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.
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.
Coordinates of the image centroid. This will be computed if it is not provided.
Maximum order of moments. Default is 3.
Central image moments. (D dimensions)
Calculate all central image moments up to a certain order.
>>> 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),See :
... moments_coords_central(coords, (0, 0))) True
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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