skimage2.measure.moments_coords_central#

skimage2.measure.moments_coords_central(coords, center=None, order=3)[source]#

Calculate all central image moments up to a certain order.

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.

centertuple of float, optional

Coordinates of the image centroid. This will be computed if it is not provided.

orderint, optional

Maximum order of moments. Default is 3.

Returns:
Mc(order + 1, order + 1, …) array

Central image moments. (D dimensions)

References

[1]

Johannes Kilian. Simple Image Analysis By Moments. Durham University, version 0.2, Durham, 2001.

Examples

>>> from _skimage2.measure import moments_coords
>>> coords = np.array([[row, col]
...                    for row in range(13, 17)
...                    for col in range(14, 18)])
>>> moments_coords_central(coords)
array([[16.,  0., 20.,  0.],
       [ 0.,  0.,  0.,  0.],
       [20.,  0., 25.,  0.],
       [ 0.,  0.,  0.,  0.]])

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)
array([[17.  ,  0.  , 22.12, -2.49],
       [ 0.  ,  3.53,  1.73,  7.4 ],
       [25.88,  6.02, 36.63,  8.83],
       [ 4.15, 19.17, 14.8 , 39.6 ]])

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)))
True