Bi-cubic interpolation for shift-free pan-sharpening |
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Affiliation: | 1. “Nello Carrara” Institute of Applied Physics of the National Research Council (IFAC-CNR), 50019 Sesto Fiorentino, Italy;2. Department of Information Engineering (DINFO), University of Florence, 50139 Florence, Italy;1. Dept. of Electrical and Electronic Engineering, Yonsei University, 50, Yonsei-ro, Seodaemun-gu, Seoul, South Korea;2. Medical Device Development Center, Daegu-Gyeongbuk Medical Innovation Foundation, 80, Cheombok-Ro, Dong-gu, Daegu 41061, South Korea;1. Department of Computer and Information Technology, Liaoning Normal University, Dalian City, Liaoning Province 116029, China;2. Department of Mathematics, Liaoning Normal University, Dalian City, Liaoning Province 116029, China;3. Department of Mathematics, Tonghua Teachers College, Tonghua City, Jilin Province 134002, China;4. Department of Computer Science and Technology, Soochow University, Suzhou City, Jiangsu Province 215006, China;1. Graphics and Imaging Laboratory, Department of Informatics and Applied Mathematics, University of Girona, Spain;2. National Engineering Research Center of Digital Life, Guangzhou, China;3. School of Information Science and Technology, Sun Yat-Sen University, Guangzhou, China;4. Fluid Mechanics and Computational Science, Cranfield University, United Kingdom |
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Abstract: | Most of pan-sharpening techniques require the re-sampling of the multi-spectral (MS) image for matching the size of the panchromatic (Pan) image, before the geometric details of Pan are injected into the MS image. This operation is usually performed in a separable fashion by means of symmetric digital low-pass filtering kernels with odd lengths that utilize piecewise local polynomials, typically implementing linear or cubic interpolation functions. Conversely, constant, i.e. nearest-neighbour, and quadratic kernels, implementing zero and two degree polynomials, respectively, introduce shifts in the magnified images, that are sub-pixel in the case of interpolation by an even factor, as it is the most usual case. However, in standard satellite systems, the point spread functions (PSF) of the MS and Pan instruments are centered in the middle of each pixel. Hence, commercial MS and Pan data products, whose scale ratio is an even number, are relatively shifted by an odd number of half pixels. Filters of even lengths may be exploited to compensate the half-pixel shifts between the MS and Pan sampling grids. In this paper, it is shown that separable polynomial interpolations of odd degrees are feasible with linear-phase kernels of even lengths. The major benefit is that bi-cubic interpolation, which is known to represent the best trade-off between performances and computational complexity, can be applied to commercial MS + Pan datasets, without the need of performing a further half-pixel registration after interpolation, to align the expanded MS with the Pan image. |
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Keywords: | Digital filtering Interpolation Linear phase MS scanners Pan-sharpening Piecewise local polynomials |
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