The Design of Interpolation Filters and their Application to Image Scaling and Rotation

Abstract: This paper describes a procedure for designing a class of digital filters for use in the interpolation of sampled data. It is assumed that the image has been sampled with sufficient resolution to prevent aliasing. One of these filters may be used to find the interpolated value of the sampled data stream at any interior point. The filter may also be designed to act as a low-pass filter as well as an interpolator. We show how these filters are specified and used to achieve arbitrary image enlargements, reductions and rotations. A new algorithm is also presented for rotating an image through an arbitrary angle. The algorithm consists of three shear operations. By limiting the operations to shears, a bitmap image can be rotated with no change in the number of black pels and the rotation is reversible. For grayscale images, the filters described in this paper can be used to produce rotated images with no perceptible degradation.