Natural Neighbor Interpolation

Introduction

Natural Neighbor Interpolation is a spatial interpolation method used in GIS (Geographic Information System) that estimates values at unsampled locations based on the values of surrounding data points. It is a non-parametric method that considers the proximity of the unsampled location to neighboring data points to determine the weights for interpolation. Natural Neighbor interpolation finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value (Sibson, 1981). It is also known as Sibson or "area-stealing" interpolation.

The algorithm used by the Natural Neighbor?interpolation tool finds the closest subset of input samples to a query point and applies weights to them based on proportionate areas to interpolate a value (Sibson 1981). It is also known as Sibson or "area-stealing" interpolation. Its basic properties are that it's local, using only a subset of samples that surround a query point, and interpolated heights are guaranteed to be within the range of the samples used. It does not infer trends and will not produce peaks, pits, ridges, or valleys that are not already represented by the input samples. The surface passes through the input samples and is smooth everywhere except at the locations of the input samples.

Advantages of Natural Neighbor Interpolation:

1. Preserves feature boundaries: Natural Neighbor Interpolation tends to produce smooth surfaces that respect the boundaries and shapes of the data points, resulting in visually pleasing and realistic representations.
2. Conserves local variability: The method considers the density and distribution of data points, allowing it to capture local variations and reflect the heterogeneity of the data.
3. No grid or tessellation required: Unlike many other interpolation methods, Natural Neighbor Interpolation does not require the data to be structured on a grid or tessellation. It can handle irregularly spaced data points.
4. Handles varying densities: Natural Neighbor Interpolation adapts to varying data densities, giving more weight to areas with denser data and less weight to areas with sparser data.

Applications of Natural Neighbor Interpolation:

1. Elevation modeling: Natural Neighbor Interpolation is commonly used for terrain modeling and the creation of digital elevation models (DEMs) to represent the topography of a region.
2. Environmental monitoring: It can be applied to estimate environmental variables such as air quality, temperature, or pollutant concentrations, which are often irregularly distributed across a study area.
3. Image and raster data interpolation: Natural Neighbor Interpolation can be used to interpolate missing values or gaps in image or raster datasets.

Limitations of Natural Neighbor Interpolation:

1. Data distribution impact: The interpolation results are sensitive to the distribution and density of data points. Sparse or clustered data can lead to inaccurate estimates.
2. Lack of uncertainty estimation: Natural Neighbor Interpolation does not provide explicit measures of uncertainty or confidence intervals for the estimated values.
3. Difficulty in extrapolation: Natural Neighbor Interpolation is primarily suitable for interpolation within the convex hull of the data points. Extrapolation outside this region may result in unreliable estimates.
4. Lack of theoretical guarantees: Unlike some other interpolation methods, Natural Neighbor Interpolation lacks theoretical convergence guarantees, making it harder to assess its accuracy objectively.
5. Computationally intensive: Natural Neighbor Interpolation can be computationally intensive, especially for large datasets, as it requires calculating the Voronoi polygons or Delaunay triangulation for each data point.
6. Sensitivity to outliers: Outliers in the data can have a significant influence on the interpolation results, potentially leading to distorted estimates.

In summary, Natural Neighbor Interpolation offers advantages such as boundary preservation, local variability representation, and flexibility in handling irregularly spaced data. However, it also has limitations concerning computation, sensitivity to outliers, and challenges with extrapolation. Its applications are diverse, including elevation modeling, environmental monitoring, and interpolating image or raster data. It is important to consider the specific characteristics of the dataset and research goals when choosing an interpolation method.