Image interpolation and resampling

By Philippe Thévenaz, Thierry Blu, Michael A. Unser. 2000

439 citations recorded by the source corpus.

This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as a discrete sum of weighted and shifted synthesis functions—in other words, a mixed convolution equation. An important issue is the choice of adequate synthesis functions that satisfy interpolation properties. Examples of finite-support ones are the square pulse (nearest-neighbor interpolation), the hat function (linear interpolation), the cubic Keys' function, and various truncated or windowed versions of the sinc function. On the other hand, splines provide examples of infinite-support interpolation functions that can be realized exactly at a finite, surprisingly small computational cost. We discuss implementation issues and illustrate the performance of each synthesis function. We also highlight several artifacts that may arise when performing interpolation, such as ringing, aliasing, blocking and blurring. We explain why the approximation order inherent in the synthesis function is important to limit these interpolation artifacts, which motivates the use of splines as a tunable way to keep them in check without any significant cost penalty.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/4a93fe354c85bbf0b3c3b903d930ea7c969406b2

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Super resolution using edge prior and single image detail synthesis (2010, background): “, [1, 14, 4, 27]) have their foundations in sampling theory and try to interpolate the HR image from the LR input.”
Linear interpolation revitalized (2004, background): “I. INTRODUCTION STANDARD piecewise-linear interpolation, which datesback to the Babylonians [1], is by far the most popular solution for many applications such as computer vision, digital photography, computer graphics, postscript optimization for printers, image calibration and registration,…”
Image registration methods: a survey (2003, background): “6), quadratic splines [42,191], cubic Bsplines [89], higher-order B-splines [108], Catmull–Rom cardinal splines [100,184], Gaussians [7], and truncated sinc functions [182] belong to the most commonly used interpolants.”
Image super-resolution using gradient profile prior (2008, methodology): “The interpolation based methods [12, 29, 18] are simple but tend to blur the high frequency details.”
Antileakage Fourier transform for seismic data regularization (2005, methodology): “We follow the definition of interpolation given by Thévenaz et al. (2000): model-based recovery of continuous data from discrete data with a known range of abscissa.”
Image upsampling via imposed edge statistics (2007, background): “In [Thvenaz et al. 2000], a more detailed survey of these techniques and their shortcomings is given.”
Sampling-50 years after Shannon (2000, background): “In addition, most of the results presented in Section IV are also available for the multifunction case [19].”
Seven Ways to Improve Example-Based Single Image Super Resolution (2015, methodology): “To address this problem, the SR literature proposes interpolation-based meth-ods [24], reconstruction-based methods [3, 12, 21, 31, 33], and learning-based methods [15, 9, 25, 26, 6, 34, 5].”
Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces (2001, methodology): “, for taking into account real acquisition and reconstruction devices, for modeling signals with smoother spectrum than is the case with bandlimited functions, or for numerical implementation [9, 13, 22, 26, 85, 86, 103, 104, 107, 110, 115, 116].”