Rebirth of T-rex

I have been searching and gathering some informations for my Master Degree preparation. However, since early of this week, I started to seriously study for some of the introductory knowledge that will be required for me to kick start my Master Degree research on Computer Imaging/Pattern Recognition. I shared some of them here.

Definitions (brief and verbal basis):
i) Moment- Image intensity projected on monomial/polynomial
ii) Feature- Characteristics
iii) Descriptor- Way to describe features, eg. wavelet
iv) Domain- Range
v) Normalized- Convert to 'standard'
vi) Moment Invariance- Under certain condition, things doesn't change, eg. centroid (center of gravity)
vii) Lagendre Moment, Zernike Moment, Pseudo-Zernike Moment- based on Lagendre Polynomial, Zernike Polynomial and Pseudo-Zernike Polynomial respectively.
viii) Elementary Area- The ratio of area between original and domain

Since I am looking into Zernike Moment for research, I wish to share some of the important mathematical background here:

The radial moment of order p with repetition q are defined as


The 2D Zernike moments of order p with repetition q of image intensity function f(r, theta) are defined as


where Zernike polynomials of order p with repetition q, Vpq(r, theta), are defined as


and the real-valued radial polynomial, Rpq(r), is given as


where 0 <= q <= p and p - q is even