numbers_and_brightness 0.1.3

Numbers and brightness analysis for microscopic image analysis implemented in python.

Numbers-and-brightness

Numbers and brightness analysis for microscopic image analysis implemented in python.

Functions both as a python package and command-line tool.

Installation

Numbers and brightness can be installed as follows:

pip install numbers_and_brightness

Usage

Python package

Numbers and brightness can be used as follows:

from numbers_and_brightness.numbers_and_brightness import numbers_and_brightness_analysis
numbers_and_brightness_analysis(file = "./Images/image.tif")

Or in batch processing mode:

from numbers_and_brightness.numbers_and_brightness import numbers_and_brightness_batch
numbers_and_brightness_batch(folder = "./Images")

Command line

The package can also be accessed using the command line:

C:\Users\User> numbers_and_brightness --file "Images/image.tif"
C:\Users\User> numbers_and_brightness --folder "Images"

Graphical user interface

The package contains a small GUI that can be accessed as follows:

Python

from numbers_and_brightness.gui import nb_gui
nb_gui()

Command line

C:\Users\User> numbers_and_brightness

Desktop shortcut

Additionally, a desktop (and start menu) shortcut can be created using the following command:

C:\Users\User> numbers_and_brightness --shortcut

Parameters

The package contains the following parameters. These parameters can be altered by passing the parameter to the function, or to the cli as '--parameter'

• background : int, default = 0
  • background noise in the signal. Will be included in the calculations as $k_0$ as described by Digman et al., 2008.
• segment : bool, default = False
  • perform automatic segmentation of the cells using cellpose
• diameter : int, default = 75
  • expected diameter of the cell, passed to cellpose model
• flow_threshold : float, default = 0.4
  • flow threshold, passed to cellpose model
• cellprob_threshold : float, default = 4
  • cellprob threshold, passed to cellpose model
• analysis : bool, default = False
  • perform analysis by plotting intensity of cell against apparent brightness
• erode : int, default = 2
  • erode the edges of the cell mask to ensure only pixels inside the cell are used for the analysis

Examples:

C:\Users\User> numbers_and_brightness --folder "Images" --analysis true

from numbers_and_brightness.numbers_and_brightness import numbers_and_brightness_batch
numbers_and_brightness_batch(folder = "./Images", analysis = True)

Core calculations

All calculations are derived from Digman et al., 2008.

Here img represents a numpy array of shape (t, y, x).

Intensity

Intensity is calculated as:

$$\langle k \rangle = \frac{\sum_i k_i}{K}$$

In python:

average_intensity = np.mean(img, axis=0)

Variance

Variance is calculated as:

$$\sigma^2 = \frac{\sum_i (k_i - \langle k \rangle)^2}{K}$$

In python:

variance = np.var(img, axis=0)

Apparent brightness

Apparent brightness is calculated as:

$$B = \frac{\sigma^2}{\langle k \rangle}$$

In python:

apparent_brightness = variance / average_intensity

Apparent number

Apparent number is calculated as:

$$N = \frac{\langle k \rangle^2}{\sigma^2}$$

In python:

apparent_number = average_intensity**2 / variance

Brightness

Brightness is calculated as:

$$\varepsilon = \frac{\sigma^2 - \langle k \rangle}{\langle k \rangle - k_0}$$

In python:

brightness = (variance - average_intensity) / (average_intensity - background)

Number

Number is calculated as:

$$n = \frac{(\langle k \rangle - k_0)^2}{\sigma^2 - \langle k \rangle}$$

In python:

number = ((average_intensity-background)**2) / np.clip((variance - average_intensity), 1e-6, None)

Here the denominator is clipped (limited) to a value of 1e-6 to prevent extremely high number values.

Output

For each image, the package generates a new folder containing extensive output:

Examples:

Automatic batch processing

Interactive data inspection