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Barnes interpolation; Bilinear interpolation; Bicubic interpolation; Bézier surface; Lanczos resampling; Delaunay triangulation; Bitmap resampling is the application of 2D multivariate interpolation in image processing. Three of the methods applied on the same dataset, from 25 values located at the black dots. The colours represent the ...
It is similar to interpolation, which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Extrapolation may also mean extension of a method , assuming similar methods will be applicable.
The simplest interpolation method is to locate the nearest data value, and assign the same value. In simple problems, this method is unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable choice for its speed and simplicity.
The four Hermite basis functions. The interpolant in each subinterval is a linear combination of these four functions. On the unit interval [,], given a starting point at = and an ending point at = with starting tangent at = and ending tangent at =, the polynomial can be defined by = (+) + (+) + (+) + (), where t ∈ [0, 1].
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 ...
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...