# scipy.ndimage.distance_transform_edt

scipy.ndimage.distance_transform_edt(input, sampling=None, return_distances=True, return_indices=False, distances=None, indices=None)

  Exact Euclidean distance transform.

  This function calculates the distance transform of the input, by replacing each foreground (non-zero) element, with its shortest distance to the background (any zero-valued element).

  In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element to each foreground element is returned in a separate array.

  Parameters:
    input array_like

      Input data to transform. Can be any type but will be converted into binary: 1 wherever input equates to True, 0 elsewhere.

    sampling float, or sequence of float, optional

      Spacing of elements along each dimension. If a sequence, must be of length equal to the input rank; if a single number, this is used for all axes. If not specified, a grid spacing of unity is implied.

    return_distances bool, optional

      Whether to calculate the distance transform. Default is True.

    return_indices bool, optional

      Whether to calculate the feature transform. Default is False.

    distances float64 ndarray, optional

      An output array to store the calculated distance transform, instead of returning it. return_distances must be True. It must be the same shape as input.

    indices int32 ndarray, optional

      An output array to store the calculated feature transform, instead of returning it. return_indicies must be True. Its shape must be (input.ndim,) + input.shape.

  Returns:
    distances float64 ndarray, optional

      The calculated distance transform. Returned only when return_distances is True and distances is not supplied. It will have the same shape as the input array.

    indices int32 ndarray, optional

      The calculated feature transform. It has an input-shaped array for each dimension of the input. See example below. Returned only when return_indices is True and indices is not supplied.

  Notes

  The Euclidean distance transform gives values of the Euclidean distance:

                    n
      y_i = sqrt(sum (x[i]-b[i])**2)
                    i

  where b[i] is the background point (value 0) with the smallest Euclidean distance to input points x[i], and n is the number of dimensions.

  Examples

      >>> from scipy import ndimage
      >>> import numpy as np
      >>> a = np.array(([0,1,1,1,1],
      ...               [0,0,1,1,1],
      ...               [0,1,1,1,1],
      ...               [0,1,1,1,0],
      ...               [0,1,1,0,0]))
      >>> ndimage.distance_transform_edt(a)
      array([[ 0.    ,  1.    ,  1.4142,  2.2361,  3.    ],
             [ 0.    ,  0.    ,  1.    ,  2.    ,  2.    ],
             [ 0.    ,  1.    ,  1.4142,  1.4142,  1.    ],
             [ 0.    ,  1.    ,  1.4142,  1.    ,  0.    ],
             [ 0.    ,  1.    ,  1.    ,  0.    ,  0.    ]])

  With a sampling of 2 units along x, 1 along y:

      >>> ndimage.distance_transform_edt(a, sampling=[2,1])
      array([[ 0.    ,  1.    ,  2.    ,  2.8284,  3.6056],
             [ 0.    ,  0.    ,  1.    ,  2.    ,  3.    ],
             [ 0.    ,  1.    ,  2.    ,  2.2361,  2.    ],
             [ 0.    ,  1.    ,  2.    ,  1.    ,  0.    ],
             [ 0.    ,  1.    ,  1.    ,  0.    ,  0.    ]])

  Asking for indices as well:

      >>> edt, inds = ndimage.distance_transform_edt(a, return_indices=True)
      >>> inds
      array([[[0, 0, 1, 1, 3],
              [1, 1, 1, 1, 3],
              [2, 2, 1, 3, 3],
              [3, 3, 4, 4, 3],
              [4, 4, 4, 4, 4]],
             [[0, 0, 1, 1, 4],
              [0, 1, 1, 1, 4],
              [0, 0, 1, 4, 4],
              [0, 0, 3, 3, 4],
              [0, 0, 3, 3, 4]]])

  With arrays provided for inplace outputs:

      >>> indices = np.zeros(((np.ndim(a),) + a.shape), dtype=np.int32)
      >>> ndimage.distance_transform_edt(a, return_indices=True, indices=indices)
      array([[ 0.    ,  1.    ,  1.4142,  2.2361,  3.    ],
             [ 0.    ,  0.    ,  1.    ,  2.    ,  2.    ],
             [ 0.    ,  1.    ,  1.4142,  1.4142,  1.    ],
             [ 0.    ,  1.    ,  1.4142,  1.    ,  0.    ],
             [ 0.    ,  1.    ,  1.    ,  0.    ,  0.    ]])
      >>> indices
      array([[[0, 0, 1, 1, 3],
              [1, 1, 1, 1, 3],
              [2, 2, 1, 3, 3],
              [3, 3, 4, 4, 3],
              [4, 4, 4, 4, 4]],
             [[0, 0, 1, 1, 4],
              [0, 1, 1, 1, 4],
              [0, 0, 1, 4, 4],
              [0, 0, 3, 3, 4],
              [0, 0, 3, 3, 4]]])