# Shape Classification Using Zernike Moments

Posted on Fri 04 April 2014 in old • 1 min read

## A: 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's the summation of the figure w.r.t function f for both axes

## A: What are Zernike moments?

Zernike moments are complex polynomial functions that we use to sum the elements of a shape. It is was first introduced in 1930s. The higher the order of it, the more complex shape appears. Order 1 ZMs are ellipsoid planes of which one side is higher than the other.

## A: What's the difference between Hu moments and Zernike moments?

The importance of Zernike moments are their rotationally invariant features. However Hu moments are said to have these properties as well. So it looks Hu Moments are simpler alternatives to this.

## A: What are their properties?

It uses polar coordinates and hence easy to describe the rotational invariance.