Skip to main content
SpringerLink
Log in

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

  • Research Article
  • Published:
Earth Science Informatics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40
Fig. 41

Similar content being viewed by others

References

  • Abbas AW, Minallh N, Ahmad N, Abid SAR, Khan MAA (2016) K-means and Isodata clustering algorithms for landcover classification using remote sensing.Sindh Univ Res Jour (Sci Ser) 48(2):315–318. https://www.researchgate.net/publication/303971825_KMeans_and_ISODATA_Clustering_Algorithms_for_Landcover_Classification_Using_Remote_Sensing

  • Bao L, Song Y, Yang Q, Yuan H, Wang G (2014) Tree filtering: efficient structure-preserving smoothing with a minimum spanning tree. IEEE Trans Image Process 23:555–569

    Article  Google Scholar 

  • Chambolle A, Lucier BJ (2001) Interpreting translation-invariant wavelet shrinkage as a new image smoothing scale space. IEEE Trans Image Process 10:993–1000

    Article  Google Scholar 

  • Davis PJ (1975) Interpolation and approximation. Courier Corporation, New York

    Google Scholar 

  • Fan Q, Yang J, Hua G, Chen B, Wipf D (2017) A generic deep architecture for single image reflection removal and image smoothing. IEEE Int Conf Comput Vision 3238–3247. https://arxiv.org/abs/1708.03474

  • Goshtasby A, Satter M (2008) An adaptive window mechanism for image smoothing. Comput Vis Image Underst 111:155–169

    Article  Google Scholar 

  • Ham B, Cho M, Ponce J (2015) Robust image filtering using joint static and dynamic guidance. IEEE CVPR. https://doi.org/10.1109/CVPR.2015.7299115

    Article  Google Scholar 

  • Hong TH, Narayanan KA, Peleg S, Rosenfeld A, Silberberg T (1982) Image smoothing and segmentation by multiresolution pixel linking: further experiments and extensions. IEEE Trans Syst Man Cybern 12:611–622

    Article  Google Scholar 

  • Karacan L, Erdem E, Erdem A (2013) Structure-preserving image smoothing via region covariances. ACM Trans Graph 176:1–11. https://doi.org/10.1145/2508363.2508403

    Article  Google Scholar 

  • Keller W, Borkowski A (2019) Thin plate spline interpolation. J Geod 93:1251–1269

    Article  Google Scholar 

  • Kiani M (2020a) Optimal image smoothing and its applications in anomaly detection in remote sensing. Second international conference on biology and earth sciences, Iran, https://arxiv.org/abs/2003.08210

  • Kiani M (2020b). Identification and classification of phenomena in multispectral satellite imagery using a new image smoother method and its applications in environmental remote sensing. Second international congress on engineering, technology, and innovation, Germany, https://arxiv.org/abs/2003.08209

  • Kincaid D, Cheney W (1990) Numerical analysis, mathematics of scientific computing. Cole Publishing Corporation, Pacific Grove

    Google Scholar 

  • Lee JS (1983) Digital image smoothing and the sigma filter. Comp Vision Graph Image Process 24:255–269

    Article  Google Scholar 

  • Liang P, Wang YF (1998) Local scale controlled anisotropic diffusion with local noise estimate for image smoothing and edge detection. IEEE Sixth Int Conf Comput Vision Bombay India. https://doi.org/10.1109/ICCV.1998.710718

  • Meer P, Park RH, Cho KJ (1994) Multiresolution adaptive image smoothing. Graph Models Image Process 56:140–148

    Article  Google Scholar 

  • Min D, Choi S, Lu J, Ham B, Sohn K, Do MN (2014) Fast global image smoothing based on weighted least squares. IEEE Trans Image Process 23:5638–5653

    Article  Google Scholar 

  • Paris S, Hasinoff SW, Kautz J (2011) Local Laplacian filters: Edgeaware image processing with a Laplacian pyramid. ACM Trans Graph 30:1–68

    Article  Google Scholar 

  • Pizarro L, Mrázek P, Didas S, Grewenig S, Weickert J (2010) Generalised nonlocal image smoothing. Int J Comput Vis 90:62–87

    Article  Google Scholar 

  • Ramponi G (1996) The rational filter for image smoothing. IEEE Signal Process Lett 3:63–65

    Article  Google Scholar 

  • Rawat W, Wang Z (2017) Deep convolutional neural networks for image classification: a comprehensive review. Neural Comput 29(9):1–98

    Article  Google Scholar 

  • Subakan ON, Vemuri BC (2011) A quaternion framework for color image smoothing and segmentation. Int J Comput Vis 91:233–250

    Article  Google Scholar 

  • Xu L, Lu C, Jia J (2011) Image smoothing via L0 gradient minimization. Proc 2011 SIGGRAPH Asia conf 174:1–12. https://doi.org/10.1145/2024156.2024208

    Article  Google Scholar 

  • Yezzi A (1998) Modified curvature motion for image smoothing and enhancement. IEEE Trans Image Process 7:345–352

    Article  Google Scholar 

  • Yu PC, Decker SJ, Lee HS, Sodini SG, Wyatt JL (1992) CMOS resistive fuses for image smoothing and segmentation. IEICE Trans Electron 75c:443–451

    Google Scholar 

  • Zhang F, Hancock ER (2008) Graph spectral image smoothing using the heat kernel. Pattern Recogn 41:3328–3342

    Article  Google Scholar 

  • Zhu F, Liang Z, Jia X, Zhang L, Yu Y (2019). A Benchmark for edge-preserving image smoothing. IEEE Trans Image Process 28(7): 3556-3570. doi: 10.1109/TIP.2019.2908778

Download references

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

  1. IEEE geoscience and remote sensing member, IEEE, Tehran, Iran

    Mostafa Kiani Shahvandi

Authors
  1. Mostafa Kiani Shahvandi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mostafa Kiani Shahvandi.

Ethics declarations

Conflict of interest

Declaration of interest: none.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by: H. Babaie

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kiani Shahvandi, M. 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. Earth Sci Inform 14, 81–97 (2021). https://doi.org/10.1007/s12145-020-00553-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12145-020-00553-7

Keywords

Search

Navigation