def asd(result, reference, voxelspacing=None, connectivity=1):
    """
    Average surface distance metric.
    
    Computes the average surface distance (ASD) between the binary objects in two images.
    
    Parameters
    ----------
    result : array_like
        Input data containing objects. Can be any type but will be converted
        into binary: background where 0, object everywhere else.
    reference : array_like
        Input data containing objects. Can be any type but will be converted
        into binary: background where 0, object everywhere else.
    voxelspacing : float or sequence of floats, optional
        The voxelspacing in a distance unit i.e. 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.
    connectivity : int
        The neighbourhood/connectivity considered when determining the surface
        of the binary objects. This value is passed to
        `scipy.ndimage.morphology.generate_binary_structure` and should usually be :math:`> 1`.
        The decision on the connectivity is important, as it can influence the results
        strongly. If in doubt, leave it as it is.
    
    Returns
    -------
    asd : float
        The average surface distance between the object(s) in ``result`` and the
        object(s) in ``reference``. The distance unit is the same as for the spacing
        of elements along each dimension, which is usually given in mm.
        
    See also
    --------
    :func:`assd`
    :func:`hd`
    
    
    Notes
    -----
    This is not a real metric, as it is directed. See `assd` for a real metric of this.
    
    The method is implemented making use of distance images and simple binary morphology
    to achieve high computational speed.
    
    Examples
    --------
    The `connectivity` determines what pixels/voxels are considered the surface of a
    binary object. Take the following binary image showing a cross
    
    >>> from scipy.ndimage.morphology import generate_binary_structure
    >>> cross = generate_binary_structure(2, 1)
    array([[0, 1, 0],
           [1, 1, 1],
           [0, 1, 0]])
           
    With `connectivity` set to `1` a 4-neighbourhood is considered when determining the
    object surface, resulting in the surface
    
    .. code-block:: python
    
        array([[0, 1, 0],
               [1, 0, 1],
               [0, 1, 0]])
           
    Changing `connectivity` to `2`, a 8-neighbourhood is considered and we get:
    
    .. code-block:: python
    
        array([[0, 1, 0],
               [1, 1, 1],
               [0, 1, 0]])
           
    , as a diagonal connection does no longer qualifies as valid object surface.
    
    This influences the  results `asd` returns. Imagine we want to compute the surface
    distance of our cross to a cube-like object:
    
    >>> cube = generate_binary_structure(2, 1)
    array([[1, 1, 1],
           [1, 1, 1],
           [1, 1, 1]])
           
    , which surface is, independent of the `connectivity` value set, always
    
    .. code-block:: python
    
        array([[1, 1, 1],
               [1, 0, 1],
               [1, 1, 1]])
           
    Using a `connectivity` of `1` we get
    
    >>> asd(cross, cube, connectivity=1)
    0.0
    
    while a value of `2` returns us
    
    >>> asd(cross, cube, connectivity=2)
    0.20000000000000001
    
    due to the center of the cross being considered surface as well.
    
    """
    sds = __surface_distances(result, reference, voxelspacing, connectivity)
    asd = sds.mean()
    return asd
def asd ( result , reference , voxelspacing = None , connectivity = 1 ) : sds = __surface_distances ( result , reference , voxelspacing , connectivity ) asd = sds . mean ( ) return asd
Average surface distance metric.
    
    Computes the average surface distance (ASD) between the binary objects in two images.
    
    Parameters
    ----------
    result : array_like
        Input data containing objects. Can be any type but will be converted
        into binary: background where 0, object everywhere else.
    reference : array_like
        Input data containing objects. Can be any type but will be converted
        into binary: background where 0, object everywhere else.
    voxelspacing : float or sequence of floats, optional
        The voxelspacing in a distance unit i.e. 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.
    connectivity : int
        The neighbourhood/connectivity considered when determining the surface
        of the binary objects. This value is passed to
        `scipy.ndimage.morphology.generate_binary_structure` and should usually be :math:`> 1`.
        The decision on the connectivity is important, as it can influence the results
        strongly. If in doubt, leave it as it is.
    
    Returns
    -------
    asd : float
        The average surface distance between the object(s) in ``result`` and the
        object(s) in ``reference``. The distance unit is the same as for the spacing
        of elements along each dimension, which is usually given in mm.
        
    See also
    --------
    :func:`assd`
    :func:`hd`
    
    
    Notes
    -----
    This is not a real metric, as it is directed. See `assd` for a real metric of this.
    
    The method is implemented making use of distance images and simple binary morphology
    to achieve high computational speed.
    
    Examples
    --------
    The `connectivity` determines what pixels/voxels are considered the surface of a
    binary object. Take the following binary image showing a cross
    
    >>> from scipy.ndimage.morphology import generate_binary_structure
    >>> cross = generate_binary_structure(2, 1)
    array([[0, 1, 0],
           [1, 1, 1],
           [0, 1, 0]])
           
    With `connectivity` set to `1` a 4-neighbourhood is considered when determining the
    object surface, resulting in the surface
    
    .. code-block:: python
    
        array([[0, 1, 0],
               [1, 0, 1],
               [0, 1, 0]])
           
    Changing `connectivity` to `2`, a 8-neighbourhood is considered and we get:
    
    .. code-block:: python
    
        array([[0, 1, 0],
               [1, 1, 1],
               [0, 1, 0]])
           
    , as a diagonal connection does no longer qualifies as valid object surface.
    
    This influences the  results `asd` returns. Imagine we want to compute the surface
    distance of our cross to a cube-like object:
    
    >>> cube = generate_binary_structure(2, 1)
    array([[1, 1, 1],
           [1, 1, 1],
           [1, 1, 1]])
           
    , which surface is, independent of the `connectivity` value set, always
    
    .. code-block:: python
    
        array([[1, 1, 1],
               [1, 0, 1],
               [1, 1, 1]])
           
    Using a `connectivity` of `1` we get
    
    >>> asd(cross, cube, connectivity=1)
    0.0
    
    while a value of `2` returns us
    
    >>> asd(cross, cube, connectivity=2)
    0.20000000000000001
    
    due to the center of the cross being considered surface as well.