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:
“It began with begging.
In the beginning it was all God’s icebox
and everyone ate raw fish or animals
and there was no fire at night to dance to,
no fire at day to cook by.”
—Anne Sexton (1928–1974)
“Revolutions are notorious for allowing even non- participants—even women!—new scope for telling the truth since they are themselves such massive moments of truth, moments of such massive participation.”
—Selma James (b. 1930)