Volume XLII-4/W10 | Copyright
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XLII-4/W10, 71-77, 2018
https://doi.org/10.5194/isprs-archives-XLII-4-W10-71-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

  12 Sep 2018

12 Sep 2018

TOPOLOGICAL 3D ELEVATION DATA INTERPOLATION OF ASTER GDEM BASED ON CONTINUOUS DEFORMATION

A. Jamali1 and F. A. Castro2 A. Jamali and F. A. Castro
  • 1Universiti Teknologi Malaysia (UTM), Faculty of Geoinformation and Real Estate, 81310 Johor, Malaysia
  • 2Yachay Tech University, School of Mathematics and Information Technology, Ecuador

Keywords: Homotopy continuation, 3D Data Interpolation, DEM, Optimization, Mathematics, ASTER GDEM

Abstract. In Geographic Information Science, polynomial methods such as linear estimation and non-polynomial methods including Inverse Distance Weighting and Kriging have been used for elevation data interpolation. In this paper, 3D data interpolation using linear and non-linear homotopy continuation as well as advanced polynomial interpolation methods are researched. Continuous deformations that reconstruct straight lines or algebraic curves between any pair of 3D data are presented. The implemented topological mathematical algorithm for 3D elevation data interpolation is compared to Inverse Distance Weighting and Triangulated Irregular Network (TIN) methods. The presented linear and non-linear mathematical algorithms show better results compared to Inverse Distance Weighting and TIN in terms of Root Mean Square Error and L-infinity.

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