filters.py

# Copyright (C) 2003-2005 Peter J. Verveer
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
#    notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above
#    copyright notice, this list of conditions and the following
#    disclaimer in the documentation and/or other materials provided
#    with the distribution.
#
# 3. The name of the author may not be used to endorse or promote
#    products derived from this software without specific prior
#    written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

from __future__ import division, print_function, absolute_import

import math
import numpy
from . import _ni_support
from . import _nd_image
from scipy.misc import doccer
from scipy._lib._version import NumpyVersion

__all__ = ['correlate1d', 'convolve1d', 'gaussian_filter1d', 'gaussian_filter',
           'prewitt', 'sobel', 'generic_laplace', 'laplace',
           'gaussian_laplace', 'generic_gradient_magnitude',
           'gaussian_gradient_magnitude', 'correlate', 'convolve',
           'uniform_filter1d', 'uniform_filter', 'minimum_filter1d',
           'maximum_filter1d', 'minimum_filter', 'maximum_filter',
           'rank_filter', 'median_filter', 'percentile_filter',
           'generic_filter1d', 'generic_filter']


_input_doc = \
"""input : array_like
    Input array to filter."""
_axis_doc = \
"""axis : int, optional
    The axis of `input` along which to calculate. Default is -1."""
_output_doc = \
"""output : array, optional
    The `output` parameter passes an array in which to store the
    filter output."""
_size_foot_doc = \
"""size : scalar or tuple, optional
    See footprint, below
footprint : array, optional
    Either `size` or `footprint` must be defined.  `size` gives
    the shape that is taken from the input array, at every element
    position, to define the input to the filter function.
    `footprint` is a boolean array that specifies (implicitly) a
    shape, but also which of the elements within this shape will get
    passed to the filter function.  Thus ``size=(n,m)`` is equivalent
    to ``footprint=np.ones((n,m))``.  We adjust `size` to the number
    of dimensions of the input array, so that, if the input array is
    shape (10,10,10), and `size` is 2, then the actual size used is
    (2,2,2).
"""
_mode_doc = \
"""mode : {'reflect', 'constant', 'nearest', 'mirror', 'wrap'}, optional
    The `mode` parameter determines how the array borders are
    handled, where `cval` is the value when mode is equal to
    'constant'. Default is 'reflect'"""
_cval_doc = \
"""cval : scalar, optional
    Value to fill past edges of input if `mode` is 'constant'. Default
    is 0.0"""
_origin_doc = \
"""origin : scalar, optional
    The `origin` parameter controls the placement of the filter.
    Default 0.0."""
_extra_arguments_doc = \
"""extra_arguments : sequence, optional
    Sequence of extra positional arguments to pass to passed function"""
_extra_keywords_doc = \
"""extra_keywords : dict, optional
    dict of extra keyword arguments to pass to passed function"""

docdict = {
    'input': _input_doc,
    'axis': _axis_doc,
    'output': _output_doc,
    'size_foot': _size_foot_doc,
    'mode': _mode_doc,
    'cval': _cval_doc,
    'origin': _origin_doc,
    'extra_arguments': _extra_arguments_doc,
    'extra_keywords': _extra_keywords_doc,
    }

docfiller = doccer.filldoc(docdict)


@docfiller
def correlate1d(input, weights, axis=-1, output=None, mode="reflect",
                cval=0.0, origin=0):
    """Calculate a one-dimensional correlation along the given axis.

    The lines of the array along the given axis are correlated with the
    given weights.

    Parameters
    ----------
    %(input)s
    weights : array
        One-dimensional sequence of numbers.
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    """
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    output, return_value = _ni_support._get_output(output, input)
    weights = numpy.asarray(weights, dtype=numpy.float64)
    if weights.ndim != 1 or weights.shape[0] < 1:
        raise RuntimeError('no filter weights given')
    if not weights.flags.contiguous:
        weights = weights.copy()
    axis = _ni_support._check_axis(axis, input.ndim)
    if (len(weights) // 2 + origin < 0) or (len(weights) // 2 +
                                            origin > len(weights)):
        raise ValueError('invalid origin')
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.correlate1d(input, weights, axis, output, mode, cval,
                          origin)
    return return_value


@docfiller
def convolve1d(input, weights, axis=-1, output=None, mode="reflect",
               cval=0.0, origin=0):
    """Calculate a one-dimensional convolution along the given axis.

    The lines of the array along the given axis are convolved with the
    given weights.

    Parameters
    ----------
    %(input)s
    weights : ndarray
        One-dimensional sequence of numbers.
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s

    Returns
    -------
    convolve1d : ndarray
        Convolved array with same shape as input

    """
    weights = weights[::-1]
    origin = -origin
    if not len(weights) & 1:
        origin -= 1
    return correlate1d(input, weights, axis, output, mode, cval, origin)


@docfiller
def gaussian_filter1d(input, sigma, axis=-1, order=0, output=None,
                      mode="reflect", cval=0.0, truncate=4.0):
    """One-dimensional Gaussian filter.

    Parameters
    ----------
    %(input)s
    sigma : scalar
        standard deviation for Gaussian kernel
    %(axis)s
    order : {0, 1, 2, 3}, optional
        An order of 0 corresponds to convolution with a Gaussian
        kernel. An order of 1, 2, or 3 corresponds to convolution with
        the first, second or third derivatives of a Gaussian. Higher
        order derivatives are not implemented
    %(output)s
    %(mode)s
    %(cval)s
    truncate : float, optional
        Truncate the filter at this many standard deviations.
        Default is 4.0.

    Returns
    -------
    gaussian_filter1d : ndarray

    """
    if order not in range(4):
        raise ValueError('Order outside 0..3 not implemented')
    sd = float(sigma)
    # make the radius of the filter equal to truncate standard deviations
    lw = int(truncate * sd + 0.5)
    weights = [0.0] * (2 * lw + 1)
    weights[lw] = 1.0
    sum = 1.0
    sd = sd * sd
    # calculate the kernel:
    for ii in range(1, lw + 1):
        tmp = math.exp(-0.5 * float(ii * ii) / sd)
        weights[lw + ii] = tmp
        weights[lw - ii] = tmp
        sum += 2.0 * tmp
    for ii in range(2 * lw + 1):
        weights[ii] /= sum
    # implement first, second and third order derivatives:
    if order == 1:  # first derivative
        weights[lw] = 0.0
        for ii in range(1, lw + 1):
            x = float(ii)
            tmp = -x / sd * weights[lw + ii]
            weights[lw + ii] = -tmp
            weights[lw - ii] = tmp
    elif order == 2:  # second derivative
        weights[lw] *= -1.0 / sd
        for ii in range(1, lw + 1):
            x = float(ii)
            tmp = (x * x / sd - 1.0) * weights[lw + ii] / sd
            weights[lw + ii] = tmp
            weights[lw - ii] = tmp
    elif order == 3:  # third derivative
        weights[lw] = 0.0
        sd2 = sd * sd
        for ii in range(1, lw + 1):
            x = float(ii)
            tmp = (3.0 - x * x / sd) * x * weights[lw + ii] / sd2
            weights[lw + ii] = -tmp
            weights[lw - ii] = tmp
    return correlate1d(input, weights, axis, output, mode, cval, 0)


@docfiller
def gaussian_filter(input, sigma, order=0, output=None,
                  mode="reflect", cval=0.0, truncate=4.0):
    """Multidimensional Gaussian filter.

    Parameters
    ----------
    %(input)s
    sigma : scalar or sequence of scalars
        Standard deviation for Gaussian kernel. The standard
        deviations of the Gaussian filter are given for each axis as a
        sequence, or as a single number, in which case it is equal for
        all axes.
    order : {0, 1, 2, 3} or sequence from same set, optional
        The order of the filter along each axis is given as a sequence
        of integers, or as a single number.  An order of 0 corresponds
        to convolution with a Gaussian kernel. An order of 1, 2, or 3
        corresponds to convolution with the first, second or third
        derivatives of a Gaussian. Higher order derivatives are not
        implemented
    %(output)s
    %(mode)s
    %(cval)s
    truncate : float
        Truncate the filter at this many standard deviations.
        Default is 4.0.

    Returns
    -------
    gaussian_filter : ndarray
        Returned array of same shape as `input`.

    Notes
    -----
    The multidimensional filter is implemented as a sequence of
    one-dimensional convolution filters. The intermediate arrays are
    stored in the same data type as the output. Therefore, for output
    types with a limited precision, the results may be imprecise
    because intermediate results may be stored with insufficient
    precision.

    Examples
    --------
    >>> from scipy.ndimage import gaussian_filter
    >>> a = np.arange(50, step=2).reshape((5,5))
    >>> a
    array([[ 0,  2,  4,  6,  8],
           [10, 12, 14, 16, 18],
           [20, 22, 24, 26, 28],
           [30, 32, 34, 36, 38],
           [40, 42, 44, 46, 48]])
    >>> gaussian_filter(a, sigma=1)
    array([[ 4,  6,  8,  9, 11],
           [10, 12, 14, 15, 17],
           [20, 22, 24, 25, 27],
           [29, 31, 33, 34, 36],
           [35, 37, 39, 40, 42]])

    """
    input = numpy.asarray(input)
    output, return_value = _ni_support._get_output(output, input)
    orders = _ni_support._normalize_sequence(order, input.ndim)
    if not set(orders).issubset(set(range(4))):
        raise ValueError('Order outside 0..4 not implemented')
    sigmas = _ni_support._normalize_sequence(sigma, input.ndim)
    axes = list(range(input.ndim))
    axes = [(axes[ii], sigmas[ii], orders[ii])
                        for ii in range(len(axes)) if sigmas[ii] > 1e-15]
    if len(axes) > 0:
        for axis, sigma, order in axes:
            gaussian_filter1d(input, sigma, axis, order, output,
                              mode, cval, truncate)
            input = output
    else:
        output[...] = input[...]
    return return_value


@docfiller
def prewitt(input, axis=-1, output=None, mode="reflect", cval=0.0):
    """Calculate a Prewitt filter.

    Parameters
    ----------
    %(input)s
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s

    Examples
    --------
    >>> from scipy import ndimage, misc
    >>> import matplotlib.pyplot as plt
    >>> ascent = misc.ascent()
    >>> result = ndimage.prewitt(ascent)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> plt.imshow(result)
    """
    input = numpy.asarray(input)
    axis = _ni_support._check_axis(axis, input.ndim)
    output, return_value = _ni_support._get_output(output, input)
    correlate1d(input, [-1, 0, 1], axis, output, mode, cval, 0)
    axes = [ii for ii in range(input.ndim) if ii != axis]
    for ii in axes:
        correlate1d(output, [1, 1, 1], ii, output, mode, cval, 0,)
    return return_value


@docfiller
def sobel(input, axis=-1, output=None, mode="reflect", cval=0.0):
    """Calculate a Sobel filter.

    Parameters
    ----------
    %(input)s
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s

    Examples
    --------
    >>> from scipy import ndimage, misc
    >>> import matplotlib.pyplot as plt
    >>> ascent = misc.ascent()
    >>> result = ndimage.sobel(ascent)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> plt.imshow(result)
    """
    input = numpy.asarray(input)
    axis = _ni_support._check_axis(axis, input.ndim)
    output, return_value = _ni_support._get_output(output, input)
    correlate1d(input, [-1, 0, 1], axis, output, mode, cval, 0)
    axes = [ii for ii in range(input.ndim) if ii != axis]
    for ii in axes:
        correlate1d(output, [1, 2, 1], ii, output, mode, cval, 0)
    return return_value


@docfiller
def generic_laplace(input, derivative2, output=None, mode="reflect",
                    cval=0.0,
                    extra_arguments=(),
                    extra_keywords = None):
    """N-dimensional Laplace filter using a provided second derivative function

    Parameters
    ----------
    %(input)s
    derivative2 : callable
        Callable with the following signature::

            derivative2(input, axis, output, mode, cval,
                        *extra_arguments, **extra_keywords)

        See `extra_arguments`, `extra_keywords` below.
    %(output)s
    %(mode)s
    %(cval)s
    %(extra_keywords)s
    %(extra_arguments)s
    """
    if extra_keywords is None:
        extra_keywords = {}
    input = numpy.asarray(input)
    output, return_value = _ni_support._get_output(output, input)
    axes = list(range(input.ndim))
    if len(axes) > 0:
        derivative2(input, axes[0], output, mode, cval,
                    *extra_arguments, **extra_keywords)
        for ii in range(1, len(axes)):
            tmp = derivative2(input, axes[ii], output.dtype, mode, cval,
                              *extra_arguments, **extra_keywords)
            output += tmp
    else:
        output[...] = input[...]
    return return_value


@docfiller
def laplace(input, output=None, mode="reflect", cval=0.0):
    """N-dimensional Laplace filter based on approximate second derivatives.

    Parameters
    ----------
    %(input)s
    %(output)s
    %(mode)s
    %(cval)s

    Examples
    --------
    >>> from scipy import ndimage, misc
    >>> import matplotlib.pyplot as plt
    >>> ascent = misc.ascent()
    >>> result = ndimage.laplace(ascent)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> plt.imshow(result)
    """
    def derivative2(input, axis, output, mode, cval):
        return correlate1d(input, [1, -2, 1], axis, output, mode, cval, 0)
    return generic_laplace(input, derivative2, output, mode, cval)


@docfiller
def gaussian_laplace(input, sigma, output=None, mode="reflect",
                     cval=0.0, **kwargs):
    """Multidimensional Laplace filter using gaussian second derivatives.

    Parameters
    ----------
    %(input)s
    sigma : scalar or sequence of scalars
        The standard deviations of the Gaussian filter are given for
        each axis as a sequence, or as a single number, in which case
        it is equal for all axes.
    %(output)s
    %(mode)s
    %(cval)s
    Extra keyword arguments will be passed to gaussian_filter().

    Examples
    --------
    >>> from scipy import ndimage, misc
    >>> import matplotlib.pyplot as plt
    >>> ascent = misc.ascent()

    >>> fig = plt.figure()
    >>> plt.gray()  # show the filtered result in grayscale
    >>> ax1 = fig.add_subplot(121)  # left side
    >>> ax2 = fig.add_subplot(122)  # right side

    >>> result = ndimage.gaussian_laplace(ascent, sigma=1)
    >>> ax1.imshow(result)

    >>> result = ndimage.gaussian_laplace(ascent, sigma=3)
    >>> ax2.imshow(result)
    >>> plt.show()
    """
    input = numpy.asarray(input)

    def derivative2(input, axis, output, mode, cval, sigma, **kwargs):
        order = [0] * input.ndim
        order[axis] = 2
        return gaussian_filter(input, sigma, order, output, mode, cval,
                               **kwargs)

    return generic_laplace(input, derivative2, output, mode, cval,
                           extra_arguments=(sigma,),
                           extra_keywords=kwargs)


@docfiller
def generic_gradient_magnitude(input, derivative, output=None,
                mode="reflect", cval=0.0,
                extra_arguments=(), extra_keywords = None):
    """Gradient magnitude using a provided gradient function.

    Parameters
    ----------
    %(input)s
    derivative : callable
        Callable with the following signature::

            derivative(input, axis, output, mode, cval,
                       *extra_arguments, **extra_keywords)

        See `extra_arguments`, `extra_keywords` below.
        `derivative` can assume that `input` and `output` are ndarrays.
        Note that the output from `derivative` is modified inplace;
        be careful to copy important inputs before returning them.
    %(output)s
    %(mode)s
    %(cval)s
    %(extra_keywords)s
    %(extra_arguments)s
    """
    if extra_keywords is None:
        extra_keywords = {}
    input = numpy.asarray(input)
    output, return_value = _ni_support._get_output(output, input)
    axes = list(range(input.ndim))
    if len(axes) > 0:
        derivative(input, axes[0], output, mode, cval,
                   *extra_arguments, **extra_keywords)
        numpy.multiply(output, output, output)
        for ii in range(1, len(axes)):
            tmp = derivative(input, axes[ii], output.dtype, mode, cval,
                             *extra_arguments, **extra_keywords)
            numpy.multiply(tmp, tmp, tmp)
            output += tmp
        # This allows the sqrt to work with a different default casting
        numpy.sqrt(output, output, casting='unsafe')
    else:
        output[...] = input[...]
    return return_value


@docfiller
def gaussian_gradient_magnitude(input, sigma, output=None,
                mode="reflect", cval=0.0, **kwargs):
    """Multidimensional gradient magnitude using Gaussian derivatives.

    Parameters
    ----------
    %(input)s
    sigma : scalar or sequence of scalars
        The standard deviations of the Gaussian filter are given for
        each axis as a sequence, or as a single number, in which case
        it is equal for all axes..
    %(output)s
    %(mode)s
    %(cval)s
    Extra keyword arguments will be passed to gaussian_filter().
    """
    input = numpy.asarray(input)

    def derivative(input, axis, output, mode, cval, sigma, **kwargs):
        order = [0] * input.ndim
        order[axis] = 1
        return gaussian_filter(input, sigma, order, output, mode,
                               cval, **kwargs)

    return generic_gradient_magnitude(input, derivative, output, mode,
                                      cval, extra_arguments=(sigma,),
                                      extra_keywords=kwargs)


def _correlate_or_convolve(input, weights, output, mode, cval, origin,
                           convolution):
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    origins = _ni_support._normalize_sequence(origin, input.ndim)
    weights = numpy.asarray(weights, dtype=numpy.float64)
    wshape = [ii for ii in weights.shape if ii > 0]
    if len(wshape) != input.ndim:
        raise RuntimeError('filter weights array has incorrect shape.')
    if convolution:
        weights = weights[tuple([slice(None, None, -1)] * weights.ndim)]
        for ii in range(len(origins)):
            origins[ii] = -origins[ii]
            if not weights.shape[ii] & 1:
                origins[ii] -= 1
    for origin, lenw in zip(origins, wshape):
        if (lenw // 2 + origin < 0) or (lenw // 2 + origin > lenw):
            raise ValueError('invalid origin')
    if not weights.flags.contiguous:
        weights = weights.copy()
    output, return_value = _ni_support._get_output(output, input)
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.correlate(input, weights, output, mode, cval, origins)
    return return_value


@docfiller
def correlate(input, weights, output=None, mode='reflect', cval=0.0,
              origin=0):
    """
    Multi-dimensional correlation.

    The array is correlated with the given kernel.

    Parameters
    ----------
    input : array-like
        input array to filter
    weights : ndarray
        array of weights, same number of dimensions as input
    output : array, optional
        The ``output`` parameter passes an array in which to store the
        filter output.
    mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
        The ``mode`` parameter determines how the array borders are
        handled, where ``cval`` is the value when mode is equal to
        'constant'. Default is 'reflect'
    cval : scalar, optional
        Value to fill past edges of input if ``mode`` is 'constant'. Default
        is 0.0
    origin : scalar, optional
        The ``origin`` parameter controls the placement of the filter.
        Default 0

    See Also
    --------
    convolve : Convolve an image with a kernel.
    """
    return _correlate_or_convolve(input, weights, output, mode, cval,
                                  origin, False)


@docfiller
def convolve(input, weights, output=None, mode='reflect', cval=0.0,
             origin=0):
    """
    Multidimensional convolution.

    The array is convolved with the given kernel.

    Parameters
    ----------
    input : array_like
        Input array to filter.
    weights : array_like
        Array of weights, same number of dimensions as input
    output : ndarray, optional
        The `output` parameter passes an array in which to store the
        filter output.
    mode : {'reflect','constant','nearest','mirror', 'wrap'}, optional
        the `mode` parameter determines how the array borders are
        handled. For 'constant' mode, values beyond borders are set to be
        `cval`. Default is 'reflect'.
    cval : scalar, optional
        Value to fill past edges of input if `mode` is 'constant'. Default
        is 0.0
    origin : array_like, optional
        The `origin` parameter controls the placement of the filter, 
        relative to the centre of the current element of the input.  
        Default of 0 is equivalent to ``(0,)*input.ndim``.

    Returns
    -------
    result : ndarray
        The result of convolution of `input` with `weights`.

    See Also
    --------
    correlate : Correlate an image with a kernel.

    Notes
    -----
    Each value in result is :math:`C_i = \\sum_j{I_{i+k-j} W_j}`, where
    W is the `weights` kernel,
    j is the n-D spatial index over :math:`W`,
    I is the `input` and k is the coordinate of the center of
    W, specified by `origin` in the input parameters.

    Examples
    --------
    Perhaps the simplest case to understand is ``mode='constant', cval=0.0``,
    because in this case borders (i.e. where the `weights` kernel, centered
    on any one value, extends beyond an edge of `input`.

    >>> a = np.array([[1, 2, 0, 0],
    ...               [5, 3, 0, 4],
    ...               [0, 0, 0, 7],
    ...               [9, 3, 0, 0]])
    >>> k = np.array([[1,1,1],[1,1,0],[1,0,0]])
    >>> from scipy import ndimage
    >>> ndimage.convolve(a, k, mode='constant', cval=0.0)
    array([[11, 10,  7,  4],
           [10,  3, 11, 11],
           [15, 12, 14,  7],
           [12,  3,  7,  0]])

    Setting ``cval=1.0`` is equivalent to padding the outer edge of `input`
    with 1.0's (and then extracting only the original region of the result).

    >>> ndimage.convolve(a, k, mode='constant', cval=1.0)
    array([[13, 11,  8,  7],
           [11,  3, 11, 14],
           [16, 12, 14, 10],
           [15,  6, 10,  5]])

    With ``mode='reflect'`` (the default), outer values are reflected at the
    edge of `input` to fill in missing values.

    >>> b = np.array([[2, 0, 0],
    ...               [1, 0, 0],
    ...               [0, 0, 0]])
    >>> k = np.array([[0,1,0], [0,1,0], [0,1,0]])
    >>> ndimage.convolve(b, k, mode='reflect')
    array([[5, 0, 0],
           [3, 0, 0],
           [1, 0, 0]])

    This includes diagonally at the corners.

    >>> k = np.array([[1,0,0],[0,1,0],[0,0,1]])
    >>> ndimage.convolve(b, k)
    array([[4, 2, 0],
           [3, 2, 0],
           [1, 1, 0]])

    With ``mode='nearest'``, the single nearest value in to an edge in
    `input` is repeated as many times as needed to match the overlapping
    `weights`.

    >>> c = np.array([[2, 0, 1],
    ...               [1, 0, 0],
    ...               [0, 0, 0]])
    >>> k = np.array([[0, 1, 0],
    ...               [0, 1, 0],
    ...               [0, 1, 0],
    ...               [0, 1, 0],
    ...               [0, 1, 0]])
    >>> ndimage.convolve(c, k, mode='nearest')
    array([[7, 0, 3],
           [5, 0, 2],
           [3, 0, 1]])

    """
    return _correlate_or_convolve(input, weights, output, mode, cval,
                                  origin, True)


@docfiller
def uniform_filter1d(input, size, axis=-1, output=None,
                     mode="reflect", cval=0.0, origin=0):
    """Calculate a one-dimensional uniform filter along the given axis.

    The lines of the array along the given axis are filtered with a
    uniform filter of given size.

    Parameters
    ----------
    %(input)s
    size : int
        length of uniform filter
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    """
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    axis = _ni_support._check_axis(axis, input.ndim)
    if size < 1:
        raise RuntimeError('incorrect filter size')
    output, return_value = _ni_support._get_output(output, input)
    if (size // 2 + origin < 0) or (size // 2 + origin >= size):
        raise ValueError('invalid origin')
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.uniform_filter1d(input, size, axis, output, mode, cval,
                               origin)
    return return_value


@docfiller
def uniform_filter(input, size=3, output=None, mode="reflect",
                   cval=0.0, origin=0):
    """Multi-dimensional uniform filter.

    Parameters
    ----------
    %(input)s
    size : int or sequence of ints, optional
        The sizes of the uniform filter are given for each axis as a
        sequence, or as a single number, in which case the size is
        equal for all axes.
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s

    Notes
    -----
    The multi-dimensional filter is implemented as a sequence of
    one-dimensional uniform filters. The intermediate arrays are stored
    in the same data type as the output. Therefore, for output types
    with a limited precision, the results may be imprecise because
    intermediate results may be stored with insufficient precision.
    """
    input = numpy.asarray(input)
    output, return_value = _ni_support._get_output(output, input)
    sizes = _ni_support._normalize_sequence(size, input.ndim)
    origins = _ni_support._normalize_sequence(origin, input.ndim)
    axes = list(range(input.ndim))
    axes = [(axes[ii], sizes[ii], origins[ii])
                           for ii in range(len(axes)) if sizes[ii] > 1]
    if len(axes) > 0:
        for axis, size, origin in axes:
            uniform_filter1d(input, int(size), axis, output, mode,
                             cval, origin)
            input = output
    else:
        output[...] = input[...]
    return return_value


@docfiller
def minimum_filter1d(input, size, axis=-1, output=None,
                     mode="reflect", cval=0.0, origin=0):
    """Calculate a one-dimensional minimum filter along the given axis.

    The lines of the array along the given axis are filtered with a
    minimum filter of given size.

    Parameters
    ----------
    %(input)s
    size : int
        length along which to calculate 1D minimum
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s

    Notes
    -----
    This function implements the MINLIST algorithm [1]_, as described by
    Richard Harter [2]_, and has a guaranteed O(n) performance, `n` being
    the `input` length, regardless of filter size.

    References
    ----------
    .. [1] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.2777
    .. [2] http://www.richardhartersworld.com/cri/2001/slidingmin.html
    """
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    axis = _ni_support._check_axis(axis, input.ndim)
    if size < 1:
        raise RuntimeError('incorrect filter size')
    output, return_value = _ni_support._get_output(output, input)
    if (size // 2 + origin < 0) or (size // 2 + origin >= size):
        raise ValueError('invalid origin')
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.min_or_max_filter1d(input, size, axis, output, mode, cval,
                                  origin, 1)
    return return_value


@docfiller
def maximum_filter1d(input, size, axis=-1, output=None,
                     mode="reflect", cval=0.0, origin=0):
    """Calculate a one-dimensional maximum filter along the given axis.

    The lines of the array along the given axis are filtered with a
    maximum filter of given size.

    Parameters
    ----------
    %(input)s
    size : int
        Length along which to calculate the 1-D maximum.
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s

    Returns
    -------
    maximum1d : ndarray, None
        Maximum-filtered array with same shape as input.
        None if `output` is not None

    Notes
    -----
    This function implements the MAXLIST algorithm [1]_, as described by
    Richard Harter [2]_, and has a guaranteed O(n) performance, `n` being
    the `input` length, regardless of filter size.

    References
    ----------
    .. [1] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.2777
    .. [2] http://www.richardhartersworld.com/cri/2001/slidingmin.html

    """
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    axis = _ni_support._check_axis(axis, input.ndim)
    if size < 1:
        raise RuntimeError('incorrect filter size')
    output, return_value = _ni_support._get_output(output, input)
    if (size // 2 + origin < 0) or (size // 2 + origin >= size):
        raise ValueError('invalid origin')
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.min_or_max_filter1d(input, size, axis, output, mode, cval,
                                  origin, 0)
    return return_value


def _min_or_max_filter(input, size, footprint, structure, output, mode,
                       cval, origin, minimum):
    if structure is None:
        if footprint is None:
            if size is None:
                raise RuntimeError("no footprint provided")
            separable = True
        else:
            footprint = numpy.asarray(footprint)
            footprint = footprint.astype(bool)
            if numpy.alltrue(numpy.ravel(footprint), axis=0):
                size = footprint.shape
                footprint = None
                separable = True
            else:
                separable = False
    else:
        structure = numpy.asarray(structure, dtype=numpy.float64)
        separable = False
        if footprint is None:
            footprint = numpy.ones(structure.shape, bool)
        else:
            footprint = numpy.asarray(footprint)
            footprint = footprint.astype(bool)
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    output, return_value = _ni_support._get_output(output, input)
    origins = _ni_support._normalize_sequence(origin, input.ndim)
    if separable:
        sizes = _ni_support._normalize_sequence(size, input.ndim)
        axes = list(range(input.ndim))
        axes = [(axes[ii], sizes[ii], origins[ii])
                               for ii in range(len(axes)) if sizes[ii] > 1]
        if minimum:
            filter_ = minimum_filter1d
        else:
            filter_ = maximum_filter1d
        if len(axes) > 0:
            for axis, size, origin in axes:
                filter_(input, int(size), axis, output, mode, cval, origin)
                input = output
        else:
            output[...] = input[...]
    else:
        fshape = [ii for ii in footprint.shape if ii > 0]
        if len(fshape) != input.ndim:
            raise RuntimeError('footprint array has incorrect shape.')
        for origin, lenf in zip(origins, fshape):
            if (lenf // 2 + origin < 0) or (lenf // 2 + origin >= lenf):
                raise ValueError('invalid origin')
        if not footprint.flags.contiguous:
            footprint = footprint.copy()
        if structure is not None:
            if len(structure.shape) != input.ndim:
                raise RuntimeError('structure array has incorrect shape')
            if not structure.flags.contiguous:
                structure = structure.copy()
        mode = _ni_support._extend_mode_to_code(mode)
        _nd_image.min_or_max_filter(input, footprint, structure, output,
                                    mode, cval, origins, minimum)
    return return_value


@docfiller
def minimum_filter(input, size=None, footprint=None, output=None,
      mode="reflect", cval=0.0, origin=0):
    """Calculates a multi-dimensional minimum filter.

    Parameters
    ----------
    %(input)s
    %(size_foot)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    """
    return _min_or_max_filter(input, size, footprint, None, output, mode,
                              cval, origin, 1)


@docfiller
def maximum_filter(input, size=None, footprint=None, output=None,
      mode="reflect", cval=0.0, origin=0):
    """Calculates a multi-dimensional maximum filter.

    Parameters
    ----------
    %(input)s
    %(size_foot)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    """
    return _min_or_max_filter(input, size, footprint, None, output, mode,
                              cval, origin, 0)


@docfiller
def _rank_filter(input, rank, size=None, footprint=None, output=None,
     mode="reflect", cval=0.0, origin=0, operation='rank'):
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    origins = _ni_support._normalize_sequence(origin, input.ndim)
    if footprint is None:
        if size is None:
            raise RuntimeError("no footprint or filter size provided")
        sizes = _ni_support._normalize_sequence(size, input.ndim)
        footprint = numpy.ones(sizes, dtype=bool)
    else:
        footprint = numpy.asarray(footprint, dtype=bool)
    fshape = [ii for ii in footprint.shape if ii > 0]
    if len(fshape) != input.ndim:
        raise RuntimeError('filter footprint array has incorrect shape.')
    for origin, lenf in zip(origins, fshape):
        if (lenf // 2 + origin < 0) or (lenf // 2 + origin >= lenf):
            raise ValueError('invalid origin')
    if not footprint.flags.contiguous:
        footprint = footprint.copy()
    filter_size = numpy.where(footprint, 1, 0).sum()
    if operation == 'median':
        rank = filter_size // 2
    elif operation == 'percentile':
        percentile = rank
        if percentile < 0.0:
            percentile += 100.0
        if percentile < 0 or percentile > 100:
            raise RuntimeError('invalid percentile')
        if percentile == 100.0:
            rank = filter_size - 1
        else:
            rank = int(float(filter_size) * percentile / 100.0)
    if rank < 0:
        rank += filter_size
    if rank < 0 or rank >= filter_size:
        raise RuntimeError('rank not within filter footprint size')
    if rank == 0:
        return minimum_filter(input, None, footprint, output, mode, cval,
                              origins)
    elif rank == filter_size - 1:
        return maximum_filter(input, None, footprint, output, mode, cval,
                              origins)
    else:
        output, return_value = _ni_support._get_output(output, input)
        mode = _ni_support._extend_mode_to_code(mode)
        _nd_image.rank_filter(input, rank, footprint, output, mode, cval,
                              origins)
        return return_value


@docfiller
def rank_filter(input, rank, size=None, footprint=None, output=None,
      mode="reflect", cval=0.0, origin=0):
    """Calculates a multi-dimensional rank filter.

    Parameters
    ----------
    %(input)s
    rank : int
        The rank parameter may be less then zero, i.e., rank = -1
        indicates the largest element.
    %(size_foot)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    """
    return _rank_filter(input, rank, size, footprint, output, mode, cval,
                        origin, 'rank')


@docfiller
def median_filter(input, size=None, footprint=None, output=None,
                  mode="reflect", cval=0.0, origin=0):
    """
    Calculates a multidimensional median filter.

    Parameters
    ----------
    %(input)s
    %(size_foot)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s

    Returns
    -------
    median_filter : ndarray
        Return of same shape as `input`.

    """
    return _rank_filter(input, 0, size, footprint, output, mode, cval,
                        origin, 'median')


@docfiller
def percentile_filter(input, percentile, size=None, footprint=None,
                 output=None, mode="reflect", cval=0.0, origin=0):
    """Calculates a multi-dimensional percentile filter.

    Parameters
    ----------
    %(input)s
    percentile : scalar
        The percentile parameter may be less then zero, i.e.,
        percentile = -20 equals percentile = 80
    %(size_foot)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    """
    return _rank_filter(input, percentile, size, footprint, output, mode,
                                   cval, origin, 'percentile')


@docfiller
def generic_filter1d(input, function, filter_size, axis=-1,
                 output=None, mode="reflect", cval=0.0, origin=0,
                 extra_arguments=(), extra_keywords = None):
    """Calculate a one-dimensional filter along the given axis.

    `generic_filter1d` iterates over the lines of the array, calling the
    given function at each line. The arguments of the line are the
    input line, and the output line. The input and output lines are 1D
    double arrays.  The input line is extended appropriately according
    to the filter size and origin. The output line must be modified
    in-place with the result.

    Parameters
    ----------
    %(input)s
    function : callable
        Function to apply along given axis.
    filter_size : scalar
        Length of the filter.
    %(axis)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    %(extra_arguments)s
    %(extra_keywords)s
    """
    if extra_keywords is None:
        extra_keywords = {}
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    output, return_value = _ni_support._get_output(output, input)
    if filter_size < 1:
        raise RuntimeError('invalid filter size')
    axis = _ni_support._check_axis(axis, input.ndim)
    if (filter_size // 2 + origin < 0) or (filter_size // 2 + origin >=
                                           filter_size):
        raise ValueError('invalid origin')
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.generic_filter1d(input, function, filter_size, axis, output,
                      mode, cval, origin, extra_arguments, extra_keywords)
    return return_value


@docfiller
def generic_filter(input, function, size=None, footprint=None,
                   output=None, mode="reflect", cval=0.0, origin=0,
                   extra_arguments=(), extra_keywords = None):
    """Calculates a multi-dimensional filter using the given function.

    At each element the provided function is called. The input values
    within the filter footprint at that element are passed to the function
    as a 1D array of double values.

    Parameters
    ----------
    %(input)s
    function : callable
        Function to apply at each element.
    %(size_foot)s
    %(output)s
    %(mode)s
    %(cval)s
    %(origin)s
    %(extra_arguments)s
    %(extra_keywords)s
    """
    if extra_keywords is None:
        extra_keywords = {}
    input = numpy.asarray(input)
    if numpy.iscomplexobj(input):
        raise TypeError('Complex type not supported')
    origins = _ni_support._normalize_sequence(origin, input.ndim)
    if footprint is None:
        if size is None:
            raise RuntimeError("no footprint or filter size provided")
        sizes = _ni_support._normalize_sequence(size, input.ndim)
        footprint = numpy.ones(sizes, dtype=bool)
    else:
        footprint = numpy.asarray(footprint)
        footprint = footprint.astype(bool)
    fshape = [ii for ii in footprint.shape if ii > 0]
    if len(fshape) != input.ndim:
        raise RuntimeError('filter footprint array has incorrect shape.')
    for origin, lenf in zip(origins, fshape):
        if (lenf // 2 + origin < 0) or (lenf // 2 + origin >= lenf):
            raise ValueError('invalid origin')
    if not footprint.flags.contiguous:
        footprint = footprint.copy()
    output, return_value = _ni_support._get_output(output, input)
    mode = _ni_support._extend_mode_to_code(mode)
    _nd_image.generic_filter(input, function, footprint, output, mode,
                         cval, origins, extra_arguments, extra_keywords)
    return return_value