Fast discrete sinc-interpolation: A gold standard for image resampling

Numerous image processing tasks and applications require digital image resampling and geometrical transformations. These operations always assume building, from available image samples, a "continuous" image model, which is then resampled into the required new sample positions. For generating the "continuous" image model, available image samples are interpolated using, usually, convolution interpolation kernels. In the design of this process, a compromise is sought between the interpolation accuracy and computational complexity. In this chapter, we describe a family of discrete sine-interpolation algorithms that can be regarded as a gold standard for interpolation of sampled signals defined by a final number of their samples. We prove that discrete sine-interpolation is the only convolutionbased interpolation method that preserves signal content in its baseband defined by the sampling rate, provide experimental evidence of its prevalence, outline its various algorithmic implementations based on fast transform, illustrate its applications for signal/image fractional shifts, image rotation, image resizing, signal integration and differentiation, and show that the availability of fast Fourier and fast DCT-based discrete sine-interpolation algorithms makes discrete sineinterpolation a very competitive alternative to other interpolation techniques in applications that are sensitive to interpolation accuracy and require image resampling in a regular equidistant sampling grid. For image resampling in irregular sampling grid, we suggest sliding window discrete sine-interpolation methods that provide the best, for the given window size, interpolation accuracy and are, in addition, capable of simultaneous image resampling and filtering for restoration or enhancement and of local adaptation of the interpolation kernel.