The authors derive an adaptive version of cubic convolution interpolation for the enlargement or reduction of digital images by arbitrary scaling factors. The adaptation is performed in each subblock (typically LxL rectangular) of an image. It consists of three phases: two scaling procedures (i.e., forward and backward interpolation) and an optimization of the interpolation kernel. In the forward interpolation phase, from the sampled data with the original resolution, we generate scaled data with different (higher or lower) resolution. The backward interpolation produces new discrete data by applying another interpolation to the scaled one. The phases are based on a cubic convolution interpolation whose kernel is modified to adapt to local properties of the data. During the optimization phase, we modify the parameter values to decrease the disparity between the original data and those resulting from another interpolation on the different-resolution output of the forward interpolating phase. The overall process is repeated iteratively. We show experimental results that demonstrate the effectiveness of the proposed interpolation method. The algorithm exhibits significant improvement in the minimization of information loss when compared with the conventional interpolation algorithms.