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 before and after applying a threshold of 73 gray values.
# %% [markdown]
# ## Thresholding bright and dim cell
# %%
# Instantiate the napari viewer
importnaparifromOpenIJTIFFimportopen_ij_tiffviewer=napari.Viewer()# %%
# Read the intensity image
image,axes,scales,units=open_ij_tiff('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__two_cells.tif')# %%
# View the intensity image
viewer.add_image(image)# Check the intensity image's datatype
print(image.dtype)# %% [markdown]
# **Napari GUI** Inspect the intensity image values in order to identify a threshold that segments both cells \
# **Napari GUI** hover with mouse \
# **Napari GUI** make a line profile using the Napari plugin `napari-plot-profile` (`pip install napari-plot-profile`)
# %%
# Threshold the image
binary_image_two_cells=image>49# %%
# Overlay the binary image
viewer.add_image(binary_image_two_cells,opacity=0.8)# Inspect data type
print(binary_image_two_cells.dtype)# %%
# Inspect value content
importnumpyasnpprint(np.unique(binary_image_two_cells))# %%
# Apply a higher threshold
# to only select the brighter cell
binary_image_one_cell=image>100viewer.add_image(binary_image_one_cell,opacity=0.8)
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");
# %% [markdown]
# ## Spots and threshold interval
# %%
# Instantiate the napari viewer
importnapariviewer=napari.Viewer()# %%
# Read the intensity image
fromOpenIJTIFFimportopen_ij_tiffimage,axes,scales,units=open_ij_tiff('https://github.com/NEUBIAS/training-resources/raw/master/image_data/xy_8bit__PCNA.tif')# View the intensity image
viewer.add_image(image)# %%
# Check the intensity image's datatype
print(image.dtype)# %% [markdown]
# **Napari GUI** Inspect the intensity image values in order to identify a threshold \
# **Napari GUI** hover with mouse \
# **Napari GUI** make a line profile using the Napari plugin `napari-plot-profile` (`pip install napari-plot-profile`)
# %%
# Threshold the image
binary_image_two_nuclei=image>5# Overlay the binary image
viewer.add_image(binary_image_two_nuclei,opacity=0.8)# %%
# Inspect data type
print(binary_image_two_nuclei.dtype)# %%
# Inspect value content
importnumpyasnpprint(np.unique(binary_image_two_nuclei))# %%
# Apply a higher threshold
# to only select the brighter dots
binary_image_bright_dots=image>44viewer.add_image(binary_image_bright_dots,opacity=0.8)# %%
# Apply two thresholds
# to only select the boundary of cells
binary_image_boundary=(image<5)*(image>=4)viewer.add_image(binary_image_boundary,opacity=0.8)
Measure the mean m and standard deviation s of the intensity in a backgroun region.
Set the threshold as t = m + N*s choosing some N larger than 1; N effectively determines the statistical significance with which the values above t are foreground pixels.
Eventually add [x] Mean gray value and [x] Standard deviation to your result table, [Results > Set Measurements]
Note the value of Mean and StdDev and compute their sum
Choose a multiple of this sum for the threshold
Test your choice [Image > Adjust > Threshold…]
Press Apply to create a binary image
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
Explanations
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.
