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scipy.ndimage.

# center_of_mass

scipy.ndimage.center_of_mass(input, labels=None, index=None)

  Calculate the center of mass of the values of an array at labels.

  Parameters:
    input ndarray

      Data from which to calculate center-of-mass. The masses can either be positive or negative.

    labels ndarray, optional

      Labels for objects in input, as generated by ndimage.label. Only used with index. Dimensions must be the same as input.

    index int or sequence of ints, optional

      Labels for which to calculate centers-of-mass. If not specified, the combined center of mass of all labels greater than zero will be calculated. Only used with labels.

  Returns:
    center_of_mass tuple, or list of tuples

      Coordinates of centers-of-mass.

  Notes

  Array API Standard Support

  `center_of_mass` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ⛔
  JAX | ⚠️ no JIT | ⛔
  Dask | ⚠️ computes graph | n/a

  > See Support for the array API standard for more information.

  Examples

      >>> import numpy as np
      >>> a = np.array(([0,0,0,0],
      ...               [0,1,1,0],
      ...               [0,1,1,0],
      ...               [0,1,1,0]))
      >>> from scipy import ndimage
      >>> ndimage.center_of_mass(a)
      (2.0, 1.5)

  Calculation of multiple objects in an image

      >>> b = np.array(([0,1,1,0],
      ...               [0,1,0,0],
      ...               [0,0,0,0],
      ...               [0,0,1,1],
      ...               [0,0,1,1]))
      >>> lbl = ndimage.label(b)[0]
      >>> ndimage.center_of_mass(b, lbl, [1,2])
      [(0.33333333333333331, 1.3333333333333333), (3.5, 2.5)]

  Negative masses are also accepted, which can occur for example when bias is removed from measured data due to random noise.

      >>> c = np.array(([-1,0,0,0],
      ...               [0,-1,-1,0],
      ...               [0,1,-1,0],
      ...               [0,1,1,0]))
      >>> ndimage.center_of_mass(c)
      (-4.0, 1.0)

  If there are division by zero issues, the function does not raise an error but rather issues a RuntimeWarning before returning inf and/or NaN.

      >>> d = np.array([-1, 1])
      >>> ndimage.center_of_mass(d)
      (inf,)