Jamali, A.Castro, F.A.Karas, I.R.2024-09-292024-09-292023978-303126851-92367-3370https://doi.org/10.1007/978-3-031-26852-6_80https://hdl.handle.net/20.500.14619/96667th International Conference on Smart City Applications, SCA 2022 -- 19 October 2022 through 21 October 2022 -- Castelo Branco -- 291469Estimating unknown values using its surrounding measured values is called spatial interpolation, a vital tool for estimating continuous spatial data such as the earth’s surface. Construction of the Digital Elevation Model is one of the most common applications of spatial interpolation methods. There are various global and local interpolation techniques, including Kriging, Inverse Distance Weighted (IDW), Thiessen polygons (TIN), Natural Neighbor (NN), and Spline interpolation. This paper introduces the interval-valued homotopy continuation for 3D spatial data interpolation. Straight lines or algebraic curves can be reconstructed using homotopy continuation between any pairs of 3D data. The novel method of the interval-valued homotopy to restore the topographic surface between spatial data is developed in MATLAB programming language. For a dataset of ASTER GDEM, the presented mathematical algorithm shows better results compared to TIN and IDW methods in terms of Mean Squared Error, Mean Absolute Error, and Root Mean Squared Error with values of 5.2897, 1.53, and 2.299 m, respectively. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.eninfo:eu-repo/semantics/closedAccess3D data interpolation3D GISDEMHomotopy continuationSpatial interpolationConference Object10.1007/978-3-031-26852-6_802-s2.0-85151152351879Q4869629 LNNS