Automatic thresholding (histogram-based)

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

Thresholding

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

Understand how an image histogram can be used to derive a threshold

Apply automatic threshold to distinguish foreground and background pixels

Motivation

The manual determination of a threshold value is tedious and subjective. This is problematic as it reduces the reproducibility of the results and may preclude determining threshold values for many different images as the dataset becomes large. It is therefore important to know about reproducible mathematical approaches to automatically determine threshold values for image segmentation.

Concept map

graph TD I("Image") --> H("Histogram") H -- algorithm --> T("Threshold value")

Figure

Input images, histograms (Huang threshold - blue, Otsu threshold - orange), binary images (Huang), binary images (Otsu).

Activities

Apply manual and automated thresholds

Manual vs. auto thresholding
- Open xy_8bit__nuclei_without_offset.tif and xy_8bit__nuclei_with_offset.tif
- Explore the differences in doing manual and auto thresholding

Show activity for:

ImageJ GUI

Manual vs. auto thresholding

Open xy_8bit__nuclei_without_offset.tif

[ Image > Adjust > Threshold… ]

[X] Dark Background

Selecting Lower threshold level = 20 is a good example. Note down this value

Press Reset

Don’t press Set or Apply

Open xy_8bit__nuclei_with_offset.tif

[ Image > Adjust > Threshold… ]

[X] Dark Background

Selecting Lower threshold level = 20 now does not work (i.e. all pixels are foreground)

Here, selecting Lower threshold level = 40 works

Press Reset

Select window xy_8bit__nuclei_without_offset.tif

[ Image > Adjust > Auto Threshold ]

Method = Try all

[X] White objects on black background

Keep all other options unchecked

Press OK

Select window xy_8bit__nuclei_with_offset.tif

[ Image > Adjust > Auto Threshold ]

Method = Try all

[X] White objects on black background

Keep all other options unchecked

Press OK

In auto thresholding several methods produce acceptable results and one can get rid of selecting manual threshold values for each different image

skimage napari

# %% [markdown]
# ## Apply manual and automated thresholds

# %%
# initial imports
import napari
import numpy as np
from OpenIJTIFF import open_ij_tiff

# %%
# Read the images
image1, axes1, scales1, units1 = open_ij_tiff('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__nuclei_without_offset.tif')
image2, axes2, scales2, units2 = open_ij_tiff('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__nuclei_with_offset.tif')

# %%
# Inspect image data type and values
print(image1.dtype, image1.shape, np.min(image1), np.max(image1))
print(image2.dtype, image2.shape, np.min(image2), np.max(image2))

# %%
# Instantiate the napari viewer and display the images
viewer = napari.Viewer()


# %%
# Add the images
viewer.add_image(image1, name='image1')
viewer.add_image(image2, name='image2')

# %%
# Explore the values of the image
info_type = np.iinfo(image1.dtype)
print('\n', info_type)
print('\n Min image1 %d max image1 %d' % (image1.min(), image1.max()))
print('\n Min image2 %d max image2 %d' % (image2.min(), image2.max()))

# %%
# Show the histogram
import matplotlib.pyplot as plt
plt.hist(image1.flatten(), bins=np.arange(image1.max()+1), log=True);
plt.hist(image2.flatten(), bins=np.arange(image2.max()+1), log=True);

# %%
# Try manual thresholding
thr1 = 25
thr2 = 75

manual_thresholded1 = image1>thr1
manual_thresholded2 = image2>thr2

viewer.add_image(manual_thresholded1, name='manual_thresholded1', opacity = 0.4, colormap='magenta')
viewer.add_image(manual_thresholded2, name='manual_thresholded2', opacity = 0.4, colormap='magenta')
# Identify possible problems with this solution

# %% [markdown]
# Explore auto-thresholding options on:
# https://scikit-image.org/docs/stable/api/skimage.filters.html

# %%
# Obtain the thresholding values
from skimage.filters import threshold_mean

thr1 = threshold_mean(image1)
print(thr1)
mean_thresholded1 = image1>thr1

thr2 = threshold_mean(image2)
print(thr2)
mean_thresholded2 = image2>thr2

# %%
# Visualize auto-thresholded images
viewer.add_image(mean_thresholded1, name='mean_thresholded1', opacity = 0.4, colormap='magenta')
viewer.add_image(mean_thresholded2, name='mean_thresholded2', opacity = 0.4, colormap='magenta')

# %% [markdown]
# Explore other thresholding options \
# Note that there exists a threshold_multiotsu function to handle cases with multi-peaks histograms

Apply automated thresholds in 3D

Open xyz_8bit__nuclei_autothresh.tif
Apply one or more automated thresholding methods to this image
Appreciate that they yield different results

Show activity for:

ImageJ GUI

Open xyz_8bit__nuclei_autothresh.tif

Try all available methods

[ Image > Adjust > Auto Threshold ]

Method = Try all

[X] White objects on black background

[X] Stack

[X] Use stack histogram

Press OK

Observe that the different methods give different outputs

Appreciate that this montage view is not suited for further analysis of the binary output

Apply one method to properly segment the stack, e.g. Otsu

[ Image > Duplicate… ]

Title = Otsu

[X] Duplicate stack

[ Image > Adjust > Auto Threshold ]

Method = Otsu

[X] Stack

[X] Use stack histogram

[X] Show threshold values in log window

Press OK

skimage napari

# %% [markdown]
# ## Apply automated thresholds in 3D

# %%
# initial imports
import numpy as np
import napari
from OpenIJTIFF import open_ij_tiff

# %%
# Read the images
image, axes, scales, units = open_ij_tiff('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xyz_8bit__nuclei_autothresh.tif')

# %%
scales

# %%
# Inspect image data type and values
print(f'Type: {image.dtype} \nShape: {image.shape} \nMin: {np.min(image)} \nMax: {np.max(image)}')

# %%
# Instantiate the napari viewer and display the image
viewer = napari.Viewer()
viewer.add_image(image, name='image', scale=scales)

# %%
# Obtain threshold value using Otsu's algorithm
from skimage.filters import threshold_otsu
thresholded_otsu = image > threshold_otsu(image)

viewer.add_labels(thresholded_otsu, name='otsu', num_colors=1, color={1: 'green'},  scale=scales)

# %% [markdown]
# **Napari GUI** Explore the results in the napari viewer. For 3D data one can change the order 
# of visible axes (bottom left in napari viewer window). If not satisfied by the
# results, we can explore other threshold algorithms

# %%
# Additional threshold methods
from skimage.filters import threshold_li
thresholded_li = image > threshold_li(image)

viewer.add_labels(thresholded_li, name='li', num_colors=1, color={1: 'orange'}, scale=scales)

Assessment

True or False

Using stack histogram yields only one threshold value for binarization when applying auto thresholding
Auto thresholding gives better segmentation results than manual thresholding in the presence of noise

Solution

True

False

Explanations

Key points

Most auto thresholding methods do two class clustering
If the histogram is bimodal, most automated methods will perform well
If the histogram has more than two peaks, automated methods could produce noisy results

Follow-up material

Recommended follow-up modules:

Learn more:

Some common automatic thresholding methods can be studied here Imagej.net Auto-threshold

Advanced material can be found in Introduction to Bioimage Analysis by Pete Bankhead