struct returned by cv::moments
The spatial moments \(\texttt{Moments::m}_{ji}\) are computed as:
\[\texttt{m} _{ji}= \sum _{x,y} \left ( \texttt{array} (x,y) \cdot x^j \cdot y^i \right )\]
The central moments \(\texttt{Moments::mu}_{ji}\) are computed as:
\[\texttt{mu} _{ji}= \sum _{x,y} \left ( \texttt{array} (x,y) \cdot (x - \bar{x} )^j \cdot (y - \bar{y} )^i \right )\]
where \((\bar{x}, \bar{y})\) is the mass center:
\[\bar{x} = \frac{\texttt{m}_{10}}{\texttt{m}_{00}} , \; \bar{y} = \frac{\texttt{m}_{01}}{\texttt{m}_{00}}\]
The normalized central moments \(\texttt{Moments::nu}_{ij}\) are computed as:
\[\texttt{nu} _{ji}= \frac{\texttt{mu}_{ji}}{\texttt{m}_{00}^{(i+j)/2+1}} .\]
- Note
- \(\texttt{mu}_{00}=\texttt{m}_{00}\), \(\texttt{nu}_{00}=1\) \(\texttt{nu}_{10}=\texttt{mu}_{10}=\texttt{mu}_{01}=\texttt{mu}_{10}=0\) , hence the values are not stored.
The moments of a contour are defined in the same way but computed using the Green's formula (see http://en.wikipedia.org/wiki/Green_theorem). So, due to a limited raster resolution, the moments computed for a contour are slightly different from the moments computed for the same rasterized contour.
- Note
- Since the contour moments are computed using Green formula, you may get seemingly odd results for contours with self-intersections, e.g. a zero area (m00) for butterfly-shaped contours.
1.8.13