Abstract: A new interpolation model is proposed based on the bivariate rational interpolation. This model contains rational fractal interpolation and bivariate rational interpolation, which is identified uniquely by the values of iterated function system parameters (scaling factor and shape parameters). Due to efficient capacity of fractal in description of complex phenomenon, the fractal dimension is employed to texture analysis. Based on the analysis of local fractal dimension (LFD), a new local adaptive threshold method is proposed. And then images can be divided into texture region and non-texture region. As for texture regions, rational fractal interpolation is used to get high resolution images. Similarly, rational interpolation is used in non-texture region. Considering the parameters in rational fractal interpolation model, we propose a new method for calculating the scaling factor. Further, in order to improve the quality of interpolated image, shape parameters optimization technique is applied. Experimental results show that the presented model achieves very competitive performance with the state-of-the-art interpolation algorithms.