Histogram

Contains measurements expressing color or gray level statistical attributes extracted from the intensity image histogram and using the label input image as a mask.

These measurements are based on the intensity input image. Using them with a label or binary intensity image is not relevant.
When applied on a color or multispectral intensity image, these measurements return one value for each intensity channel.

By default, a histogram is automatically computed between the minimum and maximum image intensities with a bin size of 1. These parameters can be customized with the Histogram attributes.

Histogram quantile

A quantile value, associated to a given percentage of observations, is the value of the cumulative distribution at the given percentage.

Such a quantile value is computed by interpolation between the first bin where the cumulated histogram is higher than the percentage of observations and its previous bin.
The cumulated histogram is given at the center of each bin, counting the half population of the current bin. For instance, with a bin size of 1, the cumulated histogram for the bin ]3, 4] is computed adding the total population of the values 0, 1 and 2 to the half population of the value 3. It is assigned to the bin center 3.5.
With the example above, where the bin size is 3, the 25% quantile value of the histogram is: $$ Q(25) = \lambda \times 7.5 + (1- \lambda) \times 10.5 $$ where : $$ \lambda = \frac{d2}{(d1+d2)} = \frac{h2}{(h1+h2)} $$ In addition to the Histogram attributes which affects the results, some quantile measurements can be user-defined with the Quantile attributes.