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Moments Class Reference
Public Member Functions

Moments Class Reference
[Structural Analysis and Shape Descriptors]

struct returned by cv::moments More...

#include <types.hpp>

Public Member Functions

 Moments ()
 the default constructor
 Moments (double m00, double m10, double m01, double m20, double m11, double m02, double m30, double m21, double m12, double m03)
 the full constructor

Data Fields

spatial moments
CV_PROP_RW double m00
CV_PROP_RW double m10
CV_PROP_RW double m01
CV_PROP_RW double m20
CV_PROP_RW double m11
CV_PROP_RW double m02
CV_PROP_RW double m30
CV_PROP_RW double m21
CV_PROP_RW double m12
CV_PROP_RW double m03
central moments
CV_PROP_RW double mu20
CV_PROP_RW double mu11
CV_PROP_RW double mu02
CV_PROP_RW double mu30
CV_PROP_RW double mu21
CV_PROP_RW double mu12
CV_PROP_RW double mu03
central normalized moments
CV_PROP_RW double nu20
CV_PROP_RW double nu11
CV_PROP_RW double nu02
CV_PROP_RW double nu30
CV_PROP_RW double nu21
CV_PROP_RW double nu12
CV_PROP_RW double nu03

Detailed Description

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.

Definition at line 838 of file types.hpp.

Constructor & Destructor Documentation

Moments (  )

the default constructor

Definition at line 443 of file moments.cpp.

Moments ( double  m00,
double  m10,
double  m01,
double  m20,
double  m11,
double  m02,
double  m30,
double  m21,
double  m12,
double  m03 
)

the full constructor

Definition at line 450 of file moments.cpp.

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