Abstract

Interpolation between evenly spaced image pixels is often required in optical metrology and other applications. The interpolation model considered here is motivated by neural network techniques and is applicable when each pixel is characterized by a single value. The model assumes that each pixel value may be approximated by a linear function of its nearest neighbors in accordance with a minimum mean-squared error criterion. This assumption is satisfied by functional forms for approximate pixel value vs interpixel distance (along each Cartesian coordinate) that consist of two possibly complex exponential terms. Linear combinations of these forms are used to synthesize functions that (1) match each pixel value and (2) provide continuous image values at all points between pixels. The resulting interpolation is accomplished at relatively low computational cost, as is demonstrated in computer simulations. This model may be advantageous compared to other interpolation methods because the assumption that each pixel value may be approximated by a linear function of its nearest neighbors is consistent with first-order analyses of the physics of many image forming processes.

© 1989 Optical Society of America