Descriptive statistics of labeled images

Descriptive statistics of labeled images#

Using pandas and numpy, we can do basic descriptive statistics. Before we start, we derive some measurements from a labeled image.

import pandas as pd
import numpy as np
from skimage.io import imread, imshow
from napari_segment_blobs_and_things_with_membranes import gauss_otsu_labeling
from skimage.measure import regionprops_table

We load the image using scikit-image’s imread and segment it using Gauss-Otsu-Labeling.

image = imread('../../data/blobs.tif')
labels = gauss_otsu_labeling(image)
imshow(labels)

C:\Users\rober\miniconda3\envs\bio_39\lib\site-packages\skimage\io\_plugins\matplotlib_plugin.py:150: UserWarning: Low image data range; displaying image with stretched contrast.
  lo, hi, cmap = _get_display_range(image)

<matplotlib.image.AxesImage at 0x2819ae7b370>
../_images/2ddad22da785740fbcc5ea1360bad5c375c120b84ea46a9be1503289729c400a.png

From the labeled image we can derive descriptive intensity, size and shape statistics using scikit-image’s regionprops_table. For post-processing the measurements, we turn them into a pandas Dataframe.

table = regionprops_table(labels, image, properties=['area', 'minor_axis_length', 'major_axis_length', 'eccentricity', 'feret_diameter_max'])
data_frame = pd.DataFrame(table)
data_frame
area minor_axis_length major_axis_length eccentricity feret_diameter_max
0 422 16.488550 34.566789 0.878900 35.227830
1 182 11.736074 20.802697 0.825665 21.377558
2 661 28.409502 30.208433 0.339934 32.756679
3 437 23.143996 24.606130 0.339576 26.925824
4 476 19.852882 31.075106 0.769317 31.384710
... ... ... ... ... ...
56 211 14.522762 18.489138 0.618893 18.973666
57 78 6.028638 17.579799 0.939361 18.027756
58 86 5.426871 21.261427 0.966876 22.000000
59 51 5.032414 13.742079 0.930534 14.035669
60 46 3.803982 15.948714 0.971139 15.033296

61 rows × 5 columns

You can take a column out of the DataFrame. In this context it works like a Python dictionary.

data_frame["area"]

0     422
1     182
2     661
3     437
4     476
     ... 
56    211
57     78
58     86
59     51
60     46
Name: area, Length: 61, dtype: int32

Even though this data structure appears more than just a vector, numpy is capable of applying basic descriptive statistics functions:

np.mean(data_frame["area"])

358.42622950819674

np.min(data_frame["area"])

5

np.max(data_frame["area"])

899

Individual cells of the DataFrame can be accessed like this:

data_frame["area"][0]

422

For loops can also iterate over table columns like this:

for area_value in data_frame["area"]:
    print(area_value)

422
182
661
437
476
277
259
219
67
19
486
630
221
78
449
516
390
419
267
353
151
400
426
246
503
278
681
176
358
544
597
181
629
596
5
263
899
476
233
164
394
411
235
375
654
376
579
64
161
457
625
535
205
562
845
280
211
78
86
51
46

Summary statistics with Pandas#

Pandas also allows you to visualize summary statistics of measurement using the describe() function.

data_frame.describe()
area minor_axis_length major_axis_length eccentricity feret_diameter_max
count 61.000000 61.000000 61.000000 61.000000 61.000000
mean 358.426230 17.127032 24.796851 0.657902 25.323368
std 210.446942 6.587838 9.074265 0.189669 8.732456
min 5.000000 1.788854 3.098387 0.312788 3.162278
25% 205.000000 14.319400 18.630719 0.503830 19.313208
50% 375.000000 17.523565 23.768981 0.645844 24.698178
75% 503.000000 21.753901 30.208433 0.825665 31.384710
max 899.000000 28.409502 54.500296 0.984887 52.201533

Correlation matrix#

If you want to learn which parameters are correlated with other parameters, you can visualize that using pandas’s corr().

data_frame.corr()
area minor_axis_length major_axis_length eccentricity feret_diameter_max
area 1.000000 0.890649 0.895282 -0.192147 0.916652
minor_axis_length 0.890649 1.000000 0.664507 -0.566486 0.716706
major_axis_length 0.895282 0.664507 1.000000 0.168454 0.995196
eccentricity -0.192147 -0.566486 0.168454 1.000000 0.103529
feret_diameter_max 0.916652 0.716706 0.995196 0.103529 1.000000

Exercise#

Process the banana dataset, e.g. using a for-loop that goes through the folder ../../data/banana/ and processes all the images. Segment all objects in the banana slice images and print out the largest area found for each slice. Collect these values in a list and visualize it as pandas DataFrame.

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