Thresholding

Prerequisites
Before starting this lesson, you should be familiar with:

Image segmentation

Basic properties of images and pixels

Data types (unsigned 8-bit)

Learning Objectives
After completing this lesson, learners should be able to:

Describe the relationship between an intensity image and a derived binary image.

Apply a threshold to segment an image into foreground and background regions

Motivation

One strategy to detect objects or specific regions in images is to first distinguish so-called background pixels, which do not contain objects or interesting regions from foreground pixels, which mark the areas of interest. This process is called two class semantic segmentation and is often referred to as image binarization. The foreground regions can then be further processed, e.g. to detect objects or perform intensity measurements.

Concept map

graph TD I("Image") --> T("Threshold") T --> BI("Binary image / Binary mask") BI --- BG("Background pixels (false, 0)") BI --- FG("Foreground pixels (true, 1, 255)")

Figure

Image thresholding

A common algorithm for binarization is thresholding. A threshold value t is chosen, either manually or automatically, and all pixels with intensities below t are set to 0, whereas pixels with intensities >= t are set to the value for the foreground. Depending on the software the foreground value can be different (e.g. 1 in MATLAB or 255 in ImageJ). At any pixel (x,y):

p_im(x,y) < t -> p_bin(x,y) = 0

p_im(x,y) >= t -> p_bin(x,y) = 1

where, p_im and p_bin are the intensity and binary images respectively.

It is also possible to define an interval of threshold values, i.e. a lower and upper threshold value. Pixels with intensity values within this interval belong to the foreground and vice versa.

Activities

Open the binary image xy_8bit_binary__nuclei.tif.
Discuss the image data type and the pixel values.
Open the image xy_8bit__two_cells.tif and binarize it by applying a manually defined threshold.

Show activity for:

ImageJ GUI

Inspect ImageJ binary image

Open xy_8bit_binary__nuclei.tif

Discuss data-type and inspect pixel values

Data-type: unsigned 8-bit, values: 0 and 255

Inspect MATLAB binary image

Open xy_8bit_binary__two_cells_matlabstyle.tif

Discuss data-type and inspect pixel values

Data-type: unsigned 8-bit, values: 0 and 1

Find/apply a threshold

Open xy_8bit__two_cells.tif

Inspect pixel values to find a threshold separating fore- and background

Hover over the image and observe the pixel values in ImageJ status bar

Draw line profile and [Analyze > Plot Profile ] or [Ctrl-K]

Inspect histogram using [Analyze > Histogram] or [Ctrl-H]

[ Image > Adjust > Manual Threshold… ]

Lower threshold level which is the value that you observed in the aforementioned step that would separate foreground and background

Upper threshold level can be set to the maximum bit depth (in this case 255)

Press OK, this will produce an overlaid image where you can see the regions above the threshold in red.

Note: The image is not binary yet (check the pixel values)!

Set binary options: [Process > Binary > Options ..] [X] Black background

[Process > Binary > Convert to Mask], now the image is binary.

Open xy_8bit__two_cells.tif

Repeat above applying a higher threshold so that only the high intensity level nucleus becomes foreground

ImageJ Macro

// Parameters
threshold1 = 49;
threshold2 = 100;

run("Close All");

// Code
open("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__two_cells.tif");
rename("input");

// apply threshold 1
selectWindow("input");
run("Duplicate...", "title=threshold1");
setThreshold(threshold1, 65535);
setOption("BlackBackground", true);
run("Convert to Mask");

// apply threshold 2
selectWindow("input");
run("Duplicate...", "title=threshold2");
setThreshold(threshold2, 65535);
setOption("BlackBackground", true);
run("Convert to Mask");

ImageJ Jython

from ij import IJ, ImagePlus
from ij.plugin import Thresholder

inputImage = IJ.openImage("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__two_cells.tif")
IJ.setRawThreshold(inputImage, 44, 255, None)
binaryImage = ImagePlus('Binary image 2 nuclei', Thresholder.createMask(inputImage))
binaryImage.show()
IJ.setRawThreshold(inputImage, 88, 255, None)
binaryImage_1 = ImagePlus('Binary image 1 nuclei', Thresholder.createMask(inputImage))
binaryImage_1.show()

MATLAB
%These matlab scripts illustrate separating the foreground from the %background using a threshold value provided by the user %Prompt user for a threshold value thres_val = input('Enter a threshold value: '); % Prompt user to choose an image, e.g. xy_8bit__two_cells.tif [file, path] = uigetfile("*.tif"); %Read input image in_image = imread(fullfile(path, file)); %display input image figure; imagesc(in_image); %Binarize input image with the threshold valuein_image bin_image = uint8(in_image>= thres_val); % Display binary image figure; imagesc(bin_image);

KNIME

Python

import numpy as np
import matplotlib.pyplot as plt
from skimage import io

# load the image from file
image_file = "/image_data/xy_8bit__two_cells.tif"
image = io.imread(image_file)

# binarize the image, so that all values larger than the threshold are foreground
threshold_value = 60
binarized = image > threshold_value

# display the original and the binarized image
fig, ax = plt.subplots(2)
ax[0].imshow(image)
ax[0].set_title("Image")
ax[1].imshow(binarized)
ax[1].set_title("Binarized")

# For associated course material in jupyter, go to https://nbviewer.jupyter.org/github/embl-bio-it/image-analysis-with-python/blob/carpentry/image-analysis-session/image-binarization.ipynb#Image-Binarization
# You can also spin up an interactive binder session: https://gke.mybinder.org/v2/gh/embl-bio-it/image-analysis-with-python/carpentry?filepath=image-analysis-session/image-binarization.ipynb

Exercises

Perform one of the following exercises.

Show exercise/solution for:

ImageJ GUI

Open image xy_8bit__PCNA.tif and

Find a threshold value so that there are 2 foreground nuclei.

Find a threshold value so that only the bright dots remain

Find threshold interval so that only the boundary of the nuclei remains.

Solution

[File > Open…] xy_8bit__PCNA.tif

[Analyze > Plot Profile ] or [Ctrl-K]

Lower threshold, i.e. at about 5

Lower threshold at about 44

Lower threshold at about 4, upper threshold at about 4-5

ImageJ Macro

Open image xy_8bit__PCNA.tif and

Find a threshold value so that there are 2 foreground nuclei.
Find a threshold value so that only the bright dots remain
Find threshold interval so that only the boundary of the nuclei remains.

Solution

open("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__PCNA.tif")
selectWindow("xy_8bit__PCNA.tif");
run("Duplicate...", "title=[2 nuclei]");
selectWindow("xy_8bit__PCNA.tif");
run("Duplicate...", "title=[boundary]");
selectWindow("xy_8bit__PCNA.tif");
run("Duplicate...", "title=[dots]");
selectWindow("2 nuclei");
setThreshold(5, 255);
setOption("BlackBackground", true);
run("Convert to Mask");
selectWindow("boundary");
setThreshold(4, 4);
setOption("BlackBackground", true);
run("Convert to Mask");
selectWindow("dots");
setThreshold(44, 255);
setOption("BlackBackground", true);
run("Convert to Mask");

ImageJ Jython

Open image xy_8bit__PCNA.tif and

Find a threshold value so that there are 2 foreground nuclei.
Find a threshold value so that only the bright dots remain
Find threshold interval so that only the boundary of the nuclei remains.

Solution

from ij import IJ, ImagePlus
from ij.plugin import Thresholder
# image is xy_8bit_PCNA.tif
inputImage = IJ.openImage("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__PCNA.tif")
IJ.setRawThreshold(inputImage, 5, 255, None)
binaryImage = ImagePlus('Binary image 2 nuclei', Thresholder.createMask(inputImage))
binaryImage.show()
IJ.setRawThreshold(inputImage, 4, 4, None)
binaryImage_boundary = ImagePlus('Binary boundary', Thresholder.createMask(inputImage))
binaryImage_boundary.show()
IJ.setRawThreshold(inputImage, 44, 255, None)
binaryImage_brightdots = ImagePlus('Binary bright dots', Thresholder.createMask(inputImage))
binaryImage_brightdots.show()

Solution with input parameters

#@ Integer (label="Lower threshold") thr1
#@ Integer (label="Upper threshold") thr2

from ij import IJ, ImagePlus
from ij.plugin import Thresholder
# image is xy_8bit_PCNA.tif should be already open
inputImage = IJ.openImage("https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__PCNA.tif")
IJ.setRawThreshold(inputImage, thr1, thr2, None)
binaryImage = ImagePlus('Thresholded image', Thresholder.createMask(inputImage))
binaryImage.show()

Assessment

Fill in the blanks

Pixels in a binary image can have maximally ___ different values.
If the threshold is larger than the maximal pixel value in the intensity image, all pixels in the binary image have a value of ___.

Solution

Pixels in a binary image can have maximally 2 different values.

If the threshold is larger than the maximal pixel value in the intensity image, all pixels in the binary image have a value of 0.

True or False

There is only one correct threshold value in order to convert an intensity image into a binary image.
Binary images are always unsigned 8-bit where the foreground is 255.

Solution

There is only one correct threshold value in order to convert an intensity image into a binary image. False

Binary images are always unsigned 8-bit where the foreground is 255. False

Follow-up material

Recommended follow-up modules:

Automatic threshold for binarization

Finding objects in a binary image

Learn more:

Wikipedia: Binary image