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.

Read more about this topic:  Image Moment

Famous quotes containing the words raw and/or moments:

    It’s the boxers who attract the real women, after all, with their raw primeval strength, beautifully toned bodies and just a touch of vulnerability.
    Eamonn McCabe (b. 1948)

    Just as we need to encourage women to test life’s many options, we need to acknowledge real limits of energy and resources. It would be pointless and cruel to prescribe role combination for every woman at each moment of her life. Life has its seasons. There are moments when a woman ought to invest emotionally in many different roles, and other moments when she may need to conserve her psychological energies.
    Faye J. Crosby (20th century)