Nearest-neighbor interpolation

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Nearest neighbor interpolation (blue lines) in one dimension on a (uniform) dataset (red points).
Example of nearest neighbor interpolation of a random set of points (black dots) in 2D. Each coloured cell indicates the area in which all the points have the black point in the cell as their nearest black point.
Nearest neighbor interpolation on a uniform 2D grid (black points).

Interpolation is a process which constructs a continuous function from a set of points. In nearest-neighbor interpolation, the idea is to use the value of the data point or measurement which is closest to the current point. The method is also known as proximal interpolation or, point sampling.