bilinear interpolation

In computer vision and image processing, bilinear interpolation is one of the basic resampling techniques.

Pixels at quarter-pixel position are obtained by bilinear interpolation.

They are often used as building blocks for more complex operations: for example, a bilinear interpolation can be accomplished in two lerps.

Since measurements within a single scan track are laid out in an approximately rectangular grid, bilinear interpolation can be performed.

The obvious extension of bilinear interpolation to three dimensions is called trilinear interpolation.

Coordinates within a grid tile are computed by a weighted bilinear interpolation of the grid corner points.

Bilinear interpolation considers the closest 2x2 neighborhood of known pixel values surrounding the unknown pixel's computed location.

Dotted red is the laser, solid blue is the projector, and dashed black is the bilinear interpolation function.

The interpolated surface is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation.

In contrast to bilinear interpolation, which only takes 4 pixels (2x2) into account, bicubic interpolation considers 16 pixels (4x4).

The bottom image shows the ideal bilinear interpolation spread of a hat function whose radius matches the 1.25 angular separation of the display's successive views.

Bilinear interpolation can be used where perfect image transformation with pixel matching is impossible, so that one can calculate and assign appropriate intensity values to pixels.

For two spatial dimensions, the extension of linear interpolation is called bilinear interpolation, and in three dimensions, trilinear interpolation.

In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables (e.g., and ) on a regular 2D grid.

Fractal interpolation maintains geometric detail very well compared to traditional interpolation methods like bilinear interpolation and bicubic interpolation.

In image processing, bicubic interpolation is often chosen over bilinear interpolation or nearest neighbor in image resampling, when speed is not an issue.

The result of bilinear interpolation is independent of the order (order here meaning which axis is interpolated first and which second) of interpolation.

A number of simpler interpolation methods/algorithms, such as inverse distance weighting, bilinear interpolation and nearest-neighbor interpolation, were already well known before geostatistics.

Interpolation weights can be generated in ESMF using bilinear interpolation, finite element patch recovery, and conservative remapping methods.

Methods include bilinear interpolation and bicubic interpolation in two dimensions, and trilinear interpolation in three dimensions.

In practice, a trilinear interpolation is identical to three successive linear interpolations, or a bilinear interpolations combined with a linear interpolation:

The fastest method is to use the nearest-neighbour interpolation, but bilinear interpolation or trilinear interpolation between mipmaps are two commonly used alternatives which reduce aliasing or jaggies.

Bilinear filtering uses these points to perform bilinear interpolation between the four texels nearest to the point that the pixel represents (in the middle or upper left of the pixel, usually).

The key idea is to interpolate multiple times in small increments using any interpolation algorithm that is better than nearest-neighbor interpolation, such as bilinear interpolation, and bicubic interpolation.

Bilinear interpolation tends, however, to produce a greater number of interpolation artifacts (such as aliasing, blurring, and edge halos) than more computationally demanding techniques such as bicubic interpolation.