Standard deviational ellipse (SDE) has long served as a versatile GIS tool for delineating the geographic distribution of concerned features. This paper firstly summarizes two existing models of calculating SDE, and then proposes a novel approach to constructing the same SDE based on spectral decomposition of the sample covariance, by which the SDE concept is naturally generalized into higher dimensional Euclidean space, named standard deviational hyper-ellipsoid (SDHE). Then, rigorous recursion formulas are derived for calculating the confidence levels of scaled SDHE with arbitrary magnification ratios in any dimensional space. Besides, an inexact-newton method based iterative algorithm is also proposed for solving the corresponding magnification ratio of a scaled SDHE when the confidence probability and space dimensionality are pre-specified. These results provide an efficient manner to supersede the traditional table lookup of tabulated chi-square distribution. Finally, synthetic data is employed to generate the 1-3 multiple SDEs and SDHEs. And exploratory analysis by means of SDEs and SDHEs are also conducted for measuring the spread concentrations of Hong Kong’s H1N1 in 2009.

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Sentinel-2 is a very new programme of the European Space Agency (ESA) that is designed for fine spatial resolution global monitoring. Sentinel-2 images provide four 10 m bands and six 20 m bands. To provide more explicit spatial information, this paper aims to downscale the six 20 m bands to 10 m spatial resolution using the four directly observed 10 m bands. The outcome of this fusion task is the production of 10 Sentinel-2 bands with 10 m spatial resolution. This new fusion problem involves four fine spatial resolution bands, which is different to, and more complex than, the common pan-sharpening fusion problem which involves only one fine band. To address this, we extend the existing two main families of image fusion approaches (i.e., component substitution, CS, and multiresolution analysis, MRA) with two different schemes, a band synthesis scheme and a band selection scheme. Moreover, the recently developed area-to-point regression kriging (ATPRK) approach was also developed and applied for the Sentinel-2 fusion task. Using two Sentinel-2 datasets released online, the three types of approaches (eight CS and MRA-based approaches, and ATPRK) were compared comprehensively in terms of their accuracies to provide recommendations for the task of fusion of Sentinel-2 images. The downscaled ten-band 10 m Sentinel-2 datasets represent important and promising products for a wide range of applications in remote sensing. They also have potential for blending with the upcoming Sentinel-3 data for fine spatio-temporal resolution monitoring at the global scale.

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