Learning OpenCV, 2nd Edition

, and

Of course, it should be immediately clear that

= (because the terms involving

p

and

q

vanish

anyhow), and that the

and central moments are both equal to zero as well. The higher order

moments are thus the same as the non-central moments but measured with respect to the “center of mass”

of (or in the coordinates of the center of mass of) the object as a whole. Because these measurements are

relative to this center, they do not change if the object appears in any arbitrary location in the image.

You will notice that there are no elements mu00, mu10, or mu01 in the object

cv::Moments. This is simply because these values are “trivial” (i.e., mu00=m00, and

mu10=mu01=0). The same is true for the normalized central moments (except that

nu00=1, while nu10 and nu01 are both zero). For this reason they are not included in

the structure, as they would just waste memory storing redundant information.

29BNormalized Central Moments Are Also Invariant Under Scaling

Just as the central moments allow for us to compare two different objects that are in different locations in

our image, it is also often important to be able to compare two different objects that are the same except for

being different sizes. (This sometimes happens because we are looking for an object of a type that appears

in nature of different sizes—e.g., bears—but more often it is simply because we do not necessarily ...