# impyramid

Image pyramid reduction and expansion

## Syntax

`B = impyramid(A, direction)`

## Description

`B = impyramid(A, direction)` computes a Gaussian pyramid reduction or expansion of `A` by one level. `direction` can be `'reduce'` or `'expand'`.

If `A` is m-by-n and `direction` is `'reduce'`, then the size of `B` is `ceil(M/2)-by-ceil(N/2)`. If `direction` is `'expand'`, then the size of `B` is `(2*M-1)-by-(2*N-1)`.

Reduction and expansion take place only in the first two dimensions. For example, if `A` is 100-by-100-by-3 and `direction` is `'reduce'`, then `B` is 50-by-50-by-3.

Note that `impyramid` uses the kernel specified on page 533 of the Burt and Adelson paper cited below:

$w=\left[\frac{1}{4}-\frac{a}{2},\frac{1}{4},a,\frac{1}{4},\frac{1}{4}-\frac{a}{2}\right]$, where .

The parameter a is chosen to be 0.375 so that the equivalent weighting function is close to a Gaussian shape and the weights can be readily applied using fixed-point arithmetic.

## Class support

`A` can be any numeric class except `uint64` or `int64`, or it can be logical. The class of `B` is the same as the class of `A`.

## Examples

Compute a four-level multiresolution pyramid of the cameraman image.

```I0 = imread('cameraman.tif'); I1 = impyramid(I0, 'reduce'); I2 = impyramid(I1, 'reduce'); I3 = impyramid(I2, 'reduce'); imshow(I0) figure, imshow(I1) figure, imshow(I2) figure, imshow(I3)```

## References

[1] Burt and Adelson, "The Laplacian Pyramid as a Compact Image Code," IEEE Transactions on Communications, vol. COM-31, no. 4, April 1983, pp. 532-540.

[2] Burt, "Fast Filter Transforms for Image Processing," Computer Graphics and Image Processing, vol. 16, 1981, pp. 20-51