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Refactor image warps

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* Fix cval bug in interpolation which was ignored
* Remove fast_homography as standalone function and automatically include
  functionality in warp
* Fix bug in warp_coords for graylevel images
* move warp functions to warp file
This commit is contained in:
Johannes Schönberger
2012-08-26 15:39:48 +02:00
parent 77f1e0ba47
commit a6532a8dae
7 changed files with 245 additions and 214 deletions
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skimage/_shared/interpolation.pyx
+9 -9
View File
@@ -18,8 +18,8 @@ cdef inline double nearest_neighbour(double* image, int rows, int cols,
Shape of image.
r, c : int
Position at which to interpolate.
mode : {'C', 'W', 'M'}
Wrapping mode. Constant, Wrap or Mirror.
mode : {'C', 'W', 'R'}
Wrapping mode. Constant, Wrap or Reflect.
cval : double
Constant value to use for constant mode.
@@ -42,8 +42,8 @@ cdef inline double bilinear_interpolation(double* image, int rows, int cols,
Shape of image.
r, c : int
Position at which to interpolate.
mode : {'C', 'W', 'M'}
Wrapping mode. Constant, Wrap or Mirror.
mode : {'C', 'W', 'R'}
Wrapping mode. Constant, Wrap or Reflect.
cval : double
Constant value to use for constant mode.
@@ -76,8 +76,8 @@ cdef inline double get_pixel(double* image, int rows, int cols, int r, int c,
Shape of image.
r, c : int
Position at which to get the pixel.
mode : {'C', 'W', 'M'}
Wrapping mode. Constant, Wrap or Mirror.
mode : {'C', 'W', 'R'}
Wrapping mode. Constant, Wrap or Reflect.
cval : double
Constant value to use for constant mode.
@@ -101,13 +101,13 @@ cdef inline int coord_map(int dim, int coord, char mode):
Maximum coordinate.
coord : int
Coord provided by user. May be < 0 or > dim.
mode : {'W', 'M'}
Whether to wrap or mirror the coordinate if it
mode : {'W', 'R'}
Whether to wrap or reflect the coordinate if it
falls outside [0, dim).
"""
dim = dim - 1
if mode == 'M': # mirror
if mode == 'R': # reflect
if (coord < 0):
# How many times times does the coordinate wrap?
if (<int>(-coord / dim) % 2 != 0):
skimage/transform/__init__.py
+2 -3
View File
@@ -1,9 +1,8 @@
from .hough_transform import *
from .radon_transform import *
from .finite_radon_transform import *
from ._project import homography as fast_homography
from .integral import *
from ._geometric import (warp, warp_coords, estimate_transform,
from ._geometric import (estimate_transform,
SimilarityTransform, AffineTransform,
ProjectiveTransform, PolynomialTransform)
from ._warps import swirl, homography
from ._warps import warp, warp_coords, swirl, homography
skimage/transform/_geometric.py
+3 -183
View File
@@ -1,30 +1,5 @@
import math
import numpy as np
from scipy import ndimage
from skimage.util import img_as_float
def _stackcopy(a, b):
"""Copy b into each color layer of a, such that::
a[:,:,0] = a[:,:,1] = ... = b
Parameters
----------
a : (M, N) or (M, N, P) ndarray
Target array.
b : (M, N)
Source array.
Notes
-----
Color images are stored as an ``(M, N, 3)`` or ``(M, N, 4)`` arrays.
"""
if a.ndim == 3:
a[:] = b[:, :, np.newaxis]
else:
a[:] = b
class GeometricTransform(object):
@@ -603,7 +578,7 @@ class PolynomialTransform(GeometricTransform):
'then apply the forward transformation.')
TRANSFORMATIONS = {
TRANSFORMS = {
'similarity': SimilarityTransform,
'affine': AffineTransform,
'projective': ProjectiveTransform,
@@ -669,11 +644,11 @@ def estimate_transform(ttype, src, dst, **kwargs):
"""
ttype = ttype.lower()
if ttype not in TRANSFORMATIONS:
if ttype not in TRANSFORMS:
raise ValueError('the transformation type \'%s\' is not'
'implemented' % ttype)
tform = TRANSFORMATIONS[ttype]()
tform = TRANSFORMS[ttype]()
tform.estimate(src, dst, **kwargs)
return tform
@@ -696,158 +671,3 @@ def matrix_transform(coords, matrix):
"""
return ProjectiveTransform(matrix)(coords)
def warp_coords(orows, ocols, bands, coord_transform_fn,
dtype=np.float64):
"""Build the source coordinates for the output pixels of an image warp.
Parameters
----------
orows : int
Number of output rows.
ocols : int
Number of output columns.
bands : int
Number of color bands (aka channels).
coord_transform_fn : callable like GeometricTransform.inverse
Return input coordinates for given output coordinates.
dtype : np.dtype or string
dtype for return value (sane choices: float32 or float64)
Returns
-------
coords : (3, orows, ocols, bands) array of dtype `dtype`
Coordinates for `scipy.ndimage.map_coordinates`, that will yield
an image of shape (orows, ocols, bands) by drawing from source
points according to the `coord_transform_fn`.
Notes
-----
This is a lower-level routine that produces the source coordinates used by
`warp()`.
It is provided separately from `warp` to give additional flexibility to
users who would like, for example, to re-use a particular coordinate
mapping, to use specific dtypes at various points along the the
image-warping process, or to implement different post-processing logic
than `warp` performs after the call to `ndimage.map_coordinates`.
Examples
--------
Produce a coordinate map that Shifts an image to the right:
>>> from skimage import data
>>> from scipy.ndimage import map_coordinates
>>>
>>> def shift_right(xy):
... xy[:, 0] -= 10
... return xy
>>>
>>> coords = warp_coords(30, 30, 3, shift_right)
>>> image = data.lena().astype(np.float32)
>>> warped_image = map_coordinates(image, coords)
"""
coords = np.empty((3, orows, ocols, bands), dtype=dtype)
# Reshape grid coordinates into a (P, 2) array of (x, y) pairs
tf_coords = np.indices((ocols, orows), dtype=dtype).reshape(2, -1).T
# Map each (x, y) pair to the source image according to
# the user-provided mapping
tf_coords = coord_transform_fn(tf_coords)
# Reshape back to a (2, M, N) coordinate grid
tf_coords = tf_coords.T.reshape((-1, ocols, orows)).swapaxes(1, 2)
# Place the y-coordinate mapping
_stackcopy(coords[1, ...], tf_coords[0, ...])
# Place the x-coordinate mapping
_stackcopy(coords[0, ...], tf_coords[1, ...])
# colour-coordinate mapping
coords[2, ...] = range(bands)
return coords
def warp(image, inverse_map=None, map_args={}, output_shape=None, order=1,
mode='constant', cval=0., reverse_map=None):
"""Warp an image according to a given coordinate transformation.
Parameters
----------
image : 2-D array
Input image.
inverse_map : transformation object, callable xy = f(xy, **kwargs)
Inverse coordinate map. A function that transforms a (N, 2) array of
``(x, y)`` coordinates in the *output image* into their corresponding
coordinates in the *source image* (e.g. a transformation object or its
inverse).
map_args : dict, optional
Keyword arguments passed to `inverse_map`.
output_shape : tuple (rows, cols)
Shape of the output image generated.
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 : float
Used in conjunction with mode 'constant', the value outside
the image boundaries.
Examples
--------
Shift an image to the right:
>>> from skimage import data
>>> image = data.camera()
>>>
>>> def shift_right(xy):
... xy[:, 0] -= 10
... return xy
>>>
>>> warp(image, shift_right)
"""
# Backward API compatibility
if reverse_map is not None:
inverse_map = reverse_map
if image.ndim < 2:
raise ValueError("Input must have more than 1 dimension.")
image = np.atleast_3d(img_as_float(image))
ishape = np.array(image.shape)
bands = ishape[2]
if output_shape is None:
output_shape = ishape
rows, cols = output_shape[:2]
def coord_transform_fn(*args):
return inverse_map(*args, **map_args)
coords = warp_coords(rows, cols, bands, coord_transform_fn)
# Prefilter not necessary for order 1 interpolation
prefilter = order > 1
mapped = ndimage.map_coordinates(image, coords, prefilter=prefilter,
mode=mode, order=order, cval=cval)
# The spline filters sometimes return results outside [0, 1],
# so clip to ensure valid data
clipped = np.clip(mapped, 0, 1)
if mode == 'constant' and not (0 <= cval <= 1):
clipped[mapped == cval] = cval
# Remove singleton dim introduced by atleast_3d
return clipped.squeeze()
skimage/transform/_warps.py
+211 -1
View File
@@ -1,5 +1,215 @@
from ._geometric import warp, ProjectiveTransform
import numpy as np
from scipy import ndimage
from skimage.util import img_as_float
from ._geometric import (SimilarityTransform, AffineTransform,
ProjectiveTransform)
from ._warps_cy import _warp_fast
HOMOGRAPHY_TRANSFORMS = (
SimilarityTransform,
AffineTransform,
ProjectiveTransform
)
def _stackcopy(a, b):
"""Copy b into each color layer of a, such that::
a[:,:,0] = a[:,:,1] = ... = b
Parameters
----------
a : (M, N) or (M, N, P) ndarray
Target array.
b : (M, N)
Source array.
Notes
-----
Color images are stored as an ``(M, N, 3)`` or ``(M, N, 4)`` arrays.
"""
if a.ndim == 3:
a[:] = b[:, :, np.newaxis]
else:
a[:] = b
def warp_coords(coord_map, shape, dtype=np.float64):
"""Build the source coordinates for the output pixels of an image warp.
Parameters
----------
coord_map : callable like GeometricTransform.inverse
Return input coordinates for given output coordinates.
shape : tuple
Shape of output image ``(rows, cols[, bands])``.
dtype : np.dtype or string
dtype for return value (sane choices: float32 or float64).
Returns
-------
coords : (ndim, rows, cols[, bands]) array of dtype `dtype`
Coordinates for `scipy.ndimage.map_coordinates`, that will yield
an image of shape (orows, ocols, bands) by drawing from source
points according to the `coord_transform_fn`.
Notes
-----
This is a lower-level routine that produces the source coordinates used by
`warp()`.
It is provided separately from `warp` to give additional flexibility to
users who would like, for example, to re-use a particular coordinate
mapping, to use specific dtypes at various points along the the
image-warping process, or to implement different post-processing logic
than `warp` performs after the call to `ndimage.map_coordinates`.
Examples
--------
Produce a coordinate map that Shifts an image to the right:
>>> from skimage import data
>>> from scipy.ndimage import map_coordinates
>>>
>>> def shift_right(xy):
... xy[:, 0] -= 10
... return xy
>>>
>>> coords = warp_coords(30, 30, 3, shift_right)
>>> image = data.lena().astype(np.float32)
>>> warped_image = map_coordinates(image, coords)
"""
rows, cols = shape[0], shape[1]
coords_shape = [len(shape), rows, cols]
if len(shape) == 3:
coords_shape.append(shape[2])
coords = np.empty(coords_shape, dtype=dtype)
# Reshape grid coordinates into a (P, 2) array of (x, y) pairs
tf_coords = np.indices((cols, rows), dtype=dtype).reshape(2, -1).T
# Map each (x, y) pair to the source image according to
# the user-provided mapping
tf_coords = coord_map(tf_coords)
# Reshape back to a (2, M, N) coordinate grid
tf_coords = tf_coords.T.reshape((-1, cols, rows)).swapaxes(1, 2)
# Place the y-coordinate mapping
_stackcopy(coords[1, ...], tf_coords[0, ...])
# Place the x-coordinate mapping
_stackcopy(coords[0, ...], tf_coords[1, ...])
if len(shape) == 3:
coords[2, ...] = range(shape[2])
return coords
def warp(image, inverse_map=None, map_args={}, output_shape=None, order=1,
mode='constant', cval=0., reverse_map=None):
"""Warp an image according to a given coordinate transformation.
Parameters
----------
image : 2-D array
Input image.
inverse_map : transformation object, callable xy = f(xy, **kwargs)
Inverse coordinate map. A function that transforms a (N, 2) array of
``(x, y)`` coordinates in the *output image* into their corresponding
coordinates in the *source image* (e.g. a transformation object or its
inverse).
map_args : dict, optional
Keyword arguments passed to `inverse_map`.
output_shape : tuple (rows, cols)
Shape of the output image generated.
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 : float
Used in conjunction with mode 'constant', the value outside
the image boundaries.
Examples
--------
Shift an image to the right:
>>> from skimage import data
>>> image = data.camera()
>>>
>>> def shift_right(xy):
... xy[:, 0] -= 10
... return xy
>>>
>>> warp(image, shift_right)
"""
# Backward API compatibility
if reverse_map is not None:
inverse_map = reverse_map
if image.ndim < 2:
raise ValueError("Input must have more than 1 dimension.")
orig_ndim = image.ndim
image = np.atleast_3d(img_as_float(image))
ishape = np.array(image.shape)
bands = ishape[2]
# use fast Cython version for specific parameters
fast_modes = ('constant', 'reflect', 'wrap')
if order in (0, 1) and mode in fast_modes and not map_args:
matrix = None
if isinstance(inverse_map, HOMOGRAPHY_TRANSFORMS):
matrix = inverse_map._matrix
elif inverse_map.__name__ == 'inverse' \
and inverse_map.im_class in HOMOGRAPHY_TRANSFORMS:
matrix = np.linalg.inv(inverse_map.im_self._matrix)
if matrix is not None:
# transform all bands
dims = []
for dim in range(image.shape[2]):
dims.append(_warp_fast(image[..., dim], matrix,
output_shape=output_shape,
order=order, mode=mode, cval=cval))
out = np.dstack(dims)
if orig_ndim == 2:
out = out[..., 0]
return out
if output_shape is None:
output_shape = ishape
rows, cols = output_shape[:2]
def coord_map(*args):
return inverse_map(*args, **map_args)
coords = warp_coords(coord_map, (rows, cols, bands))
# Prefilter not necessary for order 1 interpolation
prefilter = order > 1
mapped = ndimage.map_coordinates(image, coords, prefilter=prefilter,
mode=mode, order=order, cval=cval)
# The spline filters sometimes return results outside [0, 1],
# so clip to ensure valid data
clipped = np.clip(mapped, 0, 1)
if mode == 'constant' and not (0 <= cval <= 1):
clipped[mapped == cval] = cval
# Remove singleton dim introduced by atleast_3d
return clipped.squeeze()
def _swirl_mapping(xy, center, rotation, strength, radius):
x, y = xy.T
skimage/transform/_project.pyx → skimage/transform/_warps_cy.pyx
+9 -9
View File
@@ -33,7 +33,7 @@ cdef inline _matrix_transform(double x, double y, double* H, double *x_,
y_[0] = yy / zz
def homography(np.ndarray image, np.ndarray H, output_shape=None, int order=1,
def _warp_fast(np.ndarray image, np.ndarray H, output_shape=None, int order=1,
mode='constant', double cval=0):
"""Projective transformation (homography).
@@ -71,7 +71,7 @@ def homography(np.ndarray image, np.ndarray H, output_shape=None, int order=1,
Order of interpolation::
* 0: Nearest-neighbour interpolation.
* 1: Bilinear interpolation (default).
mode : {'constant', 'mirror', 'wrap'}
mode : {'constant', 'reflect', 'wrap'}
How to handle values outside the image borders.
cval : string
Used in conjunction with mode 'C' (constant), the value
@@ -82,18 +82,18 @@ def homography(np.ndarray image, np.ndarray H, output_shape=None, int order=1,
cdef np.ndarray[dtype=np.double_t, ndim=2, mode="c"] img = \
np.ascontiguousarray(image, dtype=np.double)
cdef np.ndarray[dtype=np.double_t, ndim=2, mode="c"] M = \
np.ascontiguousarray(np.linalg.inv(H))
np.ascontiguousarray(H)
if mode not in ('constant', 'wrap', 'mirror'):
if mode not in ('constant', 'wrap', 'reflect'):
raise ValueError("Invalid mode specified. Please use "
"`constant`, `wrap` or `mirror`.")
"`constant`, `wrap` or `reflect`.")
cdef char mode_c
if mode == 'constant':
mode_c = ord('C')
elif mode == 'wrap':
mode_c = ord('W')
elif mode == 'mirror':
mode_c = ord('M')
elif mode == 'reflect':
mode_c = ord('R')
cdef int out_r, out_c
if output_shape is None:
@@ -116,9 +116,9 @@ def homography(np.ndarray image, np.ndarray H, output_shape=None, int order=1,
_matrix_transform(tfc, tfr, <double*>M.data, &c, &r)
if order == 0:
out[tfr, tfc] = nearest_neighbour(<double*>img.data, rows,
cols, r, c, mode_c)
cols, r, c, mode_c, cval)
elif order == 1:
out[tfr, tfc] = bilinear_interpolation(<double*>img.data, rows,
cols, r, c, mode_c)
cols, r, c, mode_c, cval)
return out
skimage/transform/setup.py
+2 -2
View File
@@ -14,12 +14,12 @@ def configuration(parent_package='', top_path=None):
config.add_data_dir('tests')
cython(['_hough_transform.pyx'], working_path=base_path)
cython(['_project.pyx'], working_path=base_path)
cython(['_warps_cy.pyx'], working_path=base_path)
config.add_extension('_hough_transform', sources=['_hough_transform.c'],
include_dirs=[get_numpy_include_dirs()])
config.add_extension('_project', sources=['_project.c'],
config.add_extension('_warps_cy', sources=['_warps_cy.c'],
include_dirs=[get_numpy_include_dirs(), '../_shared'])
return config
skimage/transform/tests/test_warps.py
+9 -7
View File
@@ -2,7 +2,7 @@ from numpy.testing import assert_array_almost_equal, run_module_suite
import numpy as np
from scipy.ndimage import map_coordinates
from skimage.transform import (warp, warp_coords, fast_homography,
from skimage.transform import (warp, warp_coords,
AffineTransform,
ProjectiveTransform,
SimilarityTransform)
@@ -55,11 +55,12 @@ def test_fast_homography():
H[:2, 2] = [tx, ty]
tform = ProjectiveTransform(H)
coords = warp_coords(tform.inverse, (img.shape[0], img.shape[1]))
for order in range(2):
for mode in ('constant', 'mirror', 'wrap'):
p0 = warp(img, tform.inverse, mode=mode, order=order)
p1 = fast_homography(img, H, mode=mode, order=order)
for mode in ('constant', 'reflect', 'wrap'):
p0 = map_coordinates(img, coords, mode=mode, order=order)
p1 = warp(img, tform, mode=mode, order=order)
# import matplotlib.pyplot as plt
# f, (ax0, ax1, ax2, ax3) = plt.subplots(1, 4)
@@ -85,8 +86,9 @@ def test_swirl():
def test_const_cval_out_of_range():
img = np.random.randn(100, 100)
warped = warp(img, AffineTransform(translation=(10, 10)), cval=-10)
assert np.sum(warped < 0) == (2 * 100 * 10 - 10 * 10)
cval = - 10
warped = warp(img, AffineTransform(translation=(10, 10)), cval=cval)
assert np.sum(warped == cval) == (2 * 100 * 10 - 10 * 10)
def test_warp_identity():
@@ -107,7 +109,7 @@ def test_warp_coords_example():
image = data.lena().astype(np.float32)
assert 3 == image.shape[2]
tform = SimilarityTransform(translation=(0, -10))
coords = warp_coords(30, 30, 3, tform)
coords = warp_coords(tform, (30, 30, 3))
warped_image1 = map_coordinates(image[:, :, 0], coords[:2])