• 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?

  • $\begingroup$ Do you have any idea on the solution? It looks like homework $\endgroup$ Commented Mar 28, 2017 at 6:43
  • $\begingroup$ @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 $\endgroup$ Commented Mar 29, 2017 at 15:25

1 Answer 1


It removes the mean, hence invariant to addition of a constant.


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