Paper Review: Shape Classification Using Zernike Moments

Q: What is a moment?

A moment is defined as:

$$m_{p,q}(x,y) = \int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} x^p y^q f(x,y) dxdy$$

In other words, it is the summation of the figure with respect to the function $f$ for both axes.

Q: What are Zernike moments?

Zernike moments are complex polynomial functions used to sum the elements of a shape. They were first introduced in the 1930s. The higher the order, the more complex the shape that can be represented. Order 1 Zernike moments (ZMs) are ellipsoid planes where one side is higher than the other.

Q: What is the difference between Hu moments and Zernike moments?

The importance of Zernike moments lies in their rotational invariance. However, Hu moments are also said to have these properties. Thus, Hu moments appear to be simpler alternatives to Zernike moments.

Q: What are their properties?

Zernike moments use polar coordinates, making it easy to describe rotational invariance.