Editing Bicubic interpolation (section)

{{Short description|Extension of cubic spline interpolation}}
{{comparison of 1D and 2D interpolation.svg}}
In [[mathematics]], '''bicubic interpolation''' is an extension of [[Cubic interpolation#Interpolation on a single interval|cubic spline interpolation]] (a method of applying cubic interpolation to a data set) for [[interpolation|interpolating]] data points on a [[two-dimensional]] [[regular grid]]. The interpolated surface (meaning the kernel shape, not the image) is [[Smooth function|smoother]] than corresponding surfaces obtained by [[bilinear interpolation]] or [[nearest-neighbor interpolation]]. Bicubic interpolation can be accomplished using either [[Lagrange polynomial]]s, [[cubic spline]]s, or [[#Bicubic convolution algorithm|cubic convolution]] algorithm.

In [[image processing]], bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in [[resampling (bitmap)|image resampling]], when speed is not an issue. In contrast to bilinear interpolation, which only takes 4 [[pixel]]s (2×2) into account, bicubic interpolation considers 16 pixels (4×4). Images resampled with bicubic interpolation can have different interpolation [[Spatial anti-aliasing|artifacts]], depending on the b and c values chosen.