A new optimal image smoothing method based on generalized discrete iterated Laplacian minimization and its application i
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RESEARCH ARTICLE
A new optimal image smoothing method based on generalized discrete iterated Laplacian minimization and its application in the analysis of earth’s surface using satellite remote sensing imagery Mostafa Kiani Shahvandi 1 Received: 24 March 2020 / Accepted: 8 November 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper a new method of image smoothing and its applications in the field of remote sensing are presented. This method is based on the minimization of the iterated Laplace operator of an arbitrary degree in the Cartesian coordinate system. Using the method of finite differences, a linear combination is derived, which represents the solution of the minimization problem. For the special case of the ordinary Laplace operator, the solution is explicitly represented in a 9 × 9 template. To show the potential applications in the field of remote sensing, a study is presented for Iran. In this study, Sentinel-2 satellite imagery is used in 13 bands, with different geometric resolutions. Using the derived template, a comprehensive analysis is presented for each band. It is shown that various phenomena can be detected in the image, including location of different soil types. Comparison of the independent methods of Laplace template, L0 gradient smoothing, local Laplacian smoothing, and tree filtering, with the newly proposed method shows that the new method is more efficient in determining the various phenomena that are present in the area of interest in the satellite imagery. Keywords Iterated Laplacian . Norm minimization . Linear combination of discrete smoothing function . Geological remote sensing . Sentinel-2 satellite imagery . Deep convolutional neural networks
Introduction The field of remote sensing is the field in which the most important data, acquired by satellite sensors, are in the form of satellite imagery. These images, usually in different bands, contain radiometric values that correspond to the physical properties of the landscape from which the image is taken. Due to various reasons, including satellite sensors’ noise and the presence of a medium called atmosphere, some errors are inevitably included in the image, therefore changing the radiometric quantities. In order to remove the effect of these errors, various methods have been proposed. One such method, which is also Communicated by: H. Babaie * Mostafa Kiani Shahvandi [email protected] 1
IEEE geoscience and remote sensing member, IEEE, Tehran, Iran
one of the most important ones, is the method of image smoothing. This method is based on the assumption that a (linear) combination of the neighboring pixels can represent the best value of that specific pixel. Numerous authors have contributed to the smoothing techniques, including (Lee 1983; Xu et al. 2011; Karacan et al. 2013; Yezzi 1998; Min et al. 2014; Zhang and Hancock 2008; Ramponi 1996; Yu et al. 1992; Meer et al. 1994; Pizarro et al. 2010; Subakan and Vemuri 2011; Fan et al. 2017; Chambolle and Lucier 2001; Hong et al. 1982; Goshtasby
