# Differentiating nuclei according to signal intensity#

A common bio-image analysis task is differentiating cells according to their signal expression. In this example we take a two-channel image of nuclei which express Cy3 and eGFP. Visually, we can easily see that some nuclei expressing Cy3 also express eGFP, others don’t. This notebook demonstrates how to differentiate nuclei segmented in one channel according to the intensity in the other channel.

import pyclesperanto_prototype as cle
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

cle.get_device()

<Apple M1 Max on Platform: Apple (2 refs)>


We’re using a dataset published by Heriche et al. licensed CC BY 4.0 available in the Image Data Resource.

# load file
raw_image = imread('plate1_1_013 [Well 5, Field 1 (Spot 5)].png')

# visualize
imshow(raw_image)

<matplotlib.image.AxesImage at 0x178cbaf70>


First, we need to split channels (read more). After that, we can actually see that not all cells marked with Cy3 (channel 0) are also marked with eGFP (channel 1):

# extract channels
channel_cy3 = raw_image[...,0]
channel_egfp = raw_image[...,1]

# visualize
fig, axs = plt.subplots(1, 2, figsize=(15,15))
axs[0].imshow(channel_cy3, cmap='gray')
axs[1].imshow(channel_egfp, cmap='gray')

<matplotlib.image.AxesImage at 0x17acb54c0>


## Segmenting nuclei#

As the staining marks the nuclei in the Cy3 channel, it is reasonable to segment nuclei in this channel and afterwards measure the intensity in the other channel. We use Voronoi-Otsu-Labeling for the segmentation because it is a quick and straightforward approach.

# segmentation
nuclei_cy3 = cle.voronoi_otsu_labeling(channel_cy3, spot_sigma=20)

# visualize
fig, axs = plt.subplots(1, 2, figsize=(15,15))
cle.imshow(channel_cy3, plot=axs[0], color_map="gray")
cle.imshow(nuclei_cy3, plot=axs[1], labels=True)


Firstly, we can measure the intensity in the second channel, marked with eGFP and visualize that measurement in a parametric image. In such a parametric image, all pixels inside a nucleus have the same value, in this case the mean average intensity of the cell.

intensity_map = cle.mean_intensity_map(channel_egfp, nuclei_cy3)

# visualize
fig, axs = plt.subplots(1, 2, figsize=(15,15))
cle.imshow(channel_egfp, plot=axs[0], color_map="gray")
cle.imshow(intensity_map, plot=axs[1], color_map="gray")


From such a parametric image, we can retrieve the intensity values and get them in a vector. The first item in this list has value 0 and corresponds to the intensity of the background, which is 0 in the parametric image.

intensity_vector = cle.read_intensities_from_map(nuclei_cy3, intensity_map)
intensity_vector

cl.Array([[  0.      ,  80.87585 ,  23.529799, 118.17817 ,  80.73025 ,
95.55178 ,  72.84752 ,  92.34759 ,  78.84362 ,  85.400444,
105.108025,  65.06639 ,  73.69295 ,  77.40092 ,  81.48371 ,
77.12867 ,  96.582085,  95.94536 ,  70.883995,  89.705025,
72.01046 ,  27.257877,  84.460075,  25.497112,  80.69056 ,
147.49736 ,  28.112642,  25.16763 ,  28.448261,  25.31705 ,
38.072815, 108.81613 ]], dtype=float32)


There is by the way also an alternative way to come to the mean intensities directly, by measuring all properties of the nuclei including position and shape. It the statistics can be further processed as pandas DataFrame.

statistics = cle.statistics_of_background_and_labelled_pixels(channel_egfp, nuclei_cy3)

statistics_df = pd.DataFrame(statistics)

label original_label bbox_min_x bbox_min_y bbox_min_z bbox_max_x bbox_max_y bbox_max_z bbox_width bbox_height ... centroid_z sum_distance_to_centroid mean_distance_to_centroid sum_distance_to_mass_center mean_distance_to_mass_center standard_deviation_intensity max_distance_to_centroid max_distance_to_mass_center mean_max_distance_to_centroid_ratio mean_max_distance_to_mass_center_ratio
0 1 0 0.0 0.0 0.0 1841.0 1477.0 0.0 1842.0 1478.0 ... 0.0 1.683849e+09 640.648621 1.683884e+09 640.661621 8.487288 1187.033325 1187.743164 1.852862 1.853932
1 2 1 127.0 967.0 0.0 167.0 1033.0 0.0 41.0 67.0 ... 0.0 4.128045e+04 18.704329 4.128327e+04 18.705606 4.734930 34.280666 34.338104 1.832767 1.835712
2 3 2 259.0 205.0 0.0 314.0 265.0 0.0 56.0 61.0 ... 0.0 5.392080e+04 19.715101 5.393992e+04 19.722090 1.663604 32.079910 31.469477 1.627174 1.595646
3 4 3 432.0 1377.0 0.0 492.0 1423.0 0.0 61.0 47.0 ... 0.0 3.630314e+04 17.769527 3.636824e+04 17.801392 24.842558 36.856163 36.085430 2.074122 2.027113
4 5 4 631.0 1123.0 0.0 690.0 1194.0 0.0 60.0 72.0 ... 0.0 6.753253e+04 21.686747 6.755171e+04 21.692907 17.358543 38.805695 38.417568 1.789374 1.770974

5 rows × 37 columns

The intensity vector can then be retrieved from the tabular statistics. Note: In this case, the background intensity is not 0, because we were directly reading it from the original image.

intensity_vector2 = statistics['mean_intensity']
intensity_vector2

array([ 20.829758,  80.87585 ,  23.529799, 118.17817 ,  80.73025 ,
95.55178 ,  72.84752 ,  92.34759 ,  78.84362 ,  85.400444,
105.108025,  65.06639 ,  73.69295 ,  77.40092 ,  81.48371 ,
77.12867 ,  96.582085,  95.94536 ,  70.883995,  89.705025,
72.01046 ,  27.257877,  84.460075,  25.497112,  80.69056 ,
147.49736 ,  28.112642,  25.16763 ,  28.448261,  25.31705 ,
38.072815, 108.81613 ], dtype=float32)


To get an averview about the mean intensity measurement, we can use matplotlib to plot a histogram. We ignore the first element, because it corresponds to the background intensity.

plt.hist(intensity_vector2[1:])

(array([ 7.,  1.,  0.,  4., 10.,  5.,  2.,  1.,  0.,  1.]),
array([ 23.529799,  35.926556,  48.32331 ,  60.720066,  73.11682 ,
85.51358 ,  97.91034 , 110.30709 , 122.70385 , 135.1006  ,
147.49736 ], dtype=float32),
<BarContainer object of 10 artists>)


From such a histogram, we could conclude that objects with intensity above 50 are positive.

## Selecting labels above a given intensity threshold#

We next generate a new labels image with the nuclei having intensity > 50. Note, all the above steps for extracting the intensity vector are not necessary for this. We just did that to get an idea about a good intensity threshold.

The following label image show the nuclei segmented in the Cy3 channel which have a high intensity in the eGFP channel.

intensity_threshold = 50

nuclei_with_high_intensity_egfg = cle.exclude_labels_with_map_values_within_range(intensity_map, nuclei_cy3, maximum_value_range=intensity_threshold)
intensity_map = cle.mean_intensity_map(channel_egfp, nuclei_cy3)

# visualize
fig, axs = plt.subplots(1, 2, figsize=(15,15))
cle.imshow(channel_egfp, plot=axs[0], color_map="gray")
cle.imshow(nuclei_with_high_intensity_egfg, plot=axs[1], labels=True)


And we can also count those by determining the maximum intensity in the label image:

number_of_double_positives = nuclei_with_high_intensity_egfg.max()
print("Number of Cy3 nuclei that also express eGFP", number_of_double_positives)

Number of Cy3 nuclei that also express eGFP 23.0


## References#

Some of the functions we used might be uncommon. Hence, we can add their documentation for reference.

print(cle.voronoi_otsu_labeling.__doc__)

Labels objects directly from grey-value images.

The two sigma parameters allow tuning the segmentation result. Under the hood,
this filter applies two Gaussian blurs, spot detection, Otsu-thresholding [2] and Voronoi-labeling [3]. The
thresholded binary image is flooded using the Voronoi tesselation approach starting from the found local maxima.

Parameters
----------
source : Image
Input grey-value image
label_image_destination : Image, optional
Output image
spot_sigma : float
controls how close detected cells can be
outline_sigma : float
controls how precise segmented objects are outlined.

Returns
-------
label_image_destination

Examples
--------
>>> import pyclesperanto_prototype as cle
>>> cle.voronoi_otsu_labeling(source, label_image_destination, 10, 2)

References
----------
.. [1] https://clij.github.io/clij2-docs/reference_voronoiOtsuLabeling
.. [2] https://ieeexplore.ieee.org/document/4310076
.. [3] https://en.wikipedia.org/wiki/Voronoi_diagram


print(cle.mean_intensity_map.__doc__)

Takes an image and a corresponding label map, determines the mean
intensity per label and replaces every label with the that number.

This results in a parametric image expressing mean object intensity.

Parameters
----------
input : Image
label_map : Image
destination : Image

Returns
-------
destination

References
----------
.. [1] https://clij.github.io/clij2-docs/reference_meanIntensityMap


print(cle.read_intensities_from_map.__doc__)

Takes a label image and a parametric image to read parametric values from the labels positions.
The read intensity values are stored in a new vector.

Note: This will only work if all labels have number of voxels == 1 or if all pixels in each label have the same value.

Parameters
----------
labels: Image
map_image: Image
values_destination: Image, optional
1d vector with length == number of labels + 1

Returns
-------
values_destination, Image:
vector of intensity values with 0th element corresponding to background and subsequent entries corresponding to
the intensity in the given labeled object


print(cle.statistics_of_background_and_labelled_pixels.__doc__)

Determines bounding box, area (in pixels/voxels), min, max and mean
intensity of background and labelled objects in a label map and corresponding
pixels in the original image.

Instead of a label map, you can also use a binary image as a binary image is a
label map with just one label.

This method is executed on the CPU and not on the GPU/OpenCL device.

Parameters
----------
input : Image
labelmap : Image

Returns
-------
Dictionary of measurements

References
----------
.. [1] https://clij.github.io/clij2-docs/reference_statisticsOfBackgroundAndLabelledPixels


print(cle.exclude_labels_with_map_values_within_range.__doc__)

This operation removes labels from a labelmap and renumbers the
remaining labels.

Parameters
----------
values_map : Image
label_map_input : Image
label_map_destination : Image
minimum_value_range : Number
maximum_value_range : Number

Returns
-------
label_map_destination

References
----------
.. [1] https://clij.github.io/clij2-docs/reference_excludeLabelsWithValuesWithinRange