Jung and Yoo proposed a new image interpolation method, neighbor mean interpolation, on which they first constructed image interpolation based data hiding (IIDH) scheme. However, the authors only adopted a simple method by adding the decimal value of secret into pixels in cover image. Therefore, even though neighbor mean interpolation method is very cost effective, Jung and Yoo's IIDH scheme does not have very high-resolution stego image. In this paper, we still use neighbor mean interpolation (NMI) to generate cover image, but adopt least significant (LSB) substitution and optimal pixel adjustment process (OPAP) instead of simple addition to improve visual quality of stego image. The main contribution of this paper is to prove theoretically that our IIDH schemes have the better stego image quality than Jung and Yoo's IIDH scheme. HighlightsThis paper is theoretically to prove that our proposed IIDH (image interpolation based data hiding) schemes have the better stego image quality than Jung and Yoo's IIDH scheme.Jung and Yoo's IIDH scheme is very cost-effective, so we use simple addition approach such as LSB substitution and OPAP to enhance PSNR of stego image.We analytically estimate PSNR of three IIDH schemes: Jung and Yoo's IIDH scheme, the proposed IIDH scheme using LSB, and the proposed IIDH scheme using OPAP.The proposed IIDH scheme using OPAP has the same embedding capacity of Jung and Yoo, and meanwhile has the higher PSNR than that of Jung and Yoo's IIDH scheme.