_hessian_det_appx_pythran.py

import numpy as np


def _clip(x, low, high):
    """Clip coordinate between low and high values.

    This method was created so that `hessian_det_appx` does not have to make
    a Python call.

    Parameters
    ----------
    x : int
        Coordinate to be clipped.
    low : int
        The lower bound.
    high : int
        The higher bound.

    Returns
    -------
    x : int
        `x` clipped between `high` and `low`.
    """
    assert 0 <= low <= high

    if x > high:
        return high
    elif x < low:
        return low
    else:
        return x


def _integ(img, r, c, rl, cl):
    """Integrate over the 2D integral image in the given window.

    This method was created so that `hessian_det_appx` does not have to make
    a Python call.

    Parameters
    ----------
    img : array
        The integral image over which to integrate.
    r : int
        The row number of the top left corner.
    c : int
        The column number of the top left corner.
    rl : int
        The number of rows over which to integrate.
    cl : int
        The number of columns over which to integrate.

    Returns
    -------
    ans : int
        The integral over the given window.
    """

    r = _clip(r, 0, img.shape[0] - 1)
    c = _clip(c, 0, img.shape[1] - 1)

    r2 = _clip(r + rl, 0, img.shape[0] - 1)
    c2 = _clip(c + cl, 0, img.shape[1] - 1)

    ans = img[r, c] + img[r2, c2] - img[r, c2] - img[r2, c]
    return max(0., ans)


#pythran export _hessian_matrix_det(float64[:,:], float or int)
def _hessian_matrix_det(img, sigma):
    """Compute the approximate Hessian Determinant over a 2D image.

    This method uses box filters over integral images to compute the
    approximate Hessian Determinant as described in [1]_.

    Parameters
    ----------
    img : array
        The integral image over which to compute Hessian Determinant.
    sigma : float
        Standard deviation used for the Gaussian kernel, used for the Hessian
        matrix

    Returns
    -------
    out : array
        The array of the Determinant of Hessians.

    References
    ----------
    .. [1] Herbert Bay, Andreas Ess, Tinne Tuytelaars, Luc Van Gool,
           "SURF: Speeded Up Robust Features"
           ftp://ftp.vision.ee.ethz.ch/publications/articles/eth_biwi_00517.pdf

    Notes
    -----
    The running time of this method only depends on size of the image. It is
    independent of `sigma` as one would expect. The downside is that the
    result for `sigma` less than `3` is not accurate, i.e., not similar to
    the result obtained if someone computed the Hessian and took its
    determinant.
    """

    size = int(3 * sigma)
    height, width = img.shape
    s2 = (size - 1) // 2
    s3 = size // 3
    l = size // 3
    w = size
    b = (size - 1) // 2
    out = np.empty_like(img, dtype=np.double)
    w_i = 1.0 / size / size

    if size % 2 == 0:
        size += 1

    for r in range(height):
        for c in range(width):
            tl = _integ(img, r - s3, c - s3, s3, s3)  # top left
            br = _integ(img, r + 1, c + 1, s3, s3)  # bottom right
            bl = _integ(img, r - s3, c + 1, s3, s3)  # bottom left
            tr = _integ(img, r + 1, c - s3, s3, s3)  # top right

            dxy = bl + tr - tl - br
            dxy = -dxy * w_i

            mid = _integ(img, r - s3 + 1, c - s2, 2 * s3 - 1, w)  # middle box
            side = _integ(img, r - s3 + 1, c - s3 // 2, 2 * s3 - 1, s3)  # sides

            dxx = mid - 3 * side
            dxx = -dxx * w_i

            mid = _integ(img, r - s2, c - s3 + 1, w, 2 * s3 - 1)
            side = _integ(img, r - s3 // 2, c - s3 + 1, s3, 2 * s3 - 1)

            dyy = mid - 3 * side
            dyy = -dyy * w_i

            out[r, c] = (dxx * dyy - 0.81 * (dxy * dxy))

    return out