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Recent developments in data hiding technology have made reversible data hiding (RDH) a popular research topic. This paper is focused on medical images and the up-to-date RDH methods, and proposes an automatic contrast enhancement algorithm called the RDHACEM algorithm considering two metrics: larger embedding capacity and better image visual quality. The proposed algorithm separates medical images into regions of interest (ROI) and regions of non-interest (NROI). It automatically stretches the ROI's grayscale histogram to simultaneously enlarge the embedding capacity of the ROI and enhance the image contrast. Experimental results show that the marked medical images generated by the proposed algorithm have better visual quality and larger embedding capacity in the ROI than those generated by the up-to-date RDH methods.