A chronology of interpolation: from ancient astronomy to modern signal and image processing

Meijering, Erik; Falk, Howard

doi:10.1109/5.993400

Cited by 529 publications

(277 citation statements)

References 249 publications

(257 reference statements)

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“…Both MOD09A1 and MOD11A2 datasets provide data quality flags. For those observations with the bad quality flags (e.g., clouds and cloud shadows), the linear interpolation method was used for gap-filling time series data within a year (Meijering, 2002). The GPP estimates from the MODIS standard GPP products (both MOD17A2 Version-5 and Version-55) were also downloaded and used for comparison with the GPP estimates of the four EVI-based models.…”

Section: Modis Surface Reflectance Vegetation Index and Land Surfacementioning

confidence: 99%

Comparison of four EVI-based models for estimating gross primary production of maize and soybean croplands and tallgrass prairie under severe drought

Dong

Xiao

Wagle

et al. 2015

Remote Sensing of Environment

107

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Berrien III, "Comparison of four EVI-based models for estimating gross primary production of maize and soybean croplands and tallgrass prairie under severe drought" (2015). Accurate estimation of gross primary production (GPP) is critical for understanding ecosystem response to climate variability and change. Satellite-based diagnostic models, which use satellite images and/or climate data as input, are widely used to estimate GPP. Many models used the Normalized Difference Vegetation Index (NDVI) to estimate the fraction of absorbed photosynthetically active radiation (PAR) by vegetation canopy (FPAR canopy ) and GPP. Recently, the Enhanced Vegetation Index (EVI) has been increasingly used to estimate the fraction of PAR absorbed by chlorophyll (FPAR chl ) or green leaves (FPAR green ) and to provide more accurate estimates of GPP in such models as the Vegetation Photosynthesis Model (VPM), Temperature and Greenness (TG) model, Greenness and Radiation (GR) model, and Vegetation Index (VI) model. Although these EVI-based models perform well under non-drought conditions, their performances under severe droughts are unclear. In this study, we run the four EVI-based models at three AmeriFlux sites (rainfed soybean, irrigated maize, and grassland) during drought and non-drought years to examine their sensitivities to drought. As all the four models use EVI for FPAR estimate, our hypothesis is that their different sensitivities to drought are mainly attributed to the ways they handle light use efficiency (LUE), especially water stress. The predicted GPP from these four models had a good agreement with the GPP estimated from eddy flux tower in non-drought years with root mean squared errors (RMSEs) in the order of 2.17 (VPM), 2.47 (VI), 2.85 (GR) and 3.10 g C m −2 day −1 (TG). But their performances differed in drought years, the VPM model performed best, followed by the VI, GR and TG, with the RMSEs of 1.61, 2.32, 3.16 and 3.90 g C m −2 day −1 respectively. TG and GR models overestimated seasonal sum of GPP by 20% to 61% in rainfed sites in drought years and also overestimated or underestimated GPP in the irrigated site. This difference in model performance under severe drought is attributed to the fact that the VPM uses satellite-based Land Surface Water Index (LSWI) to address the effect of water stress (deficit) on LUE and GPP, while the other three models do not have such a mechanism. This study suggests that it is essential for these models to consider the effect of water stress on GPP, in addition to using EVI to estimate FPAR, if these models are applied to estimate GPP under drought conditions.

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Section: Modis Surface Reflectance Vegetation Index and Land Surfacementioning

confidence: 99%

Comparison of four EVI-based models for estimating gross primary production of maize and soybean croplands and tallgrass prairie under severe drought

Dong

Xiao

Wagle

et al. 2015

Remote Sensing of Environment

107

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“…Classical methods to achieve this goal are linear interpolation, cubic or quintic splines, radial basis functions and sinc-based interpolation techniques; see e.g. [10,13]. If the data are not available on a regular grid, scattered data interpolation techniques have been proposed [7,15].…”

Section: Introductionmentioning

confidence: 99%

Tensor Field Interpolation with PDEs

Weickert

Welk

2006

Mathematics and Visualization

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We present a unified framework for interpolation and regularisation of scalar-and tensor-valued images. This framework is based on elliptic partial differential equations (PDEs) and allows rotationally invariant models. Since it does not require a regular grid, it can also be used for tensor-valued scattered data interpolation and for tensor field inpainting. By choosing suitable differential operators, interpolation methods using radial basis functions are covered. Our experiments show that a novel interpolation technique based on anisotropic diffusion with a diffusion tensor should be favoured: It outperforms interpolants with radial basis functions, it allows discontinuity-preserving interpolation with no additional oscillations, and it respects positive semidefiniteness of the input tensor data.

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“…This versatile model, explained in details in the subsection ''Interpolation Model'' under Appendix, offers an excellent tradeoff between quality and computational cost. As corroborated by the mathematical theory of approximation, this choice ensures that, in some precise sense, the amount of arbitrariness employed to fill the gaps between pixels is minimal for a given computational budget (Meijering, 2002;Théve-naz et al, 2000). Moreover, it allows us to take advantage from multiresolution image pyramids that are fully consistent with the data model and that minimize the loss of information between a given resolution level and any coarser one (Unser et al, 1993).…”

Section: Methodsmentioning

confidence: 99%

User‐friendly semiautomated assembly of accurate image mosaics in microscopy

Thévenaz

Unser

2006

Microscopy Res & Technique

260

202

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We present a semiautomated software solution to the problem of extending the lateral field of view of a classical microscope. The initial requirements are a set of overlapping images, along with their user-provided coarse mosaic. Our solution then refines this initial mosaic in a fully automatic fashion. We rely on a highly accurate registration engine to perform the pairwise registration of the individual images, and on an efficient strategy to minimize the amount of computations while maintaining the highest possible global quality. We describe these ingredients, which we make available as a free multiplatform user-friendly software package. We also highlight why and how the specific aspects of the present microscopy application differ from those encountered while creating more common mosaics such as panoramas. Finally, we present experimental results that illustrate and validate our method on a real biological sample. We conclude by showing that we are able to reach subpixel accuracy. Microsc. Res. Tech. 70:135-146, 2007. V

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A chronology of interpolation: from ancient astronomy to modern signal and image processing

Cited by 529 publications

References 249 publications

Comparison of four EVI-based models for estimating gross primary production of maize and soybean croplands and tallgrass prairie under severe drought

Comparison of four EVI-based models for estimating gross primary production of maize and soybean croplands and tallgrass prairie under severe drought

Tensor Field Interpolation with PDEs

User‐friendly semiautomated assembly of accurate image mosaics in microscopy

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