Image Moment - Raw Moments

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.

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Famous quotes containing the words raw and/or moments:

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