scikit-image/skimage/transform/_warps.py

from ._geometric import warp, ProjectiveTransform
import numpy as np

def _swirl_mapping(xy, center, rotation, strength, radius):
    x, y = xy.T
    x0, y0 = center
    rho = np.sqrt((x - x0) ** 2 + (y - y0) ** 2)

    # Ensure that the transformation decays to approximately 1/1000-th
    # within the specified radius.
    radius = radius / 5 * np.log(2)

    theta = rotation + strength * \
            np.exp(-rho / radius) + \
            np.arctan2(y - y0, x - x0)

    xy[..., 0] = x0 + rho * np.cos(theta)
    xy[..., 1] = y0 + rho * np.sin(theta)

    return xy


def swirl(image, center=None, strength=1, radius=100, rotation=0,
          output_shape=None, order=1, mode='constant', cval=0):
    """Perform a swirl transformation.

    Parameters
    ----------
    image : ndarray
        Input image.
    center : (x,y) tuple or (2,) ndarray
        Center coordinate of transformation.
    strength : float
        The amount of swirling applied.
    radius : float
        The extent of the swirl in pixels.  The effect dies out
        rapidly beyond `radius`.
    rotation : float
        Additional rotation applied to the image.

    Returns
    -------
    swirled : ndarray
        Swirled version of the input.

    Other parameters
    ----------------
    output_shape : tuple or ndarray
        Size of the generated output image.
    order : int
        Order of splines used in interpolation.  See
        `scipy.ndimage.map_coordinates` for detail.
    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.

    """

    if center is None:
        center = np.array(image.shape)[:2] / 2

    warp_args = {'center': center,
                 'rotation': rotation,
                 'strength': strength,
                 'radius': radius}

    return warp(image, _swirl_mapping, map_args=warp_args,
                output_shape=output_shape,
                order=order, mode=mode, cval=cval)


def homography(image, H, output_shape=None, order=1,
               mode='constant', cval=0.):
    """Perform a projective transformation (homography) on an image.

    For each pixel, given its homogeneous coordinate :math:`\mathbf{x}
    = [x, y, 1]^T`, its target position is calculated by multiplying
    with the given matrix, :math:`H`, to give :math:`H \mathbf{x}`.
    E.g., to rotate by theta degrees clockwise, the matrix should be

    ::

      [[cos(theta) -sin(theta) 0]
       [sin(theta)  cos(theta) 0]
       [0            0         1]]

    or, to translate x by 10 and y by 20,

    ::

      [[1 0 10]
       [0 1 20]
       [0 0 1 ]].

    Parameters
    ----------
    image : 2-D array
        Input image.
    H : array of shape ``(3, 3)``
        Transformation matrix H that defines the homography.
    output_shape : tuple (rows, cols)
        Shape of the output image generated.
    order : int
        Order of splines used in interpolation.
    mode : string
        How to handle values outside the image borders.  Passed as-is
        to ndimage.
    cval : string
        Used in conjunction with mode 'constant', the value outside
        the image boundaries.

    Examples
    --------
    >>> # rotate by 90 degrees around origin and shift down by 2
    >>> x = np.arange(9, dtype=np.uint8).reshape((3, 3)) + 1
    >>> x
    array([[1, 2, 3],
           [4, 5, 6],
           [7, 8, 9]], dtype=uint8)
    >>> theta = -np.pi/2
    >>> M = np.array([[np.cos(theta),-np.sin(theta),0],
    ...               [np.sin(theta), np.cos(theta),2],
    ...               [0,             0,            1]])
    >>> x90 = homography(x, M, order=1)
    >>> x90
    array([[3, 6, 9],
           [2, 5, 8],
           [1, 4, 7]], dtype=uint8)
    >>> # translate right by 2 and down by 1
    >>> y = np.zeros((5,5), dtype=np.uint8)
    >>> y[1, 1] = 255
    >>> y
    array([[  0,   0,   0,   0,   0],
           [  0, 255,   0,   0,   0],
           [  0,   0,   0,   0,   0],
           [  0,   0,   0,   0,   0],
           [  0,   0,   0,   0,   0]], dtype=uint8)
    >>> M = np.array([[ 1.,  0.,  2.],
    ...               [ 0.,  1.,  1.],
    ...               [ 0.,  0.,  1.]])
    >>> y21 = homography(y, M, order=1)
    >>> y21
    array([[  0,   0,   0,   0,   0],
           [  0,   0,   0,   0,   0],
           [  0,   0,   0, 255,   0],
           [  0,   0,   0,   0,   0],
           [  0,   0,   0,   0,   0]], dtype=uint8)

    """
    import warnings
    warnings.warn('the homography function is deprecated; '
                  'use the `warp` and `ProjectiveTransform` class instead',
                  category=DeprecationWarning)

    tform = ProjectiveTransform(H)
    return warp(image, inverse_map=tform.inverse, output_shape=output_shape,
                order=order, mode=mode, cval=cval)