# Question about central spatial moments

• Spatial moment $$m_{pq} = \sum_{(x, y)\ \in \mathbb R} x^p y^q I(x, y)$$
• The order of each moment is $p+q$.
• Central moment $$\mu_{pq} = \sum_{(x, y)\ \in \mathbb R} (x - \bar x)^p (x - \bar y)^q I(x, y)$$

What transformation are the central spatial moments $\mu_{pq}$ invariant to that the spatial moments mpq are not?

• Do you have any idea on the solution? It looks like homework – Maximilian Matthé Mar 28 '17 at 6:43
• @Maximilian Matthé I think the answer would be one of the property of translation invariant ,scale invariant and rotation invariant in central moment, but I am not sure which one is not invariant to spatial moments – Zhetao Zhuang Mar 29 '17 at 15:25