This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Moments

### From Mathematics Is A Science

Moments are certain integrals that capture the distribution of weight in a geometric figure.

In the image analysis context, this is about the distribution of gray (or intensity) in the objects detected in the image.

Currently the only moment displayed in Pixcavator's output table is the average intensity. It is the 0-moment = the integral or the sum of values of the gray scale function.

The area can be thought of as a 0-moment if you assume that the gray is constant within the object. Then the area of an object is the 0-moment = simply the integral or the sum of values of the function equal to 1 inside the object. Saliency can also be understood as the 0-moment of the gray scale function, relative to the border of the object.

First moments are also computed but they aren't displayed. They are used to find the centroid and the center of mass. The latter appears in Pixcavator's output table.

For the mathematics, see [1].

For the probability context see Moments of distributions.

To experiment with the concepts, download the free Pixcavator Student Edition.