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:
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‘My dear—a raw country girl, such as you be,
Cannot quite expect that. You ain’t ruined,’ said she.”
—Thomas Hardy (1840–1928)
“The moments of the past do not remain still; they retain in our memory the motion which drew them towards the future, towards a future which has itself become the past, and draw us on in their train.”
—Marcel Proust (1871–1922)