Image Intensity

Image Intensity measures the brightness of one channel over the whole image: total, mean, standard deviation, minimum, maximum, median, lower and upper quartile and the median absolute deviation. It uses every pixel of the image, the background too - unlike the intensity metrics of an object, which use only the object’s pixels.

It is a measurement step: it runs once per image plane, after all tiles of the image are read, and gives one set of values per plane.

Parameters

Parameter	Description
ID	The step’s ID, unique in the project. It is given automatically (intensity_01, …) and starts the names of its values in the results.
Channel	The channel to measure.

Measurements

Nine values per image plane, all in gray values (like the objects’ intensities). Each name ends with the channel, e.g. “Mean intensity (channel 0)”.

Measurement	Unit	Description
Total intensity	gray value	The sum of all pixels.
Mean intensity	gray value	The mean of all pixels.
Standard deviation of intensity	gray value	How far the pixels spread around the mean.
Minimum intensity	gray value	The darkest pixel.
Maximum intensity	gray value	The brightest pixel.
Median intensity	gray value	Half the pixels are darker, half brighter.
Lower quartile intensity	gray value	A quarter of the pixels are darker.
Upper quartile intensity	gray value	A quarter of the pixels are brighter.
Median absolute deviation of intensity	gray value	The median distance of the pixels to the median - a spread that a few bright pixels do not change.

How it works

Over the $n$ pixels $v_i$ of the channel as it is loaded from the image - filters earlier in the pipeline do not change it. An RGB image is turned into its luminance first.

$$\text{Total} = \sum_i v_i, \qquad \text{Mean} = \frac{\text{Total}}{n}, \qquad \sigma = \sqrt{\frac{1}{n}\sum_i (v_i - \text{Mean})^2}$$

The standard deviation is that of the population: all pixels are measured, not a sample of them.

The median and quartiles are taken from a histogram of the pixels, one bin per gray value (above 16 bits, 65 536 bins over the range). Between two pixels they are interpolated linearly, as NumPy’s percentile does: the quantile $q$ lies at rank $q\,(n-1)$ of the sorted pixels.

$$\text{MAD} = \operatorname{median}_i \, |v_i - \operatorname{median}(v)|$$

Pixels that are not numbers are left out. An image without pixels gets no values.

Results

The values belong to the image plane, not to an object. In the List view they are under Columns › Measurements, named “intensity_01 · Mean intensity (channel 0)”. With A row per: Images each image shows its own value; with A row per: Objects each object row shows the value of its image plane. In the Plate view a well gets the statistic over its images’ values; images left out are not counted.

The export option Measurements - one row per value writes them with one row per value - see Exporting Results.

Use them, for example, to normalise the objects’ intensities by the image’s background (the median of a sparse image), or with Exclude Image to leave out images that are too dark.