# Copyright (C) 2013 Oskar Maier

# 

# This program is free software: you can redistribute it and/or modify

# it under the terms of the GNU General Public License as published by

# the Free Software Foundation, either version 3 of the License, or

# (at your option) any later version.

# 

# This program is distributed in the hope that it will be useful,

# but WITHOUT ANY WARRANTY; without even the implied warranty of

# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

# GNU General Public License for more details.

# 

# You should have received a copy of the GNU General Public License

# along with this program.  If not, see <http://www.gnu.org/licenses/>.

#

# author Oskar Maier

# version r0.1.1

# since 2014-03-13

# status Release

# build-in modules

# third-party modules

import numpy

from scipy.ndimage import _ni_support

from scipy.ndimage.morphology import distance_transform_edt, binary_erosion,\

    generate_binary_structure

from scipy.ndimage.measurements import label, find_objects

from scipy.stats import pearsonr

# own modules

# code

def dc(result, reference):

    r"""

    Dice coefficient

    Computes the Dice coefficient (also known as Sorensen index) between the binary

    objects in two images.

    The metric is defined as

    .. math::

        DC=\frac{2|A\cap B|}{|A|+|B|}

    , where :math:`A` is the first and :math:`B` the second set of samples (here: binary objects).

    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.

    Returns

    -------

    dc : float

        The Dice coefficient between the object(s) in ```result``` and the

        object(s) in ```reference```. It ranges from 0 (no overlap) to 1 (perfect overlap).

    Notes

    -----

    This is a real metric. The binary images can therefore be supplied in any order.

    """

    result = numpy.atleast_1d(result.astype(numpy.bool))

    reference = numpy.atleast_1d(reference.astype(numpy.bool))

    intersection = numpy.count_nonzero(result & reference)

    size_i1 = numpy.count_nonzero(result)

    size_i2 = numpy.count_nonzero(reference)

    try:

        dc = 2. * intersection / float(size_i1 + size_i2)

    except ZeroDivisionError:

        dc = 0.0

    return dc

def jc(result, reference):

    """

    Jaccard coefficient

    Computes the Jaccard coefficient 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.

    Returns

    -------

    jc: float

        The Jaccard coefficient between the object(s) in `result` and the

        object(s) in `reference`. It ranges from 0 (no overlap) to 1 (perfect overlap).

    Notes

    -----

    This is a real metric. The binary images can therefore be supplied in any order.

    """

    result = numpy.atleast_1d(result.astype(numpy.bool))

    reference = numpy.atleast_1d(reference.astype(numpy.bool))

    intersection = numpy.count_nonzero(result & reference)

    union = numpy.count_nonzero(result | reference)

    jc = float(intersection) / float(union)

    return jc

def precision(result, reference):

    """

    Precison.

    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.

    Returns

    -------

    precision : float

        The precision between two binary datasets, here mostly binary objects in images,

        which is defined as the fraction of retrieved instances that are relevant. The

        precision is not symmetric.

    See also

    --------

    :func:`recall`

    Notes

    -----

    Not symmetric. The inverse of the precision is :func:`recall`.

    High precision means that an algorithm returned substantially more relevant results than irrelevant.

    References

    ----------

    .. [1] http://en.wikipedia.org/wiki/Precision_and_recall

    .. [2] http://en.wikipedia.org/wiki/Confusion_matrix#Table_of_confusion

    """

    result = numpy.atleast_1d(result.astype(numpy.bool))

    reference = numpy.atleast_1d(reference.astype(numpy.bool))

    tp = numpy.count_nonzero(result & reference)

    fp = numpy.count_nonzero(result & ~reference)

    try:

        precision = tp / float(tp + fp)

    except ZeroDivisionError:

        precision = 0.0

    return precision

def recall(result, reference):

    """

    Recall.

    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.

    Returns

    -------

    recall : float

        The recall between two binary datasets, here mostly binary objects in images,

        which is defined as the fraction of relevant instances that are retrieved. The

        recall is not symmetric.

    See also

    --------

    :func:`precision`

    Notes

    -----

    Not symmetric. The inverse of the recall is :func:`precision`.

    High recall means that an algorithm returned most of the relevant results.

    References

    ----------

    .. [1] http://en.wikipedia.org/wiki/Precision_and_recall

    .. [2] http://en.wikipedia.org/wiki/Confusion_matrix#Table_of_confusion

    """

    result = numpy.atleast_1d(result.astype(numpy.bool))

    reference = numpy.atleast_1d(reference.astype(numpy.bool))

    tp = numpy.count_nonzero(result & reference)

    fn = numpy.count_nonzero(~result & reference)

    try:

        recall = tp / float(tp + fn)

    except ZeroDivisionError:

        recall = 0.0

    return recall

def sensitivity(result, reference):

    """

    Sensitivity.

    Same as :func:`recall`, see there for a detailed description.

    See also

    --------

    :func:`specificity` 

    """

    return recall(result, reference)

def specificity(result, reference):

    """

    Specificity.

    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.

    Returns

    -------

    specificity : float

        The specificity between two binary datasets, here mostly binary objects in images,

        which denotes the fraction of correctly returned negatives. The

        specificity is not symmetric.

    See also

    --------

    :func:`sensitivity`

    Notes

    -----

    Not symmetric. The completment of the specificity is :func:`sensitivity`.

    High recall means that an algorithm returned most of the irrelevant results.

    References

    ----------

    .. [1] https://en.wikipedia.org/wiki/Sensitivity_and_specificity

    .. [2] http://en.wikipedia.org/wiki/Confusion_matrix#Table_of_confusion

    """

    result = numpy.atleast_1d(result.astype(numpy.bool))

    reference = numpy.atleast_1d(reference.astype(numpy.bool))

    tn = numpy.count_nonzero(~result & ~reference)

    fp = numpy.count_nonzero(result & ~reference)

    try:

        specificity = tn / float(tn + fp)

    except ZeroDivisionError:

        specificity = 0.0

    return specificity

def true_negative_rate(result, reference):

    """

    True negative rate.

    Same as :func:`sensitivity`, see there for a detailed description.

    See also

    --------

    :func:`true_positive_rate` 

    :func:`positive_predictive_value`

    """

    return sensitivity(result, reference)

def true_positive_rate(result, reference):

    """

    True positive rate.

    Same as :func:`recall`, see there for a detailed description.

    See also

    --------

    :func:`positive_predictive_value` 

    :func:`true_negative_rate`

    """

    return recall(result, reference)

def positive_predictive_value(result, reference):

    """

    Positive predictive value.

    Same as :func:`precision`, see there for a detailed description.

    See also

    --------

    :func:`true_positive_rate`

    :func:`true_negative_rate`

    """

    return precision(result, reference)

def hd(result, reference, voxelspacing=None, connectivity=1):

    """

    Hausdorff Distance.

    Computes the (symmetric) Hausdorff Distance (HD) between the binary objects in two

    images. It is defined as the maximum surface distance between the objects.

    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`.

        Note that the connectivity influences the result in the case of the Hausdorff distance.

    Returns

    -------

    hd : float

        The symmetric Hausdorff 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:`asd`

    Notes

    -----

    This is a real metric. The binary images can therefore be supplied in any order.

    """

    hd1 = __surface_distances(result, reference, voxelspacing, connectivity).max()

    hd2 = __surface_distances(reference, result, voxelspacing, connectivity).max()

    hd = max(hd1, hd2)

    return hd

def hd95(result, reference, voxelspacing=None, connectivity=1):

    """

    95th percentile of the Hausdorff Distance.

    Computes the 95th percentile of the (symmetric) Hausdorff Distance (HD) between the binary objects in two

    images. Compared to the Hausdorff Distance, this metric is slightly more stable to small outliers and is

    commonly used in Biomedical Segmentation challenges.

    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`.

        Note that the connectivity influences the result in the case of the Hausdorff distance.

    Returns

    -------

    hd : float

        The symmetric Hausdorff 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:`hd`

    Notes

    -----

    This is a real metric. The binary images can therefore be supplied in any order.

    """

    hd1 = __surface_distances(result, reference, voxelspacing, connectivity)

    hd2 = __surface_distances(reference, result, voxelspacing, connectivity)

    hd95 = numpy.percentile(numpy.hstack((hd1, hd2)), 95)

    return hd95

def assd(result, reference, voxelspacing=None, connectivity=1):

    """

    Average symmetric surface distance.

    Computes the average symmetric 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

    -------

    assd : float

        The average symmetric 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:`asd`

    :func:`hd`

    Notes

    -----

    This is a real metric, obtained by calling and averaging

    >>> asd(result, reference)

    and

    >>> asd(reference, result)

    The binary images can therefore be supplied in any order.

    """

    assd = numpy.mean( (asd(result, reference, voxelspacing, connectivity), asd(reference, result, voxelspacing, connectivity)) )

    return assd

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 ravd(result, reference):

    """

    Relative absolute volume difference.

    Compute the relative absolute volume difference between the (joined) binary objects

    in the 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.

    Returns

    -------

    ravd : float

        The relative absolute volume difference between the object(s) in ``result``

        and the object(s) in ``reference``. This is a percentage value in the range

        :math:`[-1.0, +inf]` for which a :math:`0` denotes an ideal score.

    Raises

    ------

    RuntimeError

        If the reference object is empty.

    See also

    --------

    :func:`dc`

    :func:`precision`

    :func:`recall`

    Notes

    -----

    This is not a real metric, as it is directed. Negative values denote a smaller

    and positive values a larger volume than the reference.

    This implementation does not check, whether the two supplied arrays are of the same

    size.

    Examples

    --------

    Considering the following inputs

    >>> import numpy

    >>> arr1 = numpy.asarray([[0,1,0],[1,1,1],[0,1,0]])

    >>> arr1

    array([[0, 1, 0],

           [1, 1, 1],

           [0, 1, 0]])

    >>> arr2 = numpy.asarray([[0,1,0],[1,0,1],[0,1,0]])

    >>> arr2

    array([[0, 1, 0],

           [1, 0, 1],

           [0, 1, 0]])

    comparing `arr1` to `arr2` we get

    >>> ravd(arr1, arr2)

    -0.2

    and reversing the inputs the directivness of the metric becomes evident

    >>> ravd(arr2, arr1)

    0.25

    It is important to keep in mind that a perfect score of `0` does not mean that the

    binary objects fit exactely, as only the volumes are compared:

    >>> arr1 = numpy.asarray([1,0,0])

    >>> arr2 = numpy.asarray([0,0,1])

    >>> ravd(arr1, arr2)

    0.0

    """

    result = numpy.atleast_1d(result.astype(numpy.bool))

    reference = numpy.atleast_1d(reference.astype(numpy.bool))

    vol1 = numpy.count_nonzero(result)

    vol2 = numpy.count_nonzero(reference)

    if 0 == vol2:

        raise RuntimeError('The second supplied array does not contain any binary object.')

    return (vol1 - vol2) / float(vol2)

def volume_correlation(results, references):

    r"""

    Volume correlation.

    Computes the linear correlation in binary object volume between the

    contents of the successive binary images supplied. Measured through

    the Pearson product-moment correlation coefficient. 

    Parameters

    ----------

    results : sequence of array_like

        Ordered list of input data containing objects. Each array_like will be

        converted into binary: background where 0, object everywhere else.

    references : sequence of array_like

        Ordered list of input data containing objects. Each array_like will be

        converted into binary: background where 0, object everywhere else.

        The order must be the same as for ``results``.

    Returns

    -------

    r : float

        The correlation coefficient between -1 and 1.

    p : float

        The two-side p value.

    """

    results = numpy.atleast_2d(numpy.array(results).astype(numpy.bool))

    references = numpy.atleast_2d(numpy.array(references).astype(numpy.bool))

    results_volumes = [numpy.count_nonzero(r) for r in results]

    references_volumes = [numpy.count_nonzero(r) for r in references]

    return pearsonr(results_volumes, references_volumes) # returns (Pearson'

def volume_change_correlation(results, references):

    r"""

    Volume change correlation.

    Computes the linear correlation of change in binary object volume between

    the contents of the successive binary images supplied. Measured through

    the Pearson product-moment correlation coefficient. 

    Parameters

    ----------

    results : sequence of array_like

        Ordered list of input data containing objects. Each array_like will be

        converted into binary: background where 0, object everywhere else.

    references : sequence of array_like

        Ordered list of input data containing objects. Each array_like will be

        converted into binary: background where 0, object everywhere else.

        The order must be the same as for ``results``.

    Returns

    -------

    r : float

        The correlation coefficient between -1 and 1.

    p : float

        The two-side p value.

    """

    results = numpy.atleast_2d(numpy.array(results).astype(numpy.bool))

    references = numpy.atleast_2d(numpy.array(references).astype(numpy.bool))

    results_volumes = numpy.asarray([numpy.count_nonzero(r) for r in results])

    references_volumes = numpy.asarray([numpy.count_nonzero(r) for r in references])

    results_volumes_changes = results_volumes[1:] - results_volumes[:-1]

    references_volumes_changes = references_volumes[1:] - references_volumes[:-1] 

    return pearsonr(results_volumes_changes, references_volumes_changes) # returns (Pearson's correlation coefficient, 2-tailed p-value)

def obj_assd(result, reference, voxelspacing=None, connectivity=1):

    """

    Average symmetric surface distance.

    Computes the average symmetric surface distance (ASSD) 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 what accounts

        for a distinct binary object as well as 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

    -------

    assd : float

        The average symmetric surface distance between all mutually existing distinct

        binary object(s) in ``result`` and ``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:`obj_asd`

    Notes

    -----

    This is a real metric, obtained by calling and averaging

    >>> obj_asd(result, reference)

    and

    >>> obj_asd(reference, result)

    The binary images can therefore be supplied in any order.

    """

    assd = numpy.mean( (obj_asd(result, reference, voxelspacing, connectivity), obj_asd(reference, result, voxelspacing, connectivity)) )

    return assd

def obj_asd(result, reference, voxelspacing=None, connectivity=1):

    """

    Average surface distance between objects.

    First correspondences between distinct binary objects in reference and result are

    established. Then the average surface distance is only computed between corresponding

    objects. Correspondence is defined as unique and at least one voxel overlap.

    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 what accounts

        for a distinct binary object as well as 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 all mutually existing distinct binary

        object(s) in ``result`` and ``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:`obj_assd`

    :func:`obj_tpr`

    :func:`obj_fpr`

    Notes

    -----

    This is not a real metric, as it is directed. See `obj_assd` for a real metric of this.

    For the understanding of this metric, both the notions of connectedness and surface

    distance are essential. Please see :func:`obj_tpr` and :func:`obj_fpr` for more

    information on the first and :func:`asd` on the second.

    Examples

    --------

    >>> arr1 = numpy.asarray([[1,1,1],[1,1,1],[1,1,1]])

    >>> arr2 = numpy.asarray([[0,1,0],[0,1,0],[0,1,0]])

    >>> arr1

    array([[1, 1, 1],

           [1, 1, 1],

           [1, 1, 1]])

    >>> arr2

    array([[0, 1, 0],

           [0, 1, 0],

           [0, 1, 0]])

    >>> obj_asd(arr1, arr2)

    1.5

    >>> obj_asd(arr2, arr1)

    0.333333333333

    With the `voxelspacing` parameter, the distances between the voxels can be set for

    each dimension separately:

    >>> obj_asd(arr1, arr2, voxelspacing=(1,2))

    1.5

    >>> obj_asd(arr2, arr1, voxelspacing=(1,2))

    0.333333333333    

    More examples depicting the notion of object connectedness:

    >>> arr1 = numpy.asarray([[1,0,1],[1,0,0],[0,0,0]])

    >>> arr2 = numpy.asarray([[1,0,1],[1,0,0],[0,0,1]])

    >>> arr1

    array([[1, 0, 1],

           [1, 0, 0],

           [0, 0, 0]])

    >>> arr2

    array([[1, 0, 1],

           [1, 0, 0],

           [0, 0, 1]])

    >>> obj_asd(arr1, arr2)

    0.0

    >>> obj_asd(arr2, arr1)

    0.0

    >>> arr1 = numpy.asarray([[1,0,1],[1,0,1],[0,0,1]])

    >>> arr2 = numpy.asarray([[1,0,1],[1,0,0],[0,0,1]])

    >>> arr1

    array([[1, 0, 1],

           [1, 0, 1],

           [0, 0, 1]])

    >>> arr2

    array([[1, 0, 1],

           [1, 0, 0],

           [0, 0, 1]])

    >>> obj_asd(arr1, arr2)

    0.6

    >>> obj_asd(arr2, arr1)

    0.0

    Influence of `connectivity` parameter can be seen in the following example, where

    with the (default) connectivity of `1` the first array is considered to contain two

    objects, while with an increase connectivity of `2`, just one large object is

    detected.  

    >>> arr1 = numpy.asarray([[1,0,0],[0,1,1],[0,1,1]])

    >>> arr2 = numpy.asarray([[1,0,0],[0,0,0],[0,0,0]])

    >>> arr1

    array([[1, 0, 0],

           [0, 1, 1],

           [0, 1, 1]])

    >>> arr2

    array([[1, 0, 0],

           [0, 0, 0],

           [0, 0, 0]])

    >>> obj_asd(arr1, arr2)

    0.0

    >>> obj_asd(arr1, arr2, connectivity=2)

    1.742955328

    Note that the connectivity also influence the notion of what is considered an object

    surface voxels.

    """

    sds = list()

    labelmap1, labelmap2, _a, _b, mapping = __distinct_binary_object_correspondences(result, reference, connectivity)

    slicers1 = find_objects(labelmap1)

    slicers2 = find_objects(labelmap2)

    for lid2, lid1 in mapping.items():

        window = __combine_windows(slicers1[lid1 - 1], slicers2[lid2 - 1])

        object1 = labelmap1[window] == lid1

        object2 = labelmap2[window] == lid2

        sds.extend(__surface_distances(object1, object2, voxelspacing, connectivity))

    asd = numpy.mean(sds)

    return asd

def obj_fpr(result, reference, connectivity=1):

    """

    The false positive rate of distinct binary object detection.

    The false positive rates gives a percentage measure of how many distinct binary

    objects in the second array do not exists in the first array. A partial overlap

    (of minimum one voxel) is here considered sufficient.

    In cases where two distinct binary object in the second array overlap with a single

    distinct object in the first array, only one is considered to have been detected

    successfully and the other is added to the count of false positives.

    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.

    connectivity : int

        The neighbourhood/connectivity considered when determining what accounts

        for a distinct binary object. 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

    -------

    tpr : float

        A percentage measure of how many distinct binary objects in ``results`` have no

        corresponding binary object in ``reference``. It has the range :math:`[0, 1]`, where a :math:`0`

        denotes an ideal score.

    Raises

    ------

    RuntimeError

        If the second array is empty.

    See also

    --------

    :func:`obj_tpr`

    Notes

    -----

    This is not a real metric, as it is directed. Whatever array is considered as

    reference should be passed second. A perfect score of :math:`0` tells that there are no

    distinct binary objects in the second array that do not exists also in the reference

    array, but does not reveal anything about objects in the reference array also

    existing in the second array (use :func:`obj_tpr` for this).

    Examples

    --------

    >>> arr2 = numpy.asarray([[1,0,0],[1,0,1],[0,0,1]])

    >>> arr1 = numpy.asarray([[0,0,1],[1,0,1],[0,0,1]])

    >>> arr2

    array([[1, 0, 0],

           [1, 0, 1],

           [0, 0, 1]])

    >>> arr1

    array([[0, 0, 1],

           [1, 0, 1],

           [0, 0, 1]])

    >>> obj_fpr(arr1, arr2)

    0.0

    >>> obj_fpr(arr2, arr1)

    0.0

    Example of directedness:

    >>> arr2 = numpy.asarray([1,0,1,0,1])

    >>> arr1 = numpy.asarray([1,0,1,0,0])

    >>> obj_fpr(arr1, arr2)

    0.0

    >>> obj_fpr(arr2, arr1)

    0.3333333333333333

    Examples of multiple overlap treatment:

    >>> arr2 = numpy.asarray([1,0,1,0,1,1,1])

    >>> arr1 = numpy.asarray([1,1,1,0,1,0,1])

    >>> obj_fpr(arr1, arr2)

    0.3333333333333333

    >>> obj_fpr(arr2, arr1)

    0.3333333333333333

    >>> arr2 = numpy.asarray([1,0,1,1,1,0,1])

    >>> arr1 = numpy.asarray([1,1,1,0,1,1,1])

    >>> obj_fpr(arr1, arr2)

    0.0

    >>> obj_fpr(arr2, arr1)

    0.3333333333333333

    >>> arr2 = numpy.asarray([[1,0,1,0,0],

                              [1,0,0,0,0],

                              [1,0,1,1,1],

                              [0,0,0,0,0],

                              [1,0,1,0,0]])

    >>> arr1 = numpy.asarray([[1,1,1,0,0],

                              [0,0,0,0,0],

                              [1,1,1,0,1],

                              [0,0,0,0,0],

                              [1,1,1,0,0]])

    >>> obj_fpr(arr1, arr2)

    0.0

    >>> obj_fpr(arr2, arr1)

    0.2    

    """

    _, _, _, n_obj_reference, mapping = __distinct_binary_object_correspondences(reference, result, connectivity)

    return (n_obj_reference - len(mapping)) / float(n_obj_reference)

def obj_tpr(result, reference, connectivity=1):

    """

    The true positive rate of distinct binary object detection.

    The true positive rates gives a percentage measure of how many distinct binary

    objects in the first array also exists in the second array. A partial overlap

    (of minimum one voxel) is here considered sufficient.

    In cases where two distinct binary object in the first array overlaps with a single

    distinct object in the second array, only one is considered to have been detected

    successfully.  

    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.

    connectivity : int

        The neighbourhood/connectivity considered when determining what accounts

        for a distinct binary object. 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

    -------

    tpr : float

        A percentage measure of how many distinct binary objects in ``result`` also exists

        in ``reference``. It has the range :math:`[0, 1]`, where a :math:`1` denotes an ideal score.

    Raises

    ------

    RuntimeError

        If the reference object is empty.

    See also

    --------

    :func:`obj_fpr`

    Notes

    -----

    This is not a real metric, as it is directed. Whatever array is considered as

    reference should be passed second. A perfect score of :math:`1` tells that all distinct

    binary objects in the reference array also exist in the result array, but does not

    reveal anything about additional binary objects in the result array

    (use :func:`obj_fpr` for this).

    Examples

    --------

    >>> arr2 = numpy.asarray([[1,0,0],[1,0,1],[0,0,1]])

    >>> arr1 = numpy.asarray([[0,0,1],[1,0,1],[0,0,1]])

    >>> arr2

    array([[1, 0, 0],

           [1, 0, 1],

           [0, 0, 1]])

    >>> arr1

    array([[0, 0, 1],

           [1, 0, 1],

           [0, 0, 1]])

    >>> obj_tpr(arr1, arr2)

    1.0

    >>> obj_tpr(arr2, arr1)

    1.0

    Example of directedness:

    >>> arr2 = numpy.asarray([1,0,1,0,1])

    >>> arr1 = numpy.asarray([1,0,1,0,0])

    >>> obj_tpr(arr1, arr2)

    0.6666666666666666

    >>> obj_tpr(arr2, arr1)

    1.0

    Examples of multiple overlap treatment:

    >>> arr2 = numpy.asarray([1,0,1,0,1,1,1])

    >>> arr1 = numpy.asarray([1,1,1,0,1,0,1])

    >>> obj_tpr(arr1, arr2)

    0.6666666666666666

    >>> obj_tpr(arr2, arr1)

    0.6666666666666666

    >>> arr2 = numpy.asarray([1,0,1,1,1,0,1])

    >>> arr1 = numpy.asarray([1,1,1,0,1,1,1])

    >>> obj_tpr(arr1, arr2)

    0.6666666666666666

    >>> obj_tpr(arr2, arr1)

    1.0

    >>> arr2 = numpy.asarray([[1,0,1,0,0],

                              [1,0,0,0,0],

                              [1,0,1,1,1],

                              [0,0,0,0,0],

                              [1,0,1,0,0]])

    >>> arr1 = numpy.asarray([[1,1,1,0,0],

                              [0,0,0,0,0],

                              [1,1,1,0,1],

                              [0,0,0,0,0],

                              [1,1,1,0,0]])

    >>> obj_tpr(arr1, arr2)

    0.8

    >>> obj_tpr(arr2, arr1)

    1.0    

    """

    _, _, n_obj_result, _, mapping = __distinct_binary_object_correspondences(reference, result, connectivity)

    return len(mapping) / float(n_obj_result)

def __distinct_binary_object_correspondences(reference, result, connectivity=1):

    """

    Determines all distinct (where connectivity is defined by the connectivity parameter

    passed to scipy's `generate_binary_structure`) binary objects in both of the input

    parameters and returns a 1to1 mapping from the labelled objects in reference to the

    corresponding (whereas a one-voxel overlap suffices for correspondence) objects in

    result.