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:
“And we can get back to that raw state
Of feeling, so long deemed
Inconsequential and therefore appropriate to our later musings
About religion, about migrations. What is restored
Becomes stronger than the loss as it is remembered;
Is a new, separate life of its own.”
—John Ashbery (b. 1927)
“Science with its retorts would have put me to sleep; it was the opportunity to be ignorant that I improved. It suggested to me that there was something to be seen if one had eyes. It made a believer of me more than before. I believed that the woods were not tenantless, but choke-full of honest spirits as good as myself any day,—not an empty chamber, in which chemistry was left to work alone, but an inhabited house,—and for a few moments I enjoyed fellowship with them.”
—Henry David Thoreau (1817–1862)