__all__ = ['threshold_adaptive',
           'threshold_otsu',
           'threshold_yen',
           'threshold_isodata']

import numpy as np
import scipy.ndimage
from skimage.exposure import histogram


def threshold_adaptive(image, block_size, method='gaussian', offset=0,
                       mode='reflect', param=None):
    """Applies an adaptive threshold to an array.

    Also known as local or dynamic thresholding where the threshold value is
    the weighted mean for the local neighborhood of a pixel subtracted by a
    constant. Alternatively the threshold can be determined dynamically by a a
    given function using the 'generic' method.

    Parameters
    ----------
    image : (N, M) ndarray
        Input image.
    block_size : int
        Uneven size of pixel neighborhood which is used to calculate the
        threshold value (e.g. 3, 5, 7, ..., 21, ...).
    method : {'generic', 'gaussian', 'mean', 'median'}, optional
        Method used to determine adaptive threshold for local neighbourhood in
        weighted mean image.

        * 'generic': use custom function (see `param` parameter)
        * 'gaussian': apply gaussian filter (see `param` parameter for custom\
                      sigma value)
        * 'mean': apply arithmetic mean filter
        * 'median': apply median rank filter

        By default the 'gaussian' method is used.
    offset : float, optional
        Constant subtracted from weighted mean of neighborhood to calculate
        the local threshold value. Default offset is 0.
    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'.
    param : {int, function}, optional
        Either specify sigma for 'gaussian' method or function object for
        'generic' method. This functions takes the flat array of local
        neighbourhood as a single argument and returns the calculated
        threshold for the centre pixel.

    Returns
    -------
    threshold : (N, M) ndarray
        Thresholded binary image

    References
    ----------
    .. [1] http://docs.opencv.org/modules/imgproc/doc/miscellaneous_transformations.html?highlight=threshold#adaptivethreshold

    Examples
    --------
    >>> from skimage.data import camera
    >>> image = camera()[:50, :50]
    >>> binary_image1 = threshold_adaptive(image, 15, 'mean')
    >>> func = lambda arr: arr.mean()
    >>> binary_image2 = threshold_adaptive(image, 15, 'generic', param=func)
    """
    thresh_image = np.zeros(image.shape, 'double')
    if method == 'generic':
        scipy.ndimage.generic_filter(image, param, block_size,
                                     output=thresh_image, mode=mode)
    elif method == 'gaussian':
        if param is None:
            # automatically determine sigma which covers > 99% of distribution
            sigma = (block_size - 1) / 6.0
        else:
            sigma = param
        scipy.ndimage.gaussian_filter(image, sigma, output=thresh_image,
                                      mode=mode)
    elif method == 'mean':
        mask = 1. / block_size * np.ones((block_size,))
        # separation of filters to speedup convolution
        scipy.ndimage.convolve1d(image, mask, axis=0, output=thresh_image,
                                 mode=mode)
        scipy.ndimage.convolve1d(thresh_image, mask, axis=1,
                                 output=thresh_image, mode=mode)
    elif method == 'median':
        scipy.ndimage.median_filter(image, block_size, output=thresh_image,
                                    mode=mode)

    return image > (thresh_image - offset)


def threshold_otsu(image, nbins=256):
    """Return threshold value based on Otsu's method.

    Parameters
    ----------
    image : array
        Input image.
    nbins : int, optional
        Number of bins used to calculate histogram. This value is ignored for
        integer arrays.

    Returns
    -------
    threshold : float
        Upper threshold value. All pixels intensities that less or equal of
        this value assumed as foreground.

    References
    ----------
    .. [1] Wikipedia, http://en.wikipedia.org/wiki/Otsu's_Method

    Examples
    --------
    >>> from skimage.data import camera
    >>> image = camera()
    >>> thresh = threshold_otsu(image)
    >>> binary = image <= thresh
    """
    hist, bin_centers = histogram(image, nbins)
    hist = hist.astype(float)

    # class probabilities for all possible thresholds
    weight1 = np.cumsum(hist)
    weight2 = np.cumsum(hist[::-1])[::-1]
    # class means for all possible thresholds
    mean1 = np.cumsum(hist * bin_centers) / weight1
    mean2 = (np.cumsum((hist * bin_centers)[::-1]) / weight2[::-1])[::-1]

    # Clip ends to align class 1 and class 2 variables:
    # The last value of `weight1`/`mean1` should pair with zero values in
    # `weight2`/`mean2`, which do not exist.
    variance12 = weight1[:-1] * weight2[1:] * (mean1[:-1] - mean2[1:]) ** 2

    idx = np.argmax(variance12)
    threshold = bin_centers[:-1][idx]
    return threshold


def threshold_yen(image, nbins=256):
    """Return threshold value based on Yen's method.

    Parameters
    ----------
    image : array
        Input image.
    nbins : int, optional
        Number of bins used to calculate histogram. This value is ignored for
        integer arrays.

    Returns
    -------
    threshold : float
        Upper threshold value. All pixels intensities that less or equal of
        this value assumed as foreground.

    References
    ----------
    .. [1] Yen J.C., Chang F.J., and Chang S. (1995) "A New Criterion
           for Automatic Multilevel Thresholding" IEEE Trans. on Image
           Processing, 4(3): 370-378
    .. [2] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding
           Techniques and Quantitative Performance Evaluation" Journal of
           Electronic Imaging, 13(1): 146-165,
           http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf
    .. [3] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold

    Examples
    --------
    >>> from skimage.data import camera
    >>> image = camera()
    >>> thresh = threshold_yen(image)
    >>> binary = image <= thresh
    """
    hist, bin_centers = histogram(image, nbins)
    # On blank images (e.g. filled with 0) with int dtype, `histogram()`
    # returns `bin_centers` containing only one value. Speed up with it.
    if bin_centers.size == 1:
        return bin_centers[0]

    # Calculate probability mass function
    pmf = hist.astype(np.float32) / hist.sum()
    P1 = np.cumsum(pmf)  # Cumulative normalized histogram
    P1_sq = np.cumsum(pmf ** 2)
    # Get cumsum calculated from end of squared array:
    P2_sq = np.cumsum(pmf[::-1] ** 2)[::-1]
    # P2_sq indexes is shifted +1. I assume, with P1[:-1] it's help avoid '-inf'
    # in crit. ImageJ Yen implementation replaces those values by zero.
    crit = np.log(((P1_sq[:-1] * P2_sq[1:]) ** -1) *
                  (P1[:-1] * (1.0 - P1[:-1])) ** 2)
    return bin_centers[crit.argmax()]


def threshold_isodata(image, nbins=256):
    """Return threshold value based on ISODATA method.

    Histogram-based threshold, known as Ridler-Calvard method or intermeans.

    Parameters
    ----------
    image : array
        Input image.
    nbins : int, optional
        Number of bins used to calculate histogram. This value is ignored for
        integer arrays.

    Returns
    -------
    threshold : float or int, corresponding input array dtype.
        Upper threshold value. All pixels intensities that less or equal of
        this value assumed as background.

    References
    ----------
    .. [1] Ridler, TW & Calvard, S (1978), "Picture thresholding using an
           iterative selection method"
    .. [2] IEEE Transactions on Systems, Man and Cybernetics 8: 630-632,
           http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4310039
    .. [3] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding
           Techniques and Quantitative Performance Evaluation" Journal of
           Electronic Imaging, 13(1): 146-165,
           http://www.busim.ee.boun.edu.tr/~sankur/SankurFolder/Threshold_survey.pdf
    .. [4] ImageJ AutoThresholder code,
           http://fiji.sc/wiki/index.php/Auto_Threshold

    Examples
    --------
    >>> from skimage.data import coins
    >>> image = coins()
    >>> thresh = threshold_isodata(image)
    >>> binary = image > thresh
    """
    hist, bin_centers = histogram(image, nbins)
    # On blank images (e.g. filled with 0) with int dtype, `histogram()`
    # returns `bin_centers` containing only one value. Speed up with it.
    if bin_centers.size == 1:
        return bin_centers[0]
    # It is not necessary to calculate the probability mass function here,
    # because the l and h fractions already include the normalization.
    pmf = hist.astype(np.float32)  # / hist.sum()
    cpmfl = np.cumsum(pmf, dtype=np.float32)
    cpmfh = np.cumsum(pmf[::-1], dtype=np.float32)[::-1]

    binnums = np.arange(pmf.size, dtype=np.uint8)
    # l and h contain average value of pixels in sum of bins, calculated
    # from lower to higher and from higher to lower respectively.
    l = np.ma.divide(np.cumsum(pmf * binnums, dtype=np.float32), cpmfl)
    h = np.ma.divide(
        np.cumsum((pmf[::-1] * binnums[::-1]), dtype=np.float32)[::-1],
        cpmfh)

    allmean = (l + h) / 2.0
    threshold = bin_centers[np.nonzero(allmean.round() == binnums)[0][0]]
    # This implementation returns threshold where
    # `background <= threshold < foreground`.
    return threshold