Calculates seven Hu invariants

hu = cv.HuMoments(mo)

Input

• mo Input moments computed with cv.moments().

Output

• hu Output Hu invariants, a vector of length 7.

The function calculates seven Hu invariants (introduced in [Hu62]; see also http://en.wikipedia.org/wiki/Image_moment), defined as:

hu[0] =  eta_20 + eta_02
hu[1] = (eta_20 - eta_02)^2 + 4*eta_11^2
hu[2] = (eta_30 - 3*eta_12)^2 + (3*eta_21 - eta_03)^2
hu[3] = (eta_30 + eta_12)^2 + (eta_21 + eta_03)^2
hu[4] = (eta_30 - 3*eta_12)*(eta_30 + eta_12)*[(eta_30 + eta_12)^2 - 3*(eta_21 + eta_03)^2] +
        (3*eta_21 - eta_03)*(eta_21 + eta_03)*[3*(eta_30 + eta_12)^2-(eta_21 + eta_03)^2]
hu[5] = (eta_20 - eta_02)*[(eta_30 + eta_12)^2 - (eta_21 + eta_03)^2] +
        4*eta_11(eta_30 + eta_12)*(eta_21 + eta_03)
hu[6] = (3*eta_21 - eta_03)*(eta_21 + eta_03)*[3*(eta_30 + eta_12)^2-(eta_21 + eta_03)^2] -
        (eta_30 - 3*eta_12)*(eta_21 + eta_03)*[3*(eta_30 + eta_12)^2-(eta_21 + eta_03)^2]

where eta_ji stands for mo.nu[ji].

These values are proved to be invariants to the image scale, rotation, and reflection except the seventh one, whose sign is changed by reflection. This invariance is proved with the assumption of infinite image resolution. In case of raster images, the computed Hu invariants for the original and transformed images are a bit different.

References

[Hu62]:

Ming-Kuei Hu. "Visual pattern recognition by moment invariants". Information Theory, IRE Transactions on, 8(2):179-187, 1962.