skimage 0.17.2

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

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)

Calculate all central image moments up to a certain order.

Examples

This example is valid syntax, but we were not able to check execution
>>> 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:

This example is valid syntax, but we were not able to check execution
>>> coords2 = np.concatenate((coords, [[17, 17]]), axis=0)
... np.round(moments_coords_central(coords2),
...  decimals=2) # doctest: +NORMALIZE_WHITESPACE 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):

This example is valid syntax, but we were not able to check execution
>>> np.allclose(moments_coords(coords),
...  moments_coords_central(coords, (0, 0))) True
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

skimage.measure._moments.moments_coords_central

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