The effect of the distribution of measurement points around the node on the accuracy of interpolation of the digital terrain model

Gościewski, Dariusz

doi:10.1007/s10109-012-0176-x

Cited by 64 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The accuracy of the resulting 3D models is affected by the points numerosity and distribution [49]. In literature, mathematical models are proposed to take into account several independent variables, such as the surface slope, the density of points, the spatial distribution of these points, and the interpolation method, in order to explain the accuracy of a given DEM [50].…”

Section: Introductionmentioning

confidence: 99%

The Influence of Interpolated Point Location and Density on 3D Bathymetric Models Generated by Kriging Methods: An Application on the Giglio Island Seabed (Italy)

2022

View full text Add to dashboard Cite

In relation to 3D bathymetric modelling, this article aims to analyze the performance of Kriging approaches in dependence of the location and density of the measured depth points. The experiments were carried out on a multi-beam sonar (MBS) dataset that includes 240,000 soundings covering a sea-bottom area near Giglio Island (Italy). Seven subsets were derived in random way from the initial regular MBS dataset, selecting an increasing number of points uniformly spaced. Seven models were generated for both Ordinary Kriging and Universal Kriging. Each model was submitted to leave-one-out cross-validation to define the exactness of the predictive values and compared with the initial grid to better evaluate the accuracy in dependence of the point number and dissemination. To investigate this relationship, a new index called MVI (Morphological Variation Index) was introduced as a measurement of the level of variation of seabed morphology. The results validate the efficiency of the Kriging methods and remark the influence of the dataset distribution on the 3D model, highlighting MVI as a useful index to represent the seabed variation as a unique value. Finally, in no rugged areas using 1 point every 1000 m2, the RMSE of the differences between measured and interpolated values falls below 1 m, while a further increment of soundings is required in the presence of a high level of variation of seabed morphology.

show abstract

Section: Introductionmentioning

confidence: 99%

The Influence of Interpolated Point Location and Density on 3D Bathymetric Models Generated by Kriging Methods: An Application on the Giglio Island Seabed (Italy)

2022

View full text Add to dashboard Cite

show abstract

“…During the generation of GRID structures, the values in interpolation nodes are computed with the use of measurement points located near the mapped node within a given search radius R (Figure 2b). The size of the radius is determined relative to the resolution of the node network, and an interpolation algorithm is selected to control the degree of generalization of the developed surface [42][43][44][45][46]. The shape of the interpolated surface generated based on GRID nodes can differ depending on the applied algorithm and its processing parameters.…”

Section: Selection Of Interpolation Algorithmmentioning

confidence: 99%

A GRID-Based Spatial Interpolation Method as a Tool Supporting Real Estate Market Analyses

Szczepańska

Gościewski

Gerus-Gościewska

2020

IJGI

View full text Add to dashboard Cite

The spatial distribution of prices is closely linked with the urban real estate market. Property prices are one of the key indicators of economic activity because they influence economic decisions. Decision-makers and consumers often need information about the spatial distribution of prices, but spatial-temporal analyses of the real estate market are based on the prices quoted in different locations across years (epochs). Due to this idiosyncrasy, the resulting datasets are dispersed (different across years) and difficult to compare. For this reason, the existing interpolation methods are not always effective in analyses of the real estate market. A different approach to interpolating real estate prices that supports the generation of continuous interpolated surfaces while maintaining the values of measurement points is thus needed. This paper proposes a method for replacing dispersed spatial data with a regular GRID structure. The GRID structure covers the measured object with a regular network of nodes, which supports uniform interpolation at every point of the analyzed space and a comparison of interpolation models in successive epochs (years). The proposed method was tested on a selected object. The results indicate that the GRID structure can be used in analyses of highly complex real estate markets where input data are incomplete, irregular and dispersed.

show abstract

“…A regular network of nodes forming a GRID structure can be applied to better organize the data that describe digital surfaces and to provide missing data in the modelled surfaces without compromising the model's continuity [33][34][35]. In a GRID structure, the location of square vertices (nodes) on the XY plane in a given surface segment is determined by a fixed distance interval (S = constant) in both directions on the axes (Figure 2a) relative to a point with known coordinates.…”

Section: Interpolation Of Real Estate Prices With a Grid Structurementioning

confidence: 99%

The Use of a Grid Structure for Reconstructing and Forecasting the Value of Real Estate in Selected Measurement Epochs

2019

View full text Add to dashboard Cite

The absence of sufficiently long time series of data relating to real estate prices in a selected location prevents accurate analyses and the development of precise forecasts that play an important role in a market economy. New methods and solutions are being sought to address this problem. This paper proposes an original method for reconstructing, forecasting and archiving data relating to real estate value. The proposed method involves a GRID (regular square nets) structure and it relies on the prices quoted in successive years (epochs) of measurement in a selected object. Irregularly distributed measurement data (real estate prices) acquired in successive years are transformed into a regular GRID structure to develop digital surface models that describe the distribution of data. The nodes of the GRID structure are described with the coefficients of an approximating polynomial to reconstruct and forecast real estate value in a specific location at any point in time. A GRID structure supports a comparison of changes in real estate value over time in a given node or group of nodes selected from successive measurement epochs. Individual coefficients of an approximating polynomial are generated, allocated to selected nodes, and automatically adapted to local changes in value. As a result, the observed changes can be described in a given period of time. Source data covering multiple epochs are replaced with a single file containing coefficients of approximating polynomials to reduce the size of the stored datasets and facilitate data management.

show abstract

The effect of the distribution of measurement points around the node on the accuracy of interpolation of the digital terrain model

Cited by 64 publications

References 11 publications

The Influence of Interpolated Point Location and Density on 3D Bathymetric Models Generated by Kriging Methods: An Application on the Giglio Island Seabed (Italy)

The Influence of Interpolated Point Location and Density on 3D Bathymetric Models Generated by Kriging Methods: An Application on the Giglio Island Seabed (Italy)

A GRID-Based Spatial Interpolation Method as a Tool Supporting Real Estate Market Analyses

The Use of a Grid Structure for Reconstructing and Forecasting the Value of Real Estate in Selected Measurement Epochs

Contact Info

Product

Resources

About