multithresh

R2026b

Multilevel image thresholds using Otsu’s method

Syntax

thresh = multithresh(I)

thresh = multithresh(I,N)

[thresh,em] = multithresh(___)

Description

thresh = multithresh(I) calculates a single threshold thresh from grayscale image I, using Otsu's method [1]. Otsu's method chooses a threshold that minimizes the intraclass variance of the thresholded pixels.

You can use the threshold thresh with the imquantize function to convert a grayscale image to a two-level image.

thresh = multithresh(I,N) returns multilevel image thresholds thresh for N threshold values.

You can use the threshold thresh with the imquantize function to convert a grayscale image into an image with N+1 discrete levels.

[thresh,em] = multithresh(___) also returns the effectiveness metric, em.

Examples

Segment Image into Two Regions

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,[])

Segment Image into Three Levels Using Two Thresholds

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")

Compare Thresholding Entire Image Versus Plane-by-Plane Thresholding

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

Check Results Using Effectiveness Metric

Read an image.

I = imread("circlesBrightDark.png");

Count the number of unique grayscale values in the image.

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

Number of unique levels = 148

Display the image. Most pixels in the image have one of three colors: white, black, and medium-gray.

imageshow(I)

For increasing values of N, calculate the effectiveness of thresholding the image into N+1 levels.

N = [1 2 3 4 8 16];
metric = zeros(size(N));
for n = 1:length(N)
    [~, metric(n)] = multithresh(I,N(n));
end

Plot the effectiveness metric for each value of N. The knee of the curve occurs when N is 2.

plot(N,metric,"*-")
xlabel("N (Number of Levels)")
ylabel("Effectiveness Metric")

Calculate the threshold values for two threshold levels.

N = 2;
thresh = multithresh(I,N);

Convert the image into a 3-level image by using the imquantize function with the two threshold values. The quantized image has a clear separation of levels without oversegmentation.

imSeg = imquantize(I,thresh);
imageshow(imSeg,DisplayRangeMode="data-range");

Input Arguments

I — Image to be thresholded

numeric array

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

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

N — Number of threshold values

1 (default) | integer in range [1, 20]

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

thresh — Set of threshold values

1-by-N numeric vector

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 I.

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

em — Effectiveness metric

number in range [0, 1]

Effectiveness metric 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 I is less than or equal to N, em equals 0.

Data Types: double

Algorithms

multithresh finds the thresholds based on the aggregate histogram of the entire image I. 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 I, [min(I(:)) max(I(:))], 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 I 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 I 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

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• multithresh supports the generation of C code (requires MATLAB^® Coder™). Note that if you choose the generic MATLAB Host Computer target platform, multithresh 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 Types of Code Generation Support in Image Processing Toolbox.

• The input argument N must be a compile-time constant.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• The input argument N must be a compile-time constant.

Version History

Introduced in R2012b