PRIMERJAVA METOD PROSTORSKE INTERPOLACIJE IN VEČSLOJNIH NEVRONSKIH MREŽ ZA RAZLIČNE GEOMETRIJSKE RAZPOREDITVE TOČK NA DIGITALNEM MODELU VIŠIN
COMPARISON OF SPATIAL INTERPOLATION METHODS AND MULTI-LAYER NEURAL NETWORKS FOR DIFFERENT POINT DISTRIBUTIONS ON A DIGITAL ELEVATION MODEL

Kutalmis Gumus, Alper Sen

DOI: 10.15292/geodetski-vestnik.2013.03.523-543

 

Izvleček:

Interpolacija prostorsko zvezne spremenljivke iz točkovnih primerov je v geoznanosti pomembno področje prostorske analize in modelov površja. V opisani študiji je bila izvedena primerjava interpolacijskih metod v trirazsežnem prostoru, in sicer so to metoda z inverzno uteženo razdaljo (IDW), navadni kriging (OK), modificirana Shepardova metoda (MS), multikvadrična radialna funkcija (MRBF) in triangulacija z linearno interpolacijo (TWL) ter večslojni perceptron (MLP), ki je predstavnik umetnih nevronskih mrež (ANN). Cilj je bil napovedati višino za različne geometrijske razporeditve točk, kot so ukrivljenost, mreža, naključna in enotna porazdelitev na digitalnem modelu višin, ki
je podatkovni niz digitalnega modela višin ameriške geološke službe USGS. Namen študije je količinsko opredeliti učinek topografske variabilnosti in gostote vzorčenja. Napake različnih interpolacij in napovedi z umetnimi nevronskimi mrežami so bile ovrednotene glede na različne geometrijske porazdelitve točk, izbrani in analizirani so bili tri različni prerezi značilnih delov površja. Na splošno se je izkazalo, da metode navadni kriging (OK), modificirana Shepardova metoda (MS), multikvadrična radialna funkcija (MRBF) in triangulacija z linearno interpolacijo (TWL) dajejo boljše rezultate ter so bolj učinkovite glede značilnosti površja kot večslojni perceptron (MLP) in metoda z uteženo inverzno razdaljo (IDW). Čeprav je večslojni perceptron (MLP) poenostavil obrise, pridobljene iz napovedanih višin, se je izkazal kot zadovoljiv pri napovedovanju ukrivljenosti ter določitvi celične mreže za naključne in znane geometrijske porazdelitve točk.

Ključne besede: prostorska interpolacija, nevronske mreže, geometrijska razporeditev točk

 

Abstract:

Interpolation of a spatially continuous variable from point samples is an important field in spatial analysis and surface models for geosciences. In this study, spatial interpolation methods which are Inverse Distance Weighted (IDW), Ordinary Kriging (OK), Modified Shepard's (MS), Multiquadric Radial Basis Function (MRBF) and Triangulation with Linear (TWL), and Multi-Layer Perceptron (MLP) which is an Artificial Neural Networks (ANN) method were compared in order to predict height for different point distributions such as curvature, grid, random and uniform on a Digital Elevation Model which is an USGS National Elevation Dataset (NED). This study also aims to quantify the effects of topographic variability and sampling density. Errors of different interpolations and ANN prediction were evaluated for different point distributions and three different cross-sections on the characteristic parts of the surface were selected and analyzed. Generally, OK, MS, MRBF and TWL gave promising results and were more effective
in terms of characteristics of surface than MLP and IDW. Although MLP simplified the contours obtained from predicted heights, it was a satisfactory predictor for curvature, grid, random and uniform distributions.

Keywords: spatial interpolation, neural networks, point distribution

 

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