# Linear Methods for Image Interpolation

## Reference

P. Getreuer, “Linear Methods for Image Interpolation.” *Image Processing On Line*, 2011. DOI: 10.5201/ipol.2011.g_lmii.

Article permalink: http://dx.doi.org/10.5201/ipol.2011.g_lmii

`@article{getreuer2011linear,`

` title = {Linear Methods for Image Interpolation},`

` author = {Pascal Getreuer},`

` journal = {Image Processing On Line},`

` year = {2011},`

` doi = {10.5201/ipol.2011.g_lmii},`

`}`

## Abstract

Given input image *v* with uniformly-sampled pixels *v _{m}*

_{,n}, the goal of interpolation is to find a function

*u*(

*x*,

*y*) satisfying

*v _{m}*

_{,n}=

*u*(

*m*,

*n*) for all integer

*m*,

*n*,

such that u approximates the underlying function from which *v* was sampled. Another way to interpret this is *v* was created by subsampling, and interpolation attempts to invert this process. We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.