# applylut

Neighborhood operations on binary images using lookup tables

applylut is not recommended. Use bwlookup instead.

## Description

example

A = applylut(BW,lut) performs a 2-by-2 or 3-by-3 neighborhood operation on binary image BW by using a lookup table, lut. The lookup table consists of the output values for all possible 2-by-2 or 3-by-3 neighborhoods.

## Examples

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Create the lookup table.

lutfun = @(x)(sum(x(:))==4);
lut = makelut(lutfun,2);

Read image into the workspace and then apply the lookup table to the image. An output pixel is on only if all four of the input pixel's neighborhood pixels are on.

BW2 = applylut(BW1,lut);

Show the original image and the eroded image.

imshow(BW1)

imshow(BW2)

## Input Arguments

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Input image, specified as a 2-D binary image. For numeric input, any nonzero pixels are considered to be 1 (true).

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Lookup table of output pixel values, specified as a 16- or 512-element vector as returned by makelut.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

## Output Arguments

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Output image, returned as a grayscale or binary image whose distribution of pixel values are determined by the content of the lookup table, lut. The output image J is the same size as the input image I.

• If all elements of lut are 0 or 1, then A has data type logical.

• If all elements of lut are integers between 0 and 255, then A has data type uint8.

• For all other cases, A has data type double.

Data Types: double | uint8 | logical

## Algorithms

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applylut performs a neighborhood operation on a binary image by producing a matrix of indices into lut, and then replacing the indices with the actual values in lut. The specific algorithm used depends on whether you use 2-by-2 or 3-by-3 neighborhoods.

### 2-by-2 Neighborhoods

For 2-by-2 neighborhoods, length(lut) is 16. There are four pixels in each neighborhood, and two possible states for each pixel, so the total number of permutations is 24 = 16.

To produce the matrix of indices, applylut convolves the binary image BW with this matrix.

8     2
4     1

The resulting convolution contains integer values in the range [0, 15]. applylut uses the central part of the convolution, of the same size as BW, and adds 1 to each value to shift the range to [1, 16]. The function then constructs A by replacing the values in the cells of the index matrix with the values in lut that the indices point to.

### 3-by-3 Neighborhoods

For 3-by-3 neighborhoods, length(lut) is 512. There are nine pixels in each neighborhood, and two possible states for each pixel, so the total number of permutations is 29 = 512.

To produce the matrix of indices, applylut convolves the binary image BW with this matrix.

256    32     4
128    16     2
64     8     1

The resulting convolution contains integer values in the range [0, 511]. applylut uses the central part of the convolution, of the same size as BW, and adds 1 to each value to shift the range to [1, 512]. It then constructs A by replacing the values in the cells of the index matrix with the values in lut that the indices point to.

## Version History

Introduced before R2006a

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### R2012b: applylut is not recommended

Starting in R2012b, use bwlookup to perform neighborhood operations on binary images using lookup tables. For bwlookup, the data type of the returned image is the same as the data type of the lookup table. bwlookup supports code generation. There are no plans to remove applylut at this time.

To update your code, replace instances of applylut with bwlookup. You do not need to change the input arguments.