Abstract
The image resampling algorithm, fast Fourier transformation resampling (FFTR), is introduced. The FFTR uses a global function in the Fourier expansion form to represent an image, and the image resampling is achieved by the introduction of a phase shift in the Fourier expansion. The comparison with the cubic spline interpolation approach in the image resampling is presented, which shows that FFTR is more accurate in the satellite image resampling. The FFTR algorithm is also generally reversible, because both the resampled and its original images share the same Fourier spectrum. The resampling for the images with hot spots is discussed. The hot spots in an image are the pixels with the second-order derivatives that are order of magnitude larger than the average value. The images with the hot spots are resampled with the introduction of a local Gaussian function to model the hot spot data, so that the remaining data for the Fourier expansion are continuous. Its application to the infrared channel image of Geostationary Operational Environmental Satellite Imager, to mitigate a diur- nally changing band co-registration, is presented. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. (DOI: 10.1117/1.JRS.8.083683)
Highlights
The image resampling is the process of geometrically transforming a digital image into a new image
The Fourier amplitudes are obtained from the Fourier transformation of the original image, and the image resampling is achieved by introducing a phase shift in the Fourier expansion
This algorithm is accurate and reversible, as the original and the resampled images belong to the same global function based on the same set of Fourier spectrum
Summary
The image resampling is the process of geometrically transforming a digital image into a new image. There have been extensive discussions in the literature on the application of FFT in image resampling.[1] the FFTR algorithm presented here is significantly different from the existing approaches. The discrete Fourier transformation (DFT) with a fractional phase shift in the coordinate space becomes the so called z-transform, which has been discussed in the literature.[2] the application of FFT algorithm in the image resampling here focuses on the real sine and cosine functions, whereas the application of the FFT in the z-transform[3] in the signal processing uses the complex functions.
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