The methods and systems of this invention allow for independent adaptive control of ringing and overshoot effects in 2-dimensional array interpolation processes, including in image and video rescaling and analysis. The methods and systems can use either a column-wise or a row-wise interpolation, or a combination thereof. Each uses a respective preliminary interpolation of data, followed by ringing and/or overshoot control. Controllable parameters allow variability in the amount of ringing and/or overshoot retained in the interpolated data. The ringing and overshoot controls apply a local analysis of the data to adjust the preliminary interpolation results. The methods may be repeated iteratively, for example, to obtain a desired rescaling of an image data array.