multithresh

Read and display an image.

I = imread("coins.png");
imshow(I)

Calculate a single threshold value for the image.

level = multithresh(I);

Segment the image into two regions using the imquantize function, specifying the threshold level returned by the multithresh function. Display the result.

seg_I = imquantize(I,level);
imshow(seg_I,[])

Read an image, convert it to grayscale, and display the result.

I = imread("foggysf2.jpg");
I = rgb2gray(I);
imshow(I)
title("Grayscale Image")

Calculate two threshold levels.

thresh = multithresh(I,2);

Segment the image into three levels using the imquantize function.

labels = imquantize(I,thresh);

Convert the segmented image into a color image using the label2rgb function, and display the image.

labelsRGB = label2rgb(labels);
imshow(labelsRGB)
title("Segmented Image")

Read and display an RGB image.

I = imread("peppers.png");
imshow(I) 
title("RGB Image");

Generate thresholds for seven levels from the entire RGB image.

threshRGB = multithresh(I,7);

Generate thresholds for each plane of the RGB image.

threshForPlanes = zeros(3,7);			

for i = 1:3
    threshForPlanes(i,:) = multithresh(I(:,:,i),7);
end

Process the entire image with the set of threshold values computed from entire image.

value = [0 threshRGB(2:end) 255]; 
quantRGB = imquantize(I, threshRGB, value);

Process each RGB plane separately using the threshold vector computed from the given plane. Quantize each RGB plane using threshold vector generated for that plane.

quantPlane = zeros(size(I));

for i = 1:3
    value = [0 threshForPlanes(i,2:end) 255]; 
    quantPlane(:,:,i) = imquantize(I(:,:,i),threshForPlanes(i,:),value);
end

quantPlane = uint8(quantPlane);

Display both posterized images and note the visual differences in the two thresholding schemes.

montage({quantRGB,quantPlane}) 
title("Full RGB Image Quantization vs. Plane-by-Plane Quantization")

To compare the results, calculate the number of unique RGB pixel vectors in each output image. Note that the plane-by-plane thresholding scheme yields about 23% more colors than the full RGB image scheme.

dim = size(quantRGB);
quantRGBmx3 = reshape(quantRGB,prod(dim(1:2)),3);
quantPlanemx3 = reshape(quantPlane,prod(dim(1:2)),3);

colorsRGB = unique(quantRGBmx3,"rows");
disp("Unique colors in RGB image: "+length(colorsRGB));

Unique colors in RGB image: 188

colorsPlane = unique(quantPlanemx3,"rows");
disp("Unique colors in plane-by-plane image: "+length(colorsPlane));

Unique colors in plane-by-plane image: 231

Read an image.

I = imread('circlesBrightDark.png');

Find all unique grayscale values in image.

uniqLevels = unique(I(:));
disp("Number of unique levels = "+length(uniqLevels));

Number of unique levels = 148

Compute a series of thresholds at monotonically increasing values of N.

Nvals = [1 2 4 8];
for i = 1:length(Nvals)
    [thresh, metric] = multithresh(I, Nvals(i) );
    disp("N = "+Nvals(i)+"  |  metric = "+metric);
end

N = 1  |  metric = 0.54767
N = 2  |  metric = 0.98715
N = 4  |  metric = 0.99648
N = 8  |  metric = 0.99902

Apply the set of 8 threshold values to obtain a 9-level segmentation using imquantize.

seg_Neq8 = imquantize(I,thresh);
uniqLevels = unique(seg_Neq8(:))

uniqLevels = 9×1

     1
     2
     3
     4
     5
     6
     7
     8
     9

Threshold the image using seg_Neq8 as an input to multithresh. Set N equal to 8, which is 1 less than the number of levels in this segmented image. multithresh returns a metric value of 1.

[thresh,metric] = multithresh(seg_Neq8,8)

thresh = 1×8

    1.8784    2.7882    3.6667    4.5451    5.4549    6.3333    7.2118    8.1216

metric = 
1

Threshold the image again, this time increasing the value of N by 1. This value now equals the number of levels in the image. Note how the input is degenerate because the number of levels in the image is too few for the number of requested thresholds. Hence, multithresh returns a metric value of 0.

[thresh, metric] = multithresh(seg_Neq8,9)

Warning: No solution exists because the number of unique levels in the image are too few to find 9 thresholds. Returning an arbitrarily chosen solution.

thresh = 1×9

     1     2     3     4     5     6     7     8     9

metric = 
0