ABSTRACT
Accurate and fast image resampling is a key operation in many digital image processing applications such as multimodality data fusion, image mosaicking, image reconstruction from projections, image superresolution from image sequences, stabilization of video images distorted by atmosphere turbulence, target location and tracking with subpixel accuracy, and so on to name a few. Image resampling assumes reconstruction of a continuous approximation of the original nonsampled image by means of interpolation of available image samples to obtain samples “in-between” the available ones. Since image samples are obtained using shift (convolutional) discretization functions (Equation 3.4), continuous image approximation should be performed in computer through digital convolution. A number of convolutional interpolation methods are known, beginning from the simplest and the least accurate nearest-neighbor and linear (bilinear, for 2D case) interpolations to more accurate cubic (bicubic, for 2D case) and higher-order spline methods. How can one evaluate the interpolation accuracy of these methods? Is perfect interpolation of sampled data possible, which does not introduce to signals any distortions additional to those caused by signal sampling? This chapter answers these questions. In the section “Perfect Resampling Filter,” we introduce the notion of the perfect resampling filter and show that discrete sinc interpolation as a discrete implementation of the ideal low-pass filtering dictated by the sampling theory is the gold standard for resampling sampled data. In the section “Fast Algorithms for Discrete Sinc Interpolation and Their Applications,” we describe methods for efficient algorithmic implementation of discrete sinc interpolation for image subsampling, fractional shift, and rotation. In the section “Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison,” we provide experimental evidence of the superiority of the discrete sinc interpolation compared to other convolutional interpolation methods. In the sections “Numerical Differentiation and Integration” and “Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms,” we illustrate applications of discrete sinc interpolation principles to accurate signal differentiation and integration and to image reconstruction from projections.
