Pitney Bowes
MapInfo Pro™ Monthly Journal
Get on the Grid: Creating grids using Natural Neighbor interpolation

Kriti With the latest MapInfo Pro Advanced v16.0 release, we have added two new interpolation methods to create raster surfaces from point data - Natural Neighbor and Nearest Neighbor.
Natural neighbor interpolation estimates the value at the center of each raster cell by exploiting the unique properties of a Voronoi tessellation of the source data points. A Voronoi tessellation or Voronoi diagram is a network of non-overlapping polygons that enclose each input data point such that the polygon boundaries are equidistance between the closest points. The method can be used to create surface models from data that is clustered, dense in some areas and sparse in others, or data with linear spatial distributions. Natural neighbor interpolation uses an area-weighting technique to determine a value for every raster cell and it does not extrapolate beyond the range of the input values so there is no overshoot or undershoot at the minimum and maximum data values.

A Natural neighbour region is first generated for each input data point. Then at every raster cell node a new Natural neighbour polygon is generated by inserting the raster cell point location into the Voronoi diagram of the input points. This insertion creates a new polygon which effectively borrows area from various portions of the surrounding natural neighbour regions defining each of the closest input points. The value assigned to the raster cell is then calculated as the weighted average of the surrounding point values, proportionally weighted by the area borrowed from each surrounding region.

The picture below shows the Natural neighbour regions around a set of input points. The shaded region represents the "borrowed area" that would be taken from the original Voronoi diagram by inserting a raster cell coordinate ('+' symbol) into the diagram.

Natural Neighbor

Each shaded region represents the contributing portion of the intersecting Voronoi polygon. Integrated area weightings of these shaded regions are then applied to weight the value of each Raster Cell.

Additional distance based weighting can be incorporated to provide additional smoothness to the result. MapInfo Pro Advanced uses a modified version of Sibson's discretizing interpolation algorithm to compute the Voronoi diagram and then weight and accumulate the interpolated values for each cell in the output raster.

The Nearest neighbor method works by assigning input data values to the raster cells. This algorithm finds the nearest data source for the raster cells. This interpolation method is best suited for evenly or regularly distributed data sets. MapInfo Pro Advanced simplifies the process of creating raster data from points by using an optimized spatial data analysis system that automatically analyzes the spacing and distribution of the input data and computes a set of default parameters.

The create raster dialog provides you with a number of parameters and options to adjust and get desired raster.

For, applying Nearest Neighbor interpolation method in MapInfo pro go to the RASTER tab and select Create Raster from Interpolate group.

Create Raster

Navigating the Create Raster panel

From the Input File drop down list select the dataset from which you wish to create a grid. The Select Columns option allows you to select one or more data columns to be used as input. If you select multiple input columns, separate grids will be created. If the Multi resolution raster (MRR) or the GeoTIFF format are used, the grids will be part of the same MRR file in different bands. If other formats are chosen individual grid files will be created.

In the Select Method drop down, choose Nearest Neighbor. In the Raster Geometry section specify cell size and, if desired the bounding area for the output raster. In More Options, you can choose the desired projection for the grid.

In the Output File box enter the name of the file and also specify the format of the file in which you wish to store your results. By default the result will be stored in the same location as the input file. You can choose a different folder, if desired.

If you select the MRR or TIFF formats, then in Output Settings you have the option of Compression Settings. When the raster field type is Continuous, the Encoding Type option is enabled - it enables you to compress the data.

When ready, click Process. On completion of the operation, if you have selected the Display Output File check-box, the raster displays in the map window.

Natural Neighbor

The Natural Neighbor method provides options in the Method Options drop-down.

Method Options

On enabling Gaussian Distance Weighting, Gaussian based distance weighting is being applied to input data point values that are found within the search radius. There is an automatic option which suggests a distance range over which the Gaussian weighting will be applied. If the Auto Gaussian option is not selected, then one can manually enter the range in Gaussian range box.

More information

For more information on Natural Neighbor interpolation here is a Wikipedia entry:
https://en.wikipedia.org/wiki/Natural_neighbor_interpolation

For more articles on using the raster capabilities in MapInfo Pro Advanced, check out the "Get on the Grid" archive from The MapInfo Pro journal. http://web.pb.com/mapinfopro-archive/get-on-the-grid/

Article by Kriti Kohli, Associate Software Engineer
When not writing articles for MapInfo pro, Kriti works in the Pitney Bowes Engineering organization and likes to explore features of MapInfo Pro. When not working, she likes to read on many subjects and loves to drive.