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A scanned image of an opened book page often suffers from various scanning artifacts known as scanning shading and dark borders noises. These artifacts will degrade the qualities of the scanned images and cause many problems to the subsequent process of document image analysis. In this paper, we propose an effective method to rectify these scanning artifacts. Our method comes from two observations: that the shading surface of most scanned book pages is quasi-concave and that the document contents are usually printed on a sheet of plain and bright paper. Based on these observations, a shading image can be accurately extracted via convex hulls-based image reconstruction. The proposed method proves to be surprisingly effective for image shading correction and dark borders removal. It can restore a desired shading-free image and meanwhile yield an illumination surface of high quality. More importantly, the proposed method is nonparametric and thus does not involve any user interactions or parameter fine-tuning. This would make it very appealing to nonexpert users in applications. Extensive experiments based on synthetic and real-scanned document images demonstrate the efficiency of the proposed method.