Optimal image scaling using pixel classification

We introduce a new approach to optimal image scaling called resolution synthesis (RS). In RS, the pixel being interpolated is first classified in the context of a window of neighboring pixels; and then the corresponding high-resolution pixels are obtained by filtering with coefficients that depend upon the classification. RS is based on a stochastic model explicitly reflecting the fact that pixels falls into different classes such as edges of different orientation and smooth textures. We present a simple derivation to show that RS generates the minimum mean-squared error (MMSE) estimate of the high-resolution image, given the low-resolution image. The parameters that specify the stochastic model must be estimated beforehand in a training procedure that we have formulated as an instance of the well-known expectation-maximization (EM) algorithm. We demonstrate that the model parameters generated during the training may be used to obtain superior results even for input images that were not used during the training.