scipy.ndimage.morphology.distance_transform_edt

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

Exact euclidean distance transform.

In addition to the distance transform, the feature transform can be calculated. In this case the index of the closest background element is returned along the first axis of the result.

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 int, or sequence of same, 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 return distance matrix. At least one of return_distances/return_indices must be True. Default is True.

return_indices : bool, optional

Whether to return indices matrix. Default is False.

distance : ndarray, optional

Used for output of distance array, must be of type float64.

indices : ndarray, optional

Used for output of indices, must be of type int32.

Returns :

distance_transform_edt : ndarray or list of ndarrays

Either distance matrix, index matrix, or a list of the two, depending on return_x flags and distance and indices input parameters.

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

>>> 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]))
>>> from scipy import ndimage
>>> 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.rank(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]]])