Calculates all of the moments up to the third order of a polygon or rasterized shape

mo = cv.moments(array)
mo = cv.moments(array, 'OptionName', optionValue, ...)

Input

• array Raster image (single-channel, 8-bit or floating-point 2D array), or a cell array of 2D points (of int32 or single type) of the form {[x,y], ...}.

Output

• mo Output moments. A structure with the following fields:
  • Spatial moments: m00, m10, m01, m20, m11, m02, m30, m21, m12, m03
  • Central moments: mu20, mu11, mu02, mu30, mu21, mu12, mu03
  • Central normalized moments: nu20, nu11, nu02, nu30, nu21, nu12, nu03

Options

• BinaryImage If it is true, all non-zero image pixels are treated as 1's. The parameter is used for images only. default false

The function computes moments, up to the 3rd order, of a vector shape or a rasterized shape. The results are returned in the moments struct mo.

The spatial moments m_ji are computed as:

 m_ji = \sum_{x,y} (array(x,y) * x^j * y^i)

The central moments mu_ji are computed as:

 mu_ji = \sum_{x,y} (array(x,y) * (x-xbar)^j * (y-ybar)^i)

where (xbar, ybar) is the mass center:

 xbar = m10/m00, ybar = m01/m00

The The normalized central moments nu_ji are computed as:

 nu_ji = mu_ji / m00^((i+j)/2+1)

NOTE: mu00 = m00, nu00 = 1, nu10 = mu10 = mu01 = mu10 = 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 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.