Analysis of Linear Interpolation Schemes for Bi-Level Image Applications

In the office, it is often necessary to scan a picture at a certain resolution and then reproduce it at a different (usually higher) resolution. This conversion can be achieved by interpolating the scanned signal between the sample intervals. This paper discusses a class of linear interpolating methods based on resampling polynomial functions. In addition, we introduce new methods to compare the performance of these interpolating schemes. The signal models used are one-dimensional step and pulse functions. These bi-level models are sufficient to describe many black/white documents. The performance of the linear interpolators is determined by evaluating their accuracy in reconstructing the original bi-level signal. The analysis considers the effects of the coarse scan and fine print intervals as well as the quantization effects. Experiments using the IEEE facsimile chart as input verify the analytical findings. The results show the advantage of using odd-order polynomials, such as the first order and TRW cubic. Also, we discuss the relationship between the interpolating ratio and the number of quantization levels needed to represent the scanned signal.