Raw Moments
For a 2D continuous function f(x,y) the moment (sometimes called "raw moment") of order (p + q) is defined as
for p,q = 0,1,2,... Adapting this to scalar (greyscale) image with pixel intensities I(x,y), raw image moments Mij are calculated by
In some cases, this may be calculated by considering the image as a probability density function, i.e., by dividing the above by
A uniqueness theorem (Hu ) states that if f(x,y) is piecewise continuous and has nonzero values only in a finite part of the xy plane, moments of all orders exist, and the moment sequence (Mpq) is uniquely determined by f(x,y). Conversely, (Mpq) uniquely determines f(x,y). In practice, the image is summarized with functions of a few lower order moments.
Read more about this topic: Image Moment
Famous quotes containing the words raw and/or moments:
“I reverently believe that the Maker who made us all makes everything in New England but the weather. I don’t know who makes that, but I think it must be raw apprentices in the weather-clerk’s factory who experiment and learn how.... In the spring I have counted one hundred and thirty-six different kinds of weather inside of four-and-twenty hours.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Within the circuit of this plodding life
There enter moments of an azure hue,
Untarnished fair as is the violet
Or anemone, when the spring strews them
By some meandering rivulet, which make
The best philosophy untrue that aims
But to console man for his grievances.
I have remembered when the winter came,”
—Henry David Thoreau (1817–1862)