import numpy as np
from scipy.ndimage import convolve, maximum_filter


def gauss2d(sigma, fsize):
    """ Create a 2D Gaussian filter

    Args:
        sigma: width of the Gaussian filter
        fsize: (w, h) dimensions of the filter
    Returns:
        *normalized* Gaussian filter as (h, w) np.array
    """
    m, n = fsize
    x = np.arange(-m / 2 + 0.5, m / 2)
    y = np.arange(-n / 2 + 0.5, n / 2)
    xx, yy = np.meshgrid(x, y, sparse=True)
    g = np.exp(-(xx ** 2 + yy ** 2) / (2 * sigma ** 2))
    return g / np.sum(g)


def derivative_filters():
    """ Create derivative filters for x and y direction

    Returns:
        fx: derivative filter in x direction
        fy: derivative filter in y direction
    """
    fx = np.array([[0.5, 0, -0.5]])
    fy = fx.transpose()
    return fx, fy


def compute_hessian(img, gauss, fx, fy):
    """ Compute elements of the Hessian matrix

    Args:
        img:
        gauss: Gaussian filter
        fx: derivative filter in x direction
        fy: derivative filter in y direction

    Returns:
        I_xx: (h, w) np.array of 2nd derivatives in x direction
        I_yy: (h, w) np.array of 2nd derivatives in y direction
        I_xy: (h, w) np.array of 2nd derivatives in x-y direction
    """

    #
    # You code here
    #

    # set mode
    mode = "mirror"

    # smooth image
    img = convolve(img, gauss, mode = mode, cval=0)

    # first derivatives
    I_x = convolve(img, fx, mode = mode, cval=0)
    I_y = convolve(img, fy, mode = mode, cval=0)

    # second derivatives
    I_xx = convolve(I_x, fx, mode = mode, cval=0)
    I_xy = convolve(I_x, fy, mode = mode, cval=0)
    I_yy = convolve(I_y, fy, mode = mode, cval=0)

    return I_xx,I_yy,I_xy

def compute_criterion(I_xx, I_yy, I_xy, sigma):
    """ Compute criterion function

    Args:
        I_xx: (h, w) np.array of 2nd derivatives in x direction
        I_yy: (h, w) np.array of 2nd derivatives in y direction
        I_xy: (h, w) np.array of 2nd derivatives in x-y direction
        sigma: scaling factor

    Returns:
        criterion: (h, w) np.array of scaled determinant of Hessian matrix
    """

    #
    # You code here
    #

    det = I_xx * I_yy - I_xy ** 2
    return sigma ** 4 * det


def nonmaxsuppression(criterion, threshold):
    """ Apply non-maximum suppression to criterion values
        and return Hessian interest points

        Args:
            criterion: (h, w) np.array of criterion function values
            threshold: criterion threshold
        Returns:
            rows: (n,) np.array with y-positions of interest points
            cols: (n,) np.array with x-positions of interest points
    """

    #
    # You code here
    #

    criterion_max = maximum_filter(criterion, (5,5), mode= "mirror")
    criterion_thresh = np.logical_and(criterion_max > threshold, criterion >= criterion_max)

    mask = np.zeros_like(criterion_thresh)
    mask[5:-5, 5:-5] = criterion_thresh[5:-5, 5:-5]
    rows, cols = np.nonzero(mask)
    return rows, cols

import numpy as np
from scipy.ndimage import convolve, maximum_filter


def gauss2d(sigma, fsize):
    """ Create a 2D Gaussian filter

    Args:
        sigma: width of the Gaussian filter
        fsize: (w, h) dimensions of the filter
    Returns:
        *normalized* Gaussian filter as (h, w) np.array
    """
    m, n = fsize
    x = np.arange(-m / 2 + 0.5, m / 2)
    y = np.arange(-n / 2 + 0.5, n / 2)
    xx, yy = np.meshgrid(x, y, sparse=True)
    g = np.exp(-(xx ** 2 + yy ** 2) / (2 * sigma ** 2))
    return g / np.sum(g)


def derivative_filters():
    """ Create derivative filters for x and y direction

    Returns:
        fx: derivative filter in x direction
        fy: derivative filter in y direction
    """
    fx = np.array([[0.5, 0, -0.5]])
    fy = fx.transpose()
    return fx, fy


def compute_hessian(img, gauss, fx, fy):
    """ Compute elements of the Hessian matrix

    Args:
        img:
        gauss: Gaussian filter
        fx: derivative filter in x direction
        fy: derivative filter in y direction

    Returns:
        I_xx: (h, w) np.array of 2nd derivatives in x direction
        I_yy: (h, w) np.array of 2nd derivatives in y direction
        I_xy: (h, w) np.array of 2nd derivatives in x-y direction
    """

    #
    # You code here
    #

    # set mode
    mode = "mirror"

    # smooth image
    img = convolve(img, gauss, mode = mode, cval=0)

    # first derivatives
    I_x = convolve(img, fx, mode = mode, cval=0)
    I_y = convolve(img, fy, mode = mode, cval=0)

    # second derivatives
    I_xx = convolve(I_x, fx, mode = mode, cval=0)
    I_xy = convolve(I_x, fy, mode = mode, cval=0)
    I_yy = convolve(I_y, fy, mode = mode, cval=0)

    return I_xx,I_yy,I_xy

def compute_criterion(I_xx, I_yy, I_xy, sigma):
    """ Compute criterion function

    Args:
        I_xx: (h, w) np.array of 2nd derivatives in x direction
        I_yy: (h, w) np.array of 2nd derivatives in y direction
        I_xy: (h, w) np.array of 2nd derivatives in x-y direction
        sigma: scaling factor

    Returns:
        criterion: (h, w) np.array of scaled determinant of Hessian matrix
    """

    #
    # You code here
    #

    det = I_xx * I_yy - I_xy ** 2
    return sigma ** 4 * det


def nonmaxsuppression(criterion, threshold):
    """ Apply non-maximum suppression to criterion values
        and return Hessian interest points

        Args:
            criterion: (h, w) np.array of criterion function values
            threshold: criterion threshold
        Returns:
            rows: (n,) np.array with y-positions of interest points
            cols: (n,) np.array with x-positions of interest points
    """

    #
    # You code here
    #

    criterion_max = maximum_filter(criterion, (5,5), mode= "mirror")
    criterion_thresh = np.logical_and(criterion_max > threshold, criterion >= criterion_max)

    mask = np.zeros_like(criterion_thresh)
    mask[5:-5, 5:-5] = criterion_thresh[5:-5, 5:-5]
    rows, cols = np.nonzero(mask)
    return rows, cols

Create a 2D Gaussian filter      Args:         sigma: width of the Gaussian filter         fsize: (w, h) dimensions of the filter     Returns:         *normalized* Gaussian filter as (h, w) np.array Create derivative filters for x and y direction      Returns:         fx: derivative filter in x direction         fy: derivative filter in y direction Compute elements of the Hessian matrix      Args:         img:         gauss: Gaussian filter         fx: derivative filter in x direction         fy: derivative filter in y direction      Returns:         I_xx: (h, w) np.array of 2nd derivatives in x direction         I_yy: (h, w) np.array of 2nd derivatives in y direction         I_xy: (h, w) np.array of 2nd derivatives in x-y direction # # You code here # # set mode # smooth image # first derivatives # second derivatives Compute criterion function      Args:         I_xx: (h, w) np.array of 2nd derivatives in x direction         I_yy: (h, w) np.array of 2nd derivatives in y direction         I_xy: (h, w) np.array of 2nd derivatives in x-y direction         sigma: scaling factor      Returns:         criterion: (h, w) np.array of scaled determinant of Hessian matrix # # You code here # Apply non-maximum suppression to criterion values         and return Hessian interest points          Args:             criterion: (h, w) np.array of criterion function values             threshold: criterion threshold         Returns:             rows: (n,) np.array with y-positions of interest points             cols: (n,) np.array with x-positions of interest points # # You code here #