Fuzzy Logic Image Processing

This example shows how to use Fuzzy Logic Toolbox software for image processing. Specifically, this example shows how to detect edges in an image.

An edge is a boundary between two uniform regions. You can detect an edge by comparing the intensity of neighboring pixels. However, because uniform regions are not crisply defined, small intensity differences between two neighboring pixels do not always represent an edge. Instead, the intensity difference might represent a shading effect.

The fuzzy logic approach for image processing allows you to use membership functions to define the degree to which a pixel belongs to an edge or a uniform region.

Import RGB Image and Convert to Grayscale

Import the image into MATLAB.

Irgb = imread('peppers.png');

Irgb is a 384 x 512 x 3 uint8 array. The three channels of Irgb (third array dimension) represent the red, green, and blue intensities of the image.

Convert Irgb to grayscale so that you can work with a 2-D array instead of a 3-D array. Use the standard NTSC conversion formula to calculate the effective luminance of each pixel.

Igray = 0.2989*Irgb(:,:,1)+0.5870*Irgb(:,:,2)+0.1140*Irgb(:,:,3);

figure; image(Igray,'CDataMapping','scaled'); colormap('gray');
title('Input Image in Grayscale')

Alternatively, you can use the rgb2gray function in the Image Processing Toolbox software to convert Irgb to grayscale.

Convert Image to Double-Precision Data

The Fuzzy Logic Toolbox software operates on double-precision numbers only. So, convert Igray, a uint8 array, to a double array.

I = double(Igray);

Because uint8 values are in the [0 2^8-1] range, all elements of I are in that range too. Scale I so that its elements are in the [0 1] range.

classType = class(Igray);
scalingFactor = double(intmax(classType));
I = I/scalingFactor;

Alternatively, you can use the im2double function in the Image Processing Toolbox software to convert Igray to a scaled, double-precision image.

Obtain Image Gradient

The fuzzy logic edge-detection algorithm for this example relies on the image gradient to locate breaks in uniform regions. Calculate the image gradient along the x-axis and y-axis.

Gx = [-1 1];
Gy = Gx';
Ix = conv2(I,Gx,'same');
Iy = conv2(I,Gy,'same');

figure; image(Ix,'CDataMapping','scaled'); colormap('gray'); title('Ix');
figure; image(Iy,'CDataMapping','scaled'); colormap('gray'); title('Iy');

Gx and Gy are simple gradient filters. You convolve I with Gx, using the conv2 function, to obtain a matrix containing the x-axis gradients of I. The gradient values are in the [-1 1] range. Similarly, you convolve I with Gy to obtain the y-axis gradients of I. You can use other filters to obtain the image gradients, such as the Sobel operator or the Prewitt operator. For information about how you can filter an image using convolution, see Convolution.

Alternatively, if you have the Image Processing Toolbox software, you can use the imfilter, imgradientxy, or imgradient functions to obtain the image gradients.

Define Fuzzy Inference System (FIS) for Edge Detection

Create a Fuzzy Inference System (FIS) for edge detection, edgeFIS.

edgeFIS = newfis('edgeDetection');

Specify the image gradients, Ix and Iy, as the inputs of edgeFIS.

edgeFIS = addvar(edgeFIS,'input','Ix',[-1 1]);
edgeFIS = addvar(edgeFIS,'input','Iy',[-1 1]);

Specify a zero-mean Gaussian membership function for each input. If the gradient value for a pixel is 0, then it belongs to the zero membership function with a degree of 1.

sx = 0.1; sy = 0.1;
edgeFIS = addmf(edgeFIS,'input',1,'zero','gaussmf',[sx 0]);
edgeFIS = addmf(edgeFIS,'input',2,'zero','gaussmf',[sy 0]);

sx and sy specify the standard deviation for the zero membership function for the Ix and Iy inputs. You can change the values of sx and sy to adjust the edge detector performance. Increasing the values makes the algorithm less sensitive to the edges in the image and decreases the intensity of the detected edges.

Specify the intensity of the edge-detected image as an output of edgeFIS.

edgeFIS = addvar(edgeFIS,'output','Iout',[0 1]);

Specify the triangular membership functions, white and black, for Iout.

wa = 0.1; wb = 1; wc = 1;
ba = 0; bb = 0; bc = .7;
edgeFIS = addmf(edgeFIS,'output',1,'white','trimf',[wa wb wc]);
edgeFIS = addmf(edgeFIS,'output',1,'black','trimf',[ba bb bc]);

As you can with sx and sy, you can change the values of wa, wb, wc, ba, bb, and bc to adjust the edge detector performance. The triplets specify the start, peak, and end of the triangles of the membership functions. These parameters influence the intensity of the detected edges.

Plot the membership functions of the inputs/outputs of edgeFIS.

figure
subplot(2,2,1); plotmf(edgeFIS,'input',1); title('Ix');
subplot(2,2,2); plotmf(edgeFIS,'input',2); title('Iy');
subplot(2,2,[3 4]); plotmf(edgeFIS,'output',1); title('Iout')

Specify FIS Rules

Add rules to make a pixel white if it belongs to a uniform region. Otherwise, make the pixel black.

r1 = 'If Ix is zero and Iy is zero then Iout is white';
r2 = 'If Ix is not zero or Iy is not zero then Iout is black';
r = char(r1,r2);
edgeFIS = parsrule(edgeFIS,r);
showrule(edgeFIS)
ans =

1. If (Ix is zero) and (Iy is zero) then (Iout is white) (1)       
2. If (Ix is not zero) or (Iy is not zero) then (Iout is black) (1)

Evaluate FIS

Evaluate the output of the edge detector for each row of pixels in I using corresponding rows of Ix and Iy as inputs.

Ieval = zeros(size(I));% Preallocate the output matrix
for ii = 1:size(I,1)
    Ieval(ii,:) = evalfis([(Ix(ii,:));(Iy(ii,:));]',edgeFIS);
end

Plot Results

figure; image(I,'CDataMapping','scaled'); colormap('gray');
title('Original Grayscale Image')

figure; image(Ieval,'CDataMapping','scaled'); colormap('gray');
title('Edge Detection Using Fuzzy Logic')

Summary

You detected the edges in an image using a FIS, comparing the gradient of every pixel in the x and y directions. If the gradient for a pixel is not zero, then the pixel belongs to an edge (black). You defined the gradient as zero using Gaussian membership functions for your FIS inputs.

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