multithresh

Multilevel image thresholds using Otsu’s method

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Syntax

thresh = multithresh(A)
thresh = multithresh(A,N)
[thresh,metric] = multithresh(___)

Description

thresh = multithresh(A) returns the single threshold value thresh computed for image A using Otsu’s method. You can use thresh as an input argument to imquantize to convert an image into a two-level image.

example

thresh = multithresh(A,N) returns thresh a 1-by-N vector containing N threshold values using Otsu’s method. You can use thresh as an input argument to imquantize to convert image A into an image with N+1 discrete levels.

example

[thresh,metric] = multithresh(___) returns metric, a measure of the effectiveness of the computed thresholds.

example

Examples

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Open Live Script

Read and display an image.

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

Figure contains an axes object. The hidden axes object contains an object of type image.

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,[])

Figure contains an axes object. The hidden axes object contains an object of type image.

Open Live Script

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

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

Figure contains an axes object. The hidden axes object with title Grayscale Image contains an object of type 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")

Figure contains an axes object. The hidden axes object with title Segmented Image contains an object of type image.

Open Live Script

Read and display an RGB image.

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

Figure contains an axes object. The hidden axes object with title RGB Image contains an object of type 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")

Figure contains an axes object. The hidden axes object with title Full RGB Image Quantization vs. Plane-by-Plane Quantization contains an object of type image.

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
Open Live Script

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

Input Arguments

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Image to be thresholded, specified as a numeric array of any dimension.

Data Types: single | double | int16 | uint8 | uint16

Number of threshold values, specified as an integer in the range [1, 20].

For N > 2, multithresh uses search-based optimization of Otsu's criterion to find the thresholds. The search-based optimization guarantees only locally optimal results. Since the chance of converging to local optimum increases with N, it is preferable to use smaller values of N, typically N < 10.

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

Output Arguments

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Set of threshold values used to quantize an image, returned as a 1-by-N numeric vector, whose data type is the same as image A.

The thresholds are in the same range as the input image A, unlike the graythresh function, which returns a normalized threshold in the range [0, 1].

Measure of the effectiveness of the thresholds, returned as a number in the range [0, 1]. Higher values indicates greater effectiveness of the thresholds in separating the input image into N+1 classes based on Otsu's objective criterion. For degenerate inputs where the number of unique values in A is less than or equal to N, metric equals 0.

Data Types: double

Algorithms

multithresh finds the thresholds based on the aggregate histogram of the entire image A. multithresh considers an RGB image as a 3-D numeric array and computes the thresholds for the combined data from all three color planes.

multithresh uses the range of the input image A, [min(A(:)) max(A(:))], as the limits for computing the histogram used in subsequent computations. multithresh ignores any NaNs in computation. Any Infs and -Infs are counted in the first and last bin of the histogram, respectively.

For degenerate inputs where the number of unique values in A is less than or equal to N, there is no viable solution using Otsu's method. For such inputs, the return value thresh contains all the unique values from A and possibly some extra values that are chosen arbitrarily.

References

[1] Otsu, N., "A Threshold Selection Method from Gray-Level Histograms," IEEE Transactions on Systems, Man, and Cybernetics, Vol. 9, No. 1, 1979, pp. 62-66.

Extended Capabilities

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Version History

Introduced in R2012b

See Also

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