In reversible data embedding, to avoid overflow and underflow problem, before data embedding, boundary pixels are recorded as side information, which may be losslessly compressed. The existing algorithms often assume that a natural image has few boundary pixels so that the size of side information could be rather small. Accordingly, a relatively high pure payload could be achieved. However, there actually may exist a lot of boundary pixels in a natural image, implying that, the size of side information could be very large. Thus, when to directly use the existing algorithms, the pure embedding capacity may be not sufficient. In order to address this important problem, in this paper, we present a new and efficient framework to reversible data embedding in images that have lots of boundary pixels. The core idea is to losslessly preprocess boundary pixels so that it can significantly reduce the side information. We conduct extensive experiments to show the superiority and applicability of our work.