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Natural-neighbor interpolation or Sibson interpolation is a method of spatial interpolation, developed by Robin Sibson. [1] The method is based on Voronoi tessellation of a discrete set of spatial points.
A point location data structure can be built on top of the Voronoi diagram in order to answer nearest neighbor queries, where one wants to find the object that is closest to a given query point. Nearest neighbor queries have numerous applications. For example, one might want to find the nearest hospital or the most similar object in a database.
Nearest-neighbor interpolation; Triangulated irregular network-based natural neighbor; Triangulated irregular network-based linear interpolation (a type of piecewise linear function) n-simplex (e.g. tetrahedron) interpolation (see barycentric coordinate system) Inverse distance weighting; ABOS - approximation based on smoothing; Kriging
Additionally, natural neighbor interpolation and Thiessen (Voronoi) polygon generation can only be performed on Delaunay conforming triangulations. A constrained Delaunay triangulation can be considered when you need to explicitly define certain edges that are guaranteed not to be modified (that is, split into multiple edges) by the triangulator.
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around ...
Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), [1] [2] Edge-Guided Image Interpolation (EGGI), [3] Iterative Curvature-Based Interpolation (ICBI), [citation needed] and Directional Cubic Convolution Interpolation (DCCI). [4] A study found that DCCI had the best scores in PSNR and SSIM on a series of test ...
Natural neighbor interpolation; Nearest neighbor value interpolation; PDE surface; Transfinite interpolation — constructs function on planar domain given its values on the boundary; Trend surface analysis — based on low-order polynomials of spatial coordinates; uses scattered observations; Method based on polynomials are listed under ...
The interpolated surface (meaning the kernel shape, not the image) is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials , cubic splines , or cubic convolution algorithm.