`skimage.measure._moments:moments_coords_central`

source: /dev/scikit-image/src/skimage/measure/_moments.py :51

Signature

def moments_coords_central ( coords , center = None , order = 3 )

Summary

Calculate all central image moments up to a certain order.

Extended Summary

The following properties can be calculated from raw image moments:

Area as: M[0, 0].
Centroid as: {M[1, 0] / M[0, 0], M[0, 1] / M[0, 0]}.

Note that raw moments are neither translation, scale nor rotation invariant.

Parameters

coords : (N, D) double or uint8 array: Array of N points that describe an image of D dimensionality in Cartesian space. A tuple of coordinates as returned by np.nonzero is also accepted as input.
center : tuple of float, optional: Coordinates of the image centroid. This will be computed if it is not provided.
order : int, optional: Maximum order of moments. Default is 3.

Returns

Mc : (``order + 1``, ``order + 1``, ...) array: Central image moments. (D dimensions)

Examples

coords = np.array([[row, col]
                   for row in range(13, 17)
                   for col in range(14, 18)])
moments_coords_central(coords)

✓

As seen above, for symmetric objects, odd-order moments (columns 1 and 3, rows 1 and 3) are zero when centered on the centroid, or center of mass, of the object (the default). If we break the symmetry by adding a new point, this no longer holds:

coords2 = np.concatenate((coords, [[17, 17]]), axis=0)
np.round(moments_coords_central(coords2),
         decimals=2)  # doctest: +NORMALIZE_WHITESPACE

✓

Image moments and central image moments are equivalent (by definition) when the center is (0, 0):

np.allclose(moments_coords(coords),
            moments_coords_central(coords, (0, 0)))

⚠

Aliases

skimage.measure.moments_coords_central