image moment

A weighted sum of a shape's pixel coordinates that summarizes its size, position, or orientation numerically.

A raw image moment $m_{pq} = \sum_{x,y} x^p y^q I(x,y)$ weights each pixel's coordinates by powers $p,q$ and sums. $m_{00}$ is the shape's area; $m_{10}/m_{00}$ and $m_{01}/m_{00}$ give its centroid. Central moments $\mu_{pq}$ repeat the same sum measured from the centroid rather than the origin, making them invariant to translation.

Examples

A binary mask's $m_{00}$ moment simply counts its foreground pixels, giving the region's area directly.