Image interpolation is an important topic in the field of image processing. It is defined as the process of transforming low-resolution images into high-resolution ones using image processing methods. Recent studies on interpolation have shown that researchers are focusing on successful interpolation techniques that preserve edge information. Therefore, the edge detection phase plays a vital role in interpolation studies. However, these approaches typically rely on gradient-based linear computations for edge detection. On the other hand, non-linear structures that effectively simulate the human visual system have gained attention. In this study, a non-linear method was developed to detect edge information using a pixel similarity approach. Pixel similarity-based edge detection approach offers both lower computational complexity and more successful interpolation results compared to gradient-based approaches. 1D cubic interpolation was applied to the pixels identified as edges based on pixel similarity, while bicubic interpolation was applied to the remaining pixels. The algorithm was tested on 12 commonly used images and compared with various interpolation techniques. The results were evaluated using metrics such as SSIM and PSNR, as well as visual assessment. The experimental findings clearly demonstrated that the proposed method outperformed other approaches. Additionally, the method offers significant advantages, such as not requiring any parameters and having competitive computational cost.