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# bwlookup

Nonlinear filtering using lookup tables

## Syntax

• A = bwlookup(BW,lut) example
• gpuarrayA = bwlookup(gpuarrayBW,lut)

## Description

example

A = bwlookup(BW,lut) performs a 2-by-2 or 3-by-3 nonlinear neighborhood filtering operation on binary or grayscale image BW and returns the results in output image A. The neighborhood processing determines an integer index value used to access values in lookup table lut. The fetched lut value becomes the pixel value in output image A at the targeted position.

• A is the same size as BW

• A is the same data type as lut

This function supports code generation (see Tips).

gpuarrayA = bwlookup(gpuarrayBW,lut) performs the filtering operation on a GPU. The input image and output image are gpuArrays. lut can be a numeric or gpuArray vector. This syntax requires the Parallel Computing Toolbox™.

## Examples

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### 2-by-2 Neighborhood Erosion of Binary Image

Perform an erosion along the edges of a binary image using a 2-by-2 neighborhood. Vector lut is constructed such that the filtering operation places a 1 at the targeted pixel location in image A only when all 4 pixels in the 2-by-2 neighborhood of BW are set to 1. For all other 2-by-2 neighborhood combinations in BW, the targeted pixel location in image A is set to 0.

Construct lut so it is true only when all four 2-by-2 locations equal 1.

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

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1```

```BW1 = imread('text.png');
```

Perform 2-by-2 neighborhood processing with 16-element vector LUT.

```BW2 = bwlookup(BW1,lut);
```

Show zoomed before and after images.

```figure;
h1 = subplot(1,2,1); imshow(BW1), axis off; title('BW1')
h2 = subplot(1,2,2); imshow(BW2); axis off; title('BW2')

% 16X zoom to see effects of erosion on text
set(h1,'Ylim',[.5 64.5]); set(h1,'Xlim',[.5 64.5]);
set(h2,'Ylim',[.5 64.5]); set(h2,'Xlim',[.5 64.5]);
```

### 2-by-2 Neighborhood Erosion of Binary Image Using GPU

Perform an erosion along the edges of a binary image using a 2-by-2 neighborhood, running the code on a graphics processing unit (GPU).

Construct lut so it is true only when all four 2-by-2 locations equal 1

```lut = makelut('sum(x(:))==4',2);
```

```BW1 = imread('text.png');
```

Perform 2-by-2 neighborhood processing with 16-element vector LUT. To run the code on a GPU, create a gpuArray to contain the image.

```BW2 = bwlookup(gpuArray(BW1),lut);
```

Show zoomed before and after images.

```figure;
h1 = subplot(1,2,1); imshow(BW1), axis off; title('BW1')
h2 = subplot(1,2,2); imshow(BW2); axis off; title('BW2')

% 16X zoom to see effects of erosion on text
set(h1,'Ylim',[.5 64.5]); set(h1,'Xlim',[.5 64.5]);
set(h2,'Ylim',[.5 64.5]); set(h2,'Xlim',[.5 64.5]);
```

## Input Arguments

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### BW — Input imagebinary image | grayscale image

Input image transformed by nonlinear neighborhood filtering operation, specified as either a grayscale or binary (logical) image. In the case of numeric values, non-zero pixels are considered true which is equivalent to logical 1.

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

### gpuarrayBW — Input image for processing on a GPUA gpuArray containing a binary image

Input image for processing on a GPU, specified as a gpuArray containing a binary image.

### lut — Lookup table of output pixel values 16- or 512-element vector

Lookup table of output pixel values, specified as a 16- or 512-element vector. The size of lut determines which of the two neighborhood operations is performed.

• If lut contains 16 data elements, then the neighborhood matrix is 2-by-2.

• If lut contains 512 data elements, then the neighborhood matrix is 3-by-3.

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

## Output Arguments

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### A — Output imagebinary image | grayscale image

Output image, returned as a grayscale or binary image whose size matchesBW, and whose distribution of pixel values are determined by the content of lut.

• A is the same size as BW

• A is the same data type as lut

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

### gpuarrayA — Output imagegpuArray containing a grayscale or binary image

Output image, returned as agpuArray containing a grayscale or binary image.

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### Tips

• This function supports the generation of C code using MATLAB® Coder™. Note that if you choose the generic MATLAB Host Computer target platform, the function generates code that uses a precompiled, platform-specific shared library. Use of a shared library preserves performance optimizations but limits the target platforms for which code can be generated. For more information, see Code Generation Using a Shared Library.

When generating code, specify an input image of class logical.

### Algorithms

The first step in each iteration of the filtering operation performed by bwlookup entails computing the index into vector lut based on the binary pixel pattern of the neighborhood matrix on image BW. The value in lut accessed at index, lut(index), is inserted into output image A at the targeted pixel location. This results in image A being the same data type as vector lut.

Since there is a 1-to-1 correspondence in targeted pixel locations, image A is the same size as image BW. If the targeted pixel location is on an edge of image BW and if any part of the 2-by-2 or 3-by-3 neighborhood matrix extends beyond the image edge, then these non-image locations are padded with 0 in order to perform the filtering operation.

The following figures show the mapping from binary 0 and 1 patterns in the neighborhood matrices to its binary representation. Adding 1 to the binary representation yields index which is used to access lut.

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 illustrate, this example shows how the pixel pattern in a 2-by-2 matrix determines which entry in lut is placed in the targeted pixel location.

1. Create random 16-element lut vector containing uint8 data.

```scurr = rng;	   % save current random number generator seed state
rng('default')	% always generate same set of random numbers
lut = uint8( round( 255*rand(16,1) ) ) % generate lut
rng(scurr);		% restore```
```lut =

208
231
32
233
161
25
71
139
244
246
40
248
244
124
204
36```
2. Create a 2-by-2 image and assume for this example that the targeted pixel location is location BW(1,1).

`BW = [1 0; 0 1]`
```BW =

1     0
0     1```
3. By referring to the color coded mapping figure above, the binary representation for this 2-by-2 neighborhood can be computed as shown in the code snippet below. The logical 1 at BW(1,1) corresponds to blue in the figure which maps to the Least Signficant Bit (LSB) at position 0 in the 4-bit binary representation (,20= 1). The logical 1 at BW(2,2) is red which maps to the Most Significant Bit (MSB) at position 3 in the 4-bit binary representation (23= 8) .

```% BW(1,1): blue square; sets bit position 0 on right
% BW(2,2): red  square; sets bit position 3 on left
binNot = '1 0 0 1';			% binary representation of 2x2 neighborhood matrix

X = bin2dec( binNot );	% convert from binary to decimal
index = X + 1					% add 1 to compute index value for uint8 vector lut
A11 = lut(index)				% value at A(1,1)```
```index =

10

A11 =

246```
4. The above calculation predicts that output image A should contain the value 246 at targeted position A(1,1).

`A = bwlookup(BW,lut)   % perform filtering`
```A =

246   32
161  231```

A(1,1) does in fact equal 246.

 Note:   For a more robust way to perform image erosion, see function imerode.

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.

The process for computing the binary representation of 3-by-3 neighborhood processing is the same as shown above for 2-by-2 neighborhoods.