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:
“Everybody in America is soft, and hates conflict. The cure for this, both in politics and social life, is the same—hardihood. Give them raw truth.”
—John Jay Chapman (1862–1933)
“Athletes have studied how to leap and how to survive the leap some of the time and return to the ground. They don’t always do it well. But they are our philosophers of actual moments and the body and soul in them, and of our manoeuvres in our emergencies and longings.”
—Harold Brodkey (b. 1930)