Image Processing Toolbox™

applylut - Neighborhood operations on binary images using lookup tables

Syntax

A = applylut(BW,LUT)

Description

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). LUT is either a 16-element or 512-element vector returned by makelut. The vector consists of the output values for all possible 2-by-2 or 3-by-3 neighborhoods.

Class Support

BW can be numeric or logical, and it must be real, two-dimensional, and nonsparse. LUT can be numeric or logical, and it must be a real vector with 16 or 512 elements. If all the elements of LUT are 0 or 1, then A is logical. If all the elements of LUT are integers between 0 and 255, then A is uint8. For all other cases, A is double.

Algorithm

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]. 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.

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.

Examples

Perform erosion using a 2-by-2 neighborhood. An output pixel is on only if all four of the input pixel's neighborhood pixels are on.

lut = makelut('sum(x(:)) == 4',2);
BW = imread('text.png');
BW2 = applylut(BW,lut);
imshow(BW), figure, imshow(BW2)