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:
“In how few words, for instance, the Greeks would have told the story of Abelard and Heloise, making but a sentence of our classical dictionary.... We moderns, on the other hand, collect only the raw materials of biography and history, “memoirs to serve for a history,” which is but materials to serve for a mythology.”
—Henry David Thoreau (1817–1862)
“There are moments when all anxiety and stated toil are becalmed in the infinite leisure and repose of nature.”
—Henry David Thoreau (1817–1862)