Reversible data hiding (RDH) is interesting since the cover media can be losslessly recovered after extraction of hiding data. Most RDH schemes are only designed for gray-scale images and it is challenging to design an RDH scheme for binary images due to less redundancy. Relevant schemes have limitations on severe local distortions of original images, and additional patterns have to be pre-shared for data extraction, which is inconvenient and has security risks. We propose a novel method which improves the perceptual quality by using topology based histogram shifting methods, in which local topology property such as connectivity of images is preserved. More importantly, our RDH scheme for binary image is compatible with any existing RDH scheme for gray-scale images, implying hiding capacity for gray-scale images can still be improved. Theoretical analysis demonstrates the feasibility of our proposed method, and experiments show this method has better visual quality compared with a typical method.