Nonlinear filtering using lookup tables



J = bwlookup(BW,lut) performs a 2-by-2 or 3-by-3 nonlinear neighborhood filtering operation on binary or grayscale image I and returns the results in output image J. 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 J at the targeted position.

You optionally can perform the filtering using a GPU (requires Parallel Computing Toolbox™).


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Construct the vector lut such that the filtering operation places a 1 at the targeted pixel location in the input image only when all four pixels in the 2-by-2 neighborhood of BW are set to 1.

lutfun = @(x)(sum(x(:))==4);
lut = makelut(lutfun,2)
lut = 16×1


Load a binary image.

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.

h1 = subplot(1,2,1); imshow(BW1), axis off; title('Original Image')
h2 = subplot(1,2,2); imshow(BW2); axis off; title('Eroded Image')
% 16X zoom to see effects of erosion on text
set(h1,'Ylim',[1 64],'Xlim',[1 64]);
set(h2,'Ylim',[1 64],'Xlim',[1 64]);

Input Arguments

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Input image transformed by nonlinear neighborhood filtering operation, specified as a 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. 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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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 and the same data type as lut.


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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 I. The value in lut accessed at index, lut(index), is inserted into output image J at the targeted pixel location. This results in image J being the same data type as vector lut.

Since there is a 1-to-1 correspondence in targeted pixel locations, image J is the same size as image I. If the targeted pixel location is on an edge of image I 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.

2-by-2 Neighborhood Lookup

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 =
  2. Create a 2-by-2 image and assume for this example that the targeted pixel location is location I(1,1).

    I = [1 0; 0 1]
    I =
         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 I(1,1) corresponds to blue in the figure which maps to the Least Significant Bit (LSB) at position 0 in the 4-bit binary representation (,20= 1). The logical 1 at I(2,2) is red which maps to the Most Significant Bit (MSB) at position 3 in the 4-bit binary representation (23= 8) .

    % I(1,1): blue square; sets bit position 0 on right 
    % I(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 =
    A11 =
  4. The above calculation predicts that output image A should contain the value 246 at targeted position A(1,1).

    A = bwlookup(I,lut)   % perform filtering
    A =
      246   32
      161  231

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

3-by-3 Neighborhood Lookup

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 for 2-by-2 neighborhoods.

Extended Capabilities

See Also

Introduced in R2012b