# coding: utf-8
import numpy as np
from skimage import img_as_float
from skimage.restoration._denoise_cy import _denoise_bilateral, \
                                            _denoise_tv_bregman


def denoise_bilateral(image, win_size=5, sigma_range=None, sigma_spatial=1,
                      bins=10000, mode='constant', cval=0):
    """Denoise image using bilateral filter.

    This is an edge-preserving and noise reducing denoising filter. It averages
    pixels based on their spatial closeness and radiometric similarity.

    Spatial closeness is measured by the gaussian function of the euclidian
    distance between two pixels and a certain standard deviation
    (`sigma_spatial`).

    Radiometric similarity is measured by the gaussian function of the euclidian
    distance between two color values and a certain standard deviation
    (`sigma_range`).

    Parameters
    ----------
    image : ndarray
        Input image.
    win_size : int
        Window size for filtering.
    sigma_range : float
        Standard deviation for grayvalue/color distance (radiometric
        similarity). A larger value results in averaging of pixels with larger
        radiometric differences. Note, that the image will be converted using
        the `img_as_float` function and thus the standard deviation is in
        respect to the range `[0, 1]`.
    sigma_spatial : float
        Standard deviation for range distance. A larger value results in
        averaging of pixels with larger spatial differences.
    bins : int
        Number of discrete values for gaussian weights of color filtering.
        A larger value results in improved accuracy.
    mode : string
        How to handle values outside the image borders. See
        `scipy.ndimage.map_coordinates` for detail.
    cval : string
        Used in conjunction with mode 'constant', the value outside
        the image boundaries.

    Returns
    -------
    denoised : ndarray
        Denoised image.

    References
    ----------
    .. [1] http://users.soe.ucsc.edu/~manduchi/Papers/ICCV98.pdf

    """
    return _denoise_bilateral(image, win_size, sigma_range, sigma_spatial,
                              bins, mode, cval)


def denoise_tv_bregman(image, weight, max_iter=100, eps=1e-3, isotropic=True):
    """Perform total-variation denoising using split-Bregman optimization.

    Total-variation denoising (also know as total-variation regularization)
    tries to find an image with less total-variation under the constraint
    of being similar to the input image, which is controlled by the
    regularization parameter.

    Parameters
    ----------
    image : ndarray
        Input data to be denoised (converted using img_as_float`).
    weight : float, optional
        Denoising weight. The smaller the `weight`, the more denoising (at
        the expense of less similarity to the `input`). The regularization
        parameter `lambda` is chosen as `2 * weight`.
    eps : float, optional
        Relative difference of the value of the cost function that determines
        the stop criterion. The algorithm stops when::

            SUM((u(n) - u(n-1))**2) < eps

    max_iter : int, optional
        Maximal number of iterations used for the optimization.
    isotropic : boolean, optional
        Switch between isotropic and anisotropic TV denoising.

    Returns
    -------
    u : ndarray
        Denoised image.

    References
    ----------
    .. [1] http://en.wikipedia.org/wiki/Total_variation_denoising
    .. [2] Tom Goldstein and Stanley Osher, "The Split Bregman Method For L1
           Regularized Problems",
           ftp://ftp.math.ucla.edu/pub/camreport/cam08-29.pdf
    .. [3] Pascal Getreuer, "Rudin–Osher–Fatemi Total Variation Denoising
           using Split Bregman" in Image Processing On Line on 2012–05–19,
           http://www.ipol.im/pub/art/2012/g-tvd/article_lr.pdf
    .. [4] http://www.math.ucsb.edu/~cgarcia/UGProjects/BregmanAlgorithms_JacquelineBush.pdf

    """
    return _denoise_tv_bregman(image, weight, max_iter, eps, isotropic)


def _denoise_tv_chambolle_3d(im, weight=100, eps=2.e-4, n_iter_max=200):
    """Perform total-variation denoising on 3D images.

    Parameters
    ----------
    im : ndarray
        3-D input data to be denoised.
    weight : float, optional
        Denoising weight. The greater `weight`, the more denoising (at
        the expense of fidelity to `input`).
    eps : float, optional
        Relative difference of the value of the cost function that determines
        the stop criterion. The algorithm stops when:

            (E_(n-1) - E_n) < eps * E_0

    n_iter_max : int, optional
        Maximal number of iterations used for the optimization.

    Returns
    -------
    out : ndarray
        Denoised array of floats.

    Notes
    -----
    Rudin, Osher and Fatemi algorithm.

    """

    px = np.zeros_like(im)
    py = np.zeros_like(im)
    pz = np.zeros_like(im)
    gx = np.zeros_like(im)
    gy = np.zeros_like(im)
    gz = np.zeros_like(im)
    d = np.zeros_like(im)
    i = 0
    while i < n_iter_max:
        d = - px - py - pz
        d[1:] += px[:-1]
        d[:, 1:] += py[:, :-1]
        d[:, :, 1:] += pz[:, :, :-1]

        out = im + d
        E = (d**2).sum()

        gx[:-1] = np.diff(out, axis=0)
        gy[:, :-1] = np.diff(out, axis=1)
        gz[:, :, :-1] = np.diff(out, axis=2)
        norm = np.sqrt(gx**2 + gy**2 + gz**2)
        E += weight * norm.sum()
        norm *= 0.5 / weight
        norm += 1.
        px -= 1. / 6. * gx
        px /= norm
        py -= 1. / 6. * gy
        py /= norm
        pz -= 1 / 6. * gz
        pz /= norm
        E /= float(im.size)
        if i == 0:
            E_init = E
            E_previous = E
        else:
            if np.abs(E_previous - E) < eps * E_init:
                break
            else:
                E_previous = E
        i += 1
    return out


def _denoise_tv_chambolle_2d(im, weight=50, eps=2.e-4, n_iter_max=200):
    """Perform total-variation denoising on 2D images.

    Parameters
    ----------
    im : ndarray
        Input data to be denoised.
    weight : float, optional
        Denoising weight. The greater `weight`, the more denoising (at
        the expense of fidelity to `input`)
    eps : float, optional
        Relative difference of the value of the cost function that determines
        the stop criterion. The algorithm stops when:

            (E_(n-1) - E_n) < eps * E_0

    n_iter_max : int, optional
        Maximal number of iterations used for the optimization.

    Returns
    -------
    out : ndarray
        Denoised array of floats.

    Notes
    -----
    The principle of total variation denoising is explained in
    http://en.wikipedia.org/wiki/Total_variation_denoising.

    This code is an implementation of the algorithm of Rudin, Fatemi and Osher
    that was proposed by Chambolle in [1]_.

    References
    ----------
    .. [1] A. Chambolle, An algorithm for total variation minimization and
           applications, Journal of Mathematical Imaging and Vision,
           Springer, 2004, 20, 89-97.

    """

    px = np.zeros_like(im)
    py = np.zeros_like(im)
    gx = np.zeros_like(im)
    gy = np.zeros_like(im)
    d = np.zeros_like(im)
    i = 0
    while i < n_iter_max:
        d = -px - py
        d[1:] += px[:-1]
        d[:, 1:] += py[:, :-1]

        out = im + d
        E = (d**2).sum()
        gx[:-1] = np.diff(out, axis=0)
        gy[:, :-1] = np.diff(out, axis=1)
        norm = np.sqrt(gx**2 + gy**2)
        E += weight * norm.sum()
        norm *= 0.5 / weight
        norm += 1
        px -= 0.25 * gx
        px /= norm
        py -= 0.25 * gy
        py /= norm
        E /= float(im.size)
        if i == 0:
            E_init = E
            E_previous = E
        else:
            if np.abs(E_previous - E) < eps * E_init:
                break
            else:
                E_previous = E
        i += 1
    return out


def denoise_tv_chambolle(im, weight=50, eps=2.e-4, n_iter_max=200,
                         multichannel=False):
    """Perform total-variation denoising on 2D and 3D images.

    Parameters
    ----------
    im : ndarray (2d or 3d) of ints, uints or floats
        Input data to be denoised. `im` can be of any numeric type,
        but it is cast into an ndarray of floats for the computation
        of the denoised image.
    weight : float, optional
        Denoising weight. The greater `weight`, the more denoising (at
        the expense of fidelity to `input`).
    eps : float, optional
        Relative difference of the value of the cost function that
        determines the stop criterion. The algorithm stops when:

            (E_(n-1) - E_n) < eps * E_0

    n_iter_max : int, optional
        Maximal number of iterations used for the optimization.
    multichannel : bool, optional
        Apply total-variation denoising separately for each channel. This
        option should be true for color images, otherwise the denoising is
        also applied in the 3rd dimension.

    Returns
    -------
    out : ndarray
        Denoised image.

    Notes
    -----
    Make sure to set the multichannel parameter appropriately for color images.

    The principle of total variation denoising is explained in
    http://en.wikipedia.org/wiki/Total_variation_denoising

    The principle of total variation denoising is to minimize the
    total variation of the image, which can be roughly described as
    the integral of the norm of the image gradient. Total variation
    denoising tends to produce "cartoon-like" images, that is,
    piecewise-constant images.

    This code is an implementation of the algorithm of Rudin, Fatemi and Osher
    that was proposed by Chambolle in [1]_.

    References
    ----------
    .. [1] A. Chambolle, An algorithm for total variation minimization and
           applications, Journal of Mathematical Imaging and Vision,
           Springer, 2004, 20, 89-97.

    Examples
    --------
    2D example on Lena image:

    >>> from skimage import color, data
    >>> lena = color.rgb2gray(data.lena())[:50, :50]
    >>> lena += 0.5 * lena.std() * np.random.randn(*lena.shape)
    >>> denoised_lena = denoise_tv_chambolle(lena, weight=60)

    3D example on synthetic data:

    >>> x, y, z = np.ogrid[0:20, 0:20, 0:20]
    >>> mask = (x - 22)**2 + (y - 20)**2 + (z - 17)**2 < 8**2
    >>> mask = mask.astype(np.float)
    >>> mask += 0.2*np.random.randn(*mask.shape)
    >>> res = denoise_tv_chambolle(mask, weight=100)

    """

    im_type = im.dtype
    if not im_type.kind == 'f':
        im = img_as_float(im)

    if im.ndim == 2:
        out = _denoise_tv_chambolle_2d(im, weight, eps, n_iter_max)
    elif im.ndim == 3:
        if multichannel:
            out = np.zeros_like(im)
            for c in range(im.shape[2]):
                out[..., c] = _denoise_tv_chambolle_2d(im[..., c], weight, eps,
                                                       n_iter_max)
        else:
            out = _denoise_tv_chambolle_3d(im, weight, eps, n_iter_max)
    else:
        raise ValueError('only 2-d and 3-d images may be denoised with this '
                         'function')
    return out