptively compensate each shadow. However, it should be pointed out that there are still some limitations about the shadow border compensation and the internal difference in one shadow area, which need to be further studied.