def get_dH2(lab1, lab2):
"""squared hue difference term occurring in deltaE_cmc and deltaE_ciede94
Despite its name, "dH" is not a simple difference of hue values. We avoid
working directly with the hue value, since differencing angles is
troublesome. The hue term is usually written as:
c1 = sqrt(a1**2 + b1**2)
c2 = sqrt(a2**2 + b2**2)
term = (a1-a2)**2 + (b1-b2)**2 - (c1-c2)**2
dH = sqrt(term)
However, this has poor roundoff properties when a or b is dominant.
Instead, ab is a vector with elements a and b. The same dH term can be
re-written as:
|ab1-ab2|**2 - (|ab1| - |ab2|)**2
and then simplified to:
2*|ab1|*|ab2| - 2*dot(ab1, ab2)
"""
a1, b1 = cp.rollaxis(lab1, -1)[1:3]
a2, b2 = cp.rollaxis(lab2, -1)[1:3]
# magnitude of (a, b) is the chroma
C1 = cp.hypot(a1, b1)
C2 = cp.hypot(a2, b2)
term = (C1 * C2) - (a1 * a2 + b1 * b2)
return 2 * term
def dot(a, b, out=None):
"""Returns a dot product of two arrays.
For arrays with more than one axis, it computes the dot product along the
last axis of ``a`` and the second-to-last axis of ``b``. This is just a
matrix product if the both arrays are 2-D. For 1-D arrays, it uses their
unique axis as an axis to take dot product over.
Args:
a (cupy.ndarray): The left argument.
b (cupy.ndarray): The right argument.
out (cupy.ndarray): Output array.
Returns:
cupy.ndarray: The dot product of ``a`` and ``b``.
.. seealso:: :func:`numpy.dot`
"""
a_ndim = a.ndim
b_ndim = b.ndim
assert a_ndim > 0 and b_ndim > 0
a_is_vec = a_ndim == 1
b_is_vec = b_ndim == 1
if a_is_vec:
a = cupy.reshape(a, (1, a.size))
a_ndim = 2
if b_is_vec:
b = cupy.reshape(b, (b.size, 1))
b_ndim = 2
a_axis = a_ndim - 1
b_axis = b_ndim - 2
if a.shape[a_axis] != b.shape[b_axis]:
raise ValueError('Axis dimension mismatch')
if a_axis:
a = cupy.rollaxis(a, a_axis, 0)
if b_axis:
b = cupy.rollaxis(b, b_axis, 0)
k = a.shape[0]
m = b.size // k
n = a.size // k
ret_shape = a.shape[1:] + b.shape[1:]
if out is None:
if a_is_vec:
ret_shape = () if b_is_vec else ret_shape[1:]
elif b_is_vec:
ret_shape = ret_shape[:-1]
else:
if out.size != n * m:
raise ValueError('Output array has an invalid size')
if not out.flags.c_contiguous:
raise ValueError('Output array must be C-contiguous')
return _tensordot_core(a, b, out, n, m, k, ret_shape)
def deltaE_cie76(lab1, lab2):
"""Euclidean distance between two points in Lab color space
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
Returns
-------
dE : array_like
distance between colors `lab1` and `lab2`
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] A. R. Robertson, "The CIE 1976 color-difference formulae,"
Color Res. Appl. 2, 7-11 (1977).
"""
L1, a1, b1 = cp.rollaxis(lab1, -1)[:3]
L2, a2, b2 = cp.rollaxis(lab2, -1)[:3]
out = (L2 - L1) * (L2 - L1)
out += (a2 - a1) * (a2 - a1)
out += (b2 - b1) * (b2 - b1)
return cp.sqrt(out, out=out)
def dot(a, b, out=None):
"""Returns a dot product of two arrays.
For arrays with more than one axis, it computes the dot product along the
last axis of ``a`` and the second-to-last axis of ``b``. This is just a
matrix product if the both arrays are 2-D. For 1-D arrays, it uses their
unique axis as an axis to take dot product over.
Args:
a (cupy.ndarray): The left argument.
b (cupy.ndarray): The right argument.
out (cupy.ndarray): Output array.
Returns:
cupy.ndarray: The dot product of ``a`` and ``b``.
.. seealso:: :func:`numpy.dot`
"""
a_ndim = a.ndim
b_ndim = b.ndim
assert a_ndim > 0 and b_ndim > 0
a_is_vec = a_ndim == 1
b_is_vec = b_ndim == 1
if a_is_vec:
a = cupy.reshape(a, (1, a.size))
a_ndim = 2
if b_is_vec:
b = cupy.reshape(b, (b.size, 1))
b_ndim = 2
a_axis = a_ndim - 1
b_axis = b_ndim - 2
if a.shape[a_axis] != b.shape[b_axis]:
raise ValueError('Axis dimension mismatch')
if a_axis:
a = cupy.rollaxis(a, a_axis, 0)
if b_axis:
b = cupy.rollaxis(b, b_axis, 0)
k = a.shape[0]
m = b.size // k
n = a.size // k
ret_shape = a.shape[1:] + b.shape[1:]
if out is None:
if a_is_vec:
ret_shape = () if b_is_vec else ret_shape[1:]
elif b_is_vec:
ret_shape = ret_shape[:-1]
else:
if out.size != n * m:
raise ValueError('Output array has an invalid size')
if not out.flags.c_contiguous:
raise ValueError('Output array must be C-contiguous')
return _tensordot_core(a, b, out, n, m, k, ret_shape)
def moments_central(image, center=None, order=3, **kwargs):
"""Calculate all central image moments up to a certain order.
The center coordinates (cr, cc) can be calculated from the raw moments as:
{``M[1, 0] / M[0, 0]``, ``M[0, 1] / M[0, 0]``}.
Note that central moments are translation invariant but not scale and
rotation invariant.
Parameters
----------
image : nD double or uint8 array
Rasterized shape as image.
center : tuple of float, optional
Coordinates of the image centroid. This will be computed if it
is not provided.
order : int, optional
The maximum order of moments computed.
Returns
-------
mu : (``order + 1``, ``order + 1``) array
Central image moments.
References
----------
.. [1] Wilhelm Burger, Mark Burge. Principles of Digital Image Processing:
Core Algorithms. Springer-Verlag, London, 2009.
.. [2] B. Jähne. Digital Image Processing. Springer-Verlag,
Berlin-Heidelberg, 6. edition, 2005.
.. [3] T. H. Reiss. Recognizing Planar Objects Using Invariant Image
Features, from Lecture notes in computer science, p. 676. Springer,
Berlin, 1993.
.. [4] https://en.wikipedia.org/wiki/Image_moment
Examples
--------
>>> image = cp.zeros((20, 20), dtype=cp.double)
>>> image[13:17, 13:17] = 1
>>> M = moments(image)
>>> centroid = (M[1, 0] / M[0, 0], M[0, 1] / M[0, 0])
>>> moments_central(image, centroid)
array([[16., 0., 20., 0.],
[ 0., 0., 0., 0.],
[20., 0., 25., 0.],
[ 0., 0., 0., 0.]])
"""
if center is None:
center = centroid(image)
calc = image.astype(float)
for dim, dim_length in enumerate(image.shape):
delta = cp.arange(dim_length, dtype=float) - center[dim]
powers_of_delta = delta[:, cp.newaxis] ** cp.arange(order + 1)
calc = cp.rollaxis(calc, dim, image.ndim)
calc = cp.dot(calc, powers_of_delta)
calc = cp.rollaxis(calc, -1, dim)
return calc
def convolve2d(in1, in2, mode='full'):
"""
note only support H * W * N * 1 convolve 2d
"""
in1 = in1.transpose(2, 3, 0, 1) # to N * C * H * W
in2 = in2.transpose(2, 3, 0, 1)
out_c, _, kh, kw = in2.shape
n, _, h, w = in1.shape
if mode == 'full':
ph, pw = kh - 1, kw - 1
out_h, out_w = h - kh + 1 + ph * 2, w - kw + 1 + pw * 2 # TODO
elif mode == 'valid':
ph, pw = 0, 0
out_h, out_w = h - kh + 1, w - kw + 1 # TODO
else:
raise NotImplementedError
y = cp.empty((n, out_c, out_h, out_w), dtype=in1.dtype)
col = im2col_gpu(in1, kh, kw, 1, 1, ph, pw)
y = cp.tensordot(col, in2, ((1, 2, 3), (1, 2, 3))).astype(in1.dtype,
copy=False)
y = cp.rollaxis(y, 3, 1)
return y.transpose(2, 3, 0, 1)
def reshape_x_cupy(
data: np.ndarray, dtype=cp.float16, hide_map_prob: float = 0.0
) -> np.ndarray:
"""
Get images from data as a list and preprocess them (using GPU).
Input:
- data: ndarray [num_examples x 6]
-dtype: numpy dtype for the output array
-hide_map_prob: Probability for removing the minimap (black square)
from the sequence of images (0<=hide_map_prob<=1)
Output:
- ndarray [num_examples * 5, num_channels, H, W]
"""
mean = cp.array([0.485, 0.456, 0.406], dtype=dtype)
std = cp.array([0.229, 0.224, 0.225], dtype=dtype)
reshaped = np.zeros((len(data) * 5, 3, 270, 480), dtype=dtype)
for i in range(0, len(data)):
black_minimap: bool = (random.random() <= hide_map_prob)
for j in range(0, 5):
img = cp.array(data[i][j], dtype=dtype)
if black_minimap: # Put a black square over the minimap
img[215:, :80] = cp.zeros((55, 80, 3), dtype=dtype)
reshaped[i * 5 + j] = cp.asnumpy(
cp.rollaxis((img / dtype(255.0)) - mean / std, 2, 0,)
)
return reshaped
def take(a, indices, axis=None, out=None):
"""Takes elements of an array at specified indices along an axis.
This is an implementation of "fancy indexing" at single axis.
This function does not support ``mode`` option.
Args:
a (cupy.ndarray): Array to extract elements.
indices (int or array-like): Indices of elements that this function
takes.
axis (int): The axis along which to select indices. The flattened input
is used by default.
out (cupy.ndarray): Output array. If provided, it should be of
appropriate shape and dtype.
Returns:
cupy.ndarray: The result of fancy indexing.
.. seealso:: :func:`numpy.take`
"""
if axis is None:
a = a.ravel()
lshape = ()
rshape = ()
else:
if axis >= a.ndim:
raise ValueError('Axis overrun')
lshape = a.shape[:axis]
rshape = a.shape[axis + 1:]
if numpy.isscalar(indices):
a = cupy.rollaxis(a, axis)
if out is None:
return a[indices].copy()
else:
out[:] = a[indices]
return out
elif not isinstance(indices, cupy.ndarray):
indices = cupy.array(indices, dtype=int)
out_shape = lshape + indices.shape + rshape
if out is None:
out = cupy.empty(out_shape, dtype=a.dtype)
else:
if out.dtype != a.dtype:
raise TypeError('Output dtype mismatch')
if out.shape != out_shape:
raise ValueError('Output shape mismatch')
cdim = indices.size
rdim = internal.prod(rshape)
indices = cupy.reshape(
indices, (1,) * len(lshape) + indices.shape + (1,) * len(rshape))
return _take_kernel(a, indices, cdim, rdim, out)
def calc_single_view(ioperand, subscript):
"""Calculates 'ii->i' by cupy.diagonal if needed.
Args:
ioperand (cupy.ndarray): Array to be calculated diagonal.
subscript (str):
Specifies the subscripts. If the same label appears
more than once, calculate diagonal for those axes.
"""
if '@' in subscript:
assert subscript.count('@') == 1
assert ioperand.ndim >= len(subscript) - 1
else:
assert ioperand.ndim == len(subscript)
subscripts_excluded_at = subscript.replace('@', '')
labels = set(subscripts_excluded_at)
label_to_axis = collections.defaultdict(list)
for i, label in enumerate(subscript):
label_to_axis[label].append(i)
result = ioperand
count_dict = collections.Counter(subscript)
ellipsis_pos = subscript.find('@')
for label in labels:
if count_dict[label] == 1:
continue
axes_to_diag = []
for i, char in enumerate(subscripts_excluded_at):
if char == label:
if ellipsis_pos == -1 or i < ellipsis_pos:
axes_to_diag.append(i)
else:
axes_to_diag.append(i - len(subscripts_excluded_at))
axes_to_diag = cupy.core.normalize_axis_tuple(axes_to_diag,
result.ndim)
for axis in reversed(axes_to_diag[1:]):
shape_a = result.shape[axis]
shape_b = result.shape[axes_to_diag[0]]
if shape_a != shape_b:
raise ValueError('dimensions in operand 0 for collapsing'
' index \'{0}\' don\'t match'
' ({1} != {2})'.format(label, shape_a,
shape_b))
result = result.diagonal(0, axis, axes_to_diag[0])
result = cupy.rollaxis(result, -1, axes_to_diag[0])
if ellipsis_pos != -1 and axis > ellipsis_pos:
axis -= result.ndim - len(subscript) + 1
subscript = subscript[:axis] + subscript[axis + 1:]
subscripts_excluded_at = subscript.replace('@', '')
return result, subscript
def inner(a, b):
"""Returns the inner product of two arrays.
It uses the last axis of each argument to take sum product.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
Returns:
cupy.ndarray: The inner product of ``a`` and ``b``.
.. seealso:: :func:`numpy.inner`
"""
a_ndim = a.ndim
b_ndim = b.ndim
if a_ndim == 0 or b_ndim == 0:
return cupy.multiply(a, b)
a_axis = a_ndim - 1
b_axis = b_ndim - 1
if a.shape[-1] != b.shape[-1]:
raise ValueError('Axis dimension mismatch')
if a_axis:
a = cupy.rollaxis(a, a_axis, 0)
if b_axis:
b = cupy.rollaxis(b, b_axis, 0)
ret_shape = a.shape[1:] + b.shape[1:]
k = a.shape[0]
n = a.size // k
m = b.size // k
return core.tensordot_core(a, b, None, n, m, k, ret_shape)
def inner(a, b):
"""Returns the inner product of two arrays.
It uses the last axis of each argument to take sum product.
Args:
a (cupy.ndarray): The first argument.
b (cupy.ndarray): The second argument.
Returns:
cupy.ndarray: The inner product of ``a`` and ``b``.
.. seealso:: :func:`numpy.inner`
"""
a_ndim = a.ndim
b_ndim = b.ndim
if a_ndim == 0 or b_ndim == 0:
return cupy.multiply(a, b)
a_axis = a_ndim - 1
b_axis = b_ndim - 1
if a.shape[-1] != b.shape[-1]:
raise ValueError('Axis dimension mismatch')
if a_axis:
a = cupy.rollaxis(a, a_axis, 0)
if b_axis:
b = cupy.rollaxis(b, b_axis, 0)
ret_shape = a.shape[1:] + b.shape[1:]
k = a.shape[0]
n = a.size // k
m = b.size // k
return _tensordot_core(a, b, None, n, m, k, ret_shape)
def reshape_x_cupy(
data: np.ndarray,
dtype=cp.float16,
hide_map_prob: float = 0.0,
dropout_images_prob: List[float] = None,
) -> np.ndarray:
"""
Get images from data as a list and preprocess them (using GPU).
Input:
- data: ndarray [num_examples x 6]
-dtype: numpy dtype for the output array
-hide_map_prob: Probability for removing the minimap (black square)
from the sequence of images (0<=hide_map_prob<=1)
Output:
- ndarray [num_examples * 5, num_channels, H, W]
"""
mean = cp.array([0.485, 0.456, 0.406], dtype=dtype)
std = cp.array([0.229, 0.224, 0.225], dtype=dtype)
reshaped = np.zeros(
(len(data) * 5, 3, data[0][0].shape[0], data[0][0].shape[1]),
dtype=dtype)
for i in range(0, len(data)):
black_minimap: bool = (random.random() <= hide_map_prob)
for j in range(0, 5):
black_image: bool = False
if dropout_images_prob is not None:
black_image = random.random() <= dropout_images_prob[j]
if black_image:
reshaped[i * 5 + j] = np.zeros(
(3, data[i][j].shape[0], data[i][j].shape[1]), dtype=dtype)
else:
img = cp.array(data[i][j], dtype=dtype)
if black_minimap: # Put a black square over the minimap
img[140:, :55] = cp.zeros((40, 55, 3), dtype=dtype)
reshaped[i * 5 + j] = cp.asnumpy(
cp.rollaxis(
(img / dtype(255.0)) - mean / std,
2,
0,
))
return reshaped
def reshape_x_cupy(data: np.ndarray, dtype=cp.float16) -> np.ndarray:
"""
Get images from data as a list and preprocess them (using GPU).
Input:
- data: ndarray [num_examples x 6]
-dtype: numpy dtype for the output array
from the sequence of images
Output:
- ndarray [num_examples * 5, num_channels, H, W]
"""
mean = cp.array([0.485, 0.456, 0.406], dtype=dtype)
std = cp.array([0.229, 0.224, 0.225], dtype=dtype)
reshaped = np.zeros((len(data) * 5, 3, 270, 480), dtype=dtype)
for i in range(0, len(data)):
for j in range(0, 5):
img = cp.array(data[i][j], dtype=dtype) / 255
reshaped[i * 5 + j] = cp.asnumpy(
cp.rollaxis((img - mean) / std, 2))
return reshaped
def calc_single_view(ioperand, subscript):
"""Calculates 'ii->i' by cupy.diagonal if needed.
Args:
ioperand (cupy.ndarray): Array to be calculated diagonal.
subscript (str):
Specifies the subscripts. If the same label appears
more than once, calculate diagonal for those axes.
"""
assert ioperand.ndim == len(subscript)
labels = set(subscript)
label_to_axis = collections.defaultdict(list)
for i, label in enumerate(subscript):
label_to_axis[label].append(i)
result = ioperand
count_dict = collections.Counter(subscript)
for label in labels:
if count_dict[label] == 1:
continue
axes_to_diag = []
for i, char in enumerate(subscript):
if char == label:
axes_to_diag.append(i)
for axis in reversed(axes_to_diag[1:]):
shape_a = result.shape[axis]
shape_b = result.shape[axes_to_diag[0]]
if shape_a != shape_b:
raise ValueError('dimensions in operand 0 for collapsing'
' index \'{0}\' don\'t match'
' ({1} != {2})'.format(
label, shape_a, shape_b))
result = result.diagonal(0, axis, axes_to_diag[0])
result = cupy.rollaxis(result, -1, axes_to_diag[0])
subscript = subscript[:axis] + subscript[axis + 1:]
return result, subscript
def deltaE_ciede94(lab1, lab2, kH=1, kC=1, kL=1, k1=0.045, k2=0.015):
"""Color difference according to CIEDE 94 standard
Accommodates perceptual non-uniformities through the use of application
specific scale factors (`kH`, `kC`, `kL`, `k1`, and `k2`).
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
kH : float, optional
Hue scale
kC : float, optional
Chroma scale
kL : float, optional
Lightness scale
k1 : float, optional
first scale parameter
k2 : float, optional
second scale parameter
Returns
-------
dE : array_like
color difference between `lab1` and `lab2`
Notes
-----
deltaE_ciede94 is not symmetric with respect to lab1 and lab2. CIEDE94
defines the scales for the lightness, hue, and chroma in terms of the first
color. Consequently, the first color should be regarded as the "reference"
color.
`kL`, `k1`, `k2` depend on the application and default to the values
suggested for graphic arts
========== ============== ==========
Parameter Graphic Arts Textiles
========== ============== ==========
`kL` 1.000 2.000
`k1` 0.045 0.048
`k2` 0.015 0.014
========== ============== ==========
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE94.html
"""
L1, C1 = cp.rollaxis(lab2lch(lab1), -1)[:2]
L2, C2 = cp.rollaxis(lab2lch(lab2), -1)[:2]
dL = L1 - L2
dC = C1 - C2
dH2 = get_dH2(lab1, lab2)
SL = 1
SC = 1 + k1 * C1
SH = 1 + k2 * C1
dE2 = dL / (kL * SL)
dE2 *= dE2
tmp = dC / (kC * SC)
tmp *= tmp
dE2 += tmp
tmp = kH * SH
tmp *= tmp
dE2 += dH2 / tmp
return cp.sqrt(cp.maximum(dE2, 0, out=dE2), out=dE2)
def test_each_channel():
filtered = edges_each(COLOR_IMAGE)
for i, channel in enumerate(cp.rollaxis(filtered, axis=-1)):
expected = img_as_float(filters.sobel(COLOR_IMAGE[:, :, i]))
assert_allclose(channel, expected)
def test_each_channel_with_filter_argument():
filtered = smooth_each(COLOR_IMAGE, SIGMA)
for i, channel in enumerate(cp.rollaxis(filtered, axis=-1)):
assert_allclose(channel, smooth(COLOR_IMAGE[:, :, i]))
def deltaE_ciede2000(lab1, lab2, kL=1, kC=1, kH=1):
"""Color difference as given by the CIEDE 2000 standard.
CIEDE 2000 is a major revision of CIDE94. The perceptual calibration is
largely based on experience with automotive paint on smooth surfaces.
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
kL : float (range), optional
lightness scale factor, 1 for "acceptably close"; 2 for "imperceptible"
see deltaE_cmc
kC : float (range), optional
chroma scale factor, usually 1
kH : float (range), optional
hue scale factor, usually 1
Returns
-------
deltaE : array_like
The distance between `lab1` and `lab2`
Notes
-----
CIEDE 2000 assumes parametric weighting factors for the lightness, chroma,
and hue (`kL`, `kC`, `kH` respectively). These default to 1.
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf
:DOI:`10.1364/AO.33.008069`
.. [3] M. Melgosa, J. Quesada, and E. Hita, "Uniformity of some recent
color metrics tested with an accurate color-difference tolerance
dataset," Appl. Opt. 33, 8069-8077 (1994).
"""
warnings.warn(
"The numerical accuracy of this function on the GPU is reduced "
"relative to the CPU version"
)
unroll = False
if lab1.ndim == 1 and lab2.ndim == 1:
unroll = True
if lab1.ndim == 1:
lab1 = lab1[None, :]
if lab2.ndim == 1:
lab2 = lab2[None, :]
L1, a1, b1 = cp.rollaxis(lab1, -1)[:3]
L2, a2, b2 = cp.rollaxis(lab2, -1)[:3]
# distort `a` based on average chroma
# then convert to lch coordines from distorted `a`
# all subsequence calculations are in the new coordiantes
# (often denoted "prime" in the literature)
Cbar = 0.5 * (cp.hypot(a1, b1) + cp.hypot(a2, b2))
c7 = Cbar ** 7
G = 0.5 * (1 - cp.sqrt(c7 / (c7 + 25 ** 7)))
scale = 1 + G
C1, h1 = _cart2polar_2pi(a1 * scale, b1)
C2, h2 = _cart2polar_2pi(a2 * scale, b2)
# recall that c, h are polar coordiantes. c==r, h==theta
# cide2000 has four terms to delta_e:
# 1) Luminance term
# 2) Hue term
# 3) Chroma term
# 4) hue Rotation term
# lightness term
Lbar = 0.5 * (L1 + L2)
tmp = Lbar - 50
tmp *= tmp
SL = 1 + 0.015 * tmp / cp.sqrt(20 + tmp)
L_term = (L2 - L1) / (kL * SL)
# chroma term
Cbar = 0.5 * (C1 + C2) # new coordiantes
SC = 1 + 0.045 * Cbar
C_term = (C2 - C1) / (kC * SC)
# hue term
h_diff = h2 - h1
h_sum = h1 + h2
CC = C1 * C2
dH = h_diff.copy()
dH[h_diff > np.pi] -= 2 * np.pi
dH[h_diff < -np.pi] += 2 * np.pi
dH[CC == 0.] = 0. # if r == 0, dtheta == 0
dH_term = 2 * cp.sqrt(CC) * cp.sin(dH / 2)
Hbar = h_sum.copy()
mask = cp.logical_and(CC != 0., cp.abs(h_diff) > np.pi)
Hbar[mask * (h_sum < 2 * np.pi)] += 2 * np.pi
Hbar[mask * (h_sum >= 2 * np.pi)] -= 2 * np.pi
Hbar[CC == 0.] *= 2
Hbar *= 0.5
T = (1 -
0.17 * cp.cos(Hbar - np.deg2rad(30)) +
0.24 * cp.cos(2 * Hbar) +
0.32 * cp.cos(3 * Hbar + np.deg2rad(6)) -
0.20 * cp.cos(4 * Hbar - np.deg2rad(63))
)
SH = 1 + 0.015 * Cbar * T
H_term = dH_term / (kH * SH)
# hue rotation
c7 = Cbar ** 7
Rc = 2 * cp.sqrt(c7 / (c7 + 25 ** 7))
tmp = (cp.rad2deg(Hbar) - 275) / 25
tmp *= tmp
dtheta = np.deg2rad(30) * cp.exp(-tmp)
R_term = -cp.sin(2 * dtheta) * Rc * C_term * H_term
# put it all together
dE2 = L_term * L_term
dE2 += C_term * C_term
dE2 += H_term * H_term
dE2 += R_term
cp.sqrt(cp.maximum(dE2, 0, out=dE2), out=dE2)
if unroll:
dE2 = dE2[0]
return dE2
def deltaE_cmc(lab1, lab2, kL=1, kC=1):
"""Color difference from the CMC l:c standard.
This color difference was developed by the Colour Measurement Committee
(CMC) of the Society of Dyers and Colourists (United Kingdom). It is
intended for use in the textile industry.
The scale factors `kL`, `kC` set the weight given to differences in
lightness and chroma relative to differences in hue. The usual values are
``kL=2``, ``kC=1`` for "acceptability" and ``kL=1``, ``kC=1`` for
"imperceptibility". Colors with ``dE > 1`` are "different" for the given
scale factors.
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
Returns
-------
dE : array_like
distance between colors `lab1` and `lab2`
Notes
-----
deltaE_cmc the defines the scales for the lightness, hue, and chroma
in terms of the first color. Consequently
``deltaE_cmc(lab1, lab2) != deltaE_cmc(lab2, lab1)``
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE94.html
.. [3] F. J. J. Clarke, R. McDonald, and B. Rigg, "Modification to the
JPC79 colour-difference formula," J. Soc. Dyers Colour. 100, 128-132
(1984).
"""
L1, C1, h1 = cp.rollaxis(lab2lch(lab1), -1)[:3]
L2, C2, h2 = cp.rollaxis(lab2lch(lab2), -1)[:3]
dC = C1 - C2
dL = L1 - L2
dH2 = get_dH2(lab1, lab2)
T = cp.where(cp.logical_and(cp.rad2deg(h1) >= 164, cp.rad2deg(h1) <= 345),
0.56 + 0.2 * cp.abs(np.cos(h1 + cp.deg2rad(168))),
0.36 + 0.4 * cp.abs(np.cos(h1 + cp.deg2rad(35)))
)
c1_4 = C1 ** 4
F = cp.sqrt(c1_4 / (c1_4 + 1900))
SL = cp.where(L1 < 16, 0.511, 0.040975 * L1 / (1. + 0.01765 * L1))
SC = 0.638 + 0.0638 * C1 / (1. + 0.0131 * C1)
SH = SC * (F * T + 1 - F)
dE2 = (dL / (kL * SL)) ** 2
dE2 += (dC / (kC * SC)) ** 2
dE2 += dH2 / (SH ** 2)
return cp.sqrt(cp.maximum(dE2, 0, out=dE2), out=dE2)
def percentile(a, q, axis=None, out=None, interpolation='linear',
keepdims=False):
"""Computes the q-th percentile of the data along the specified axis.
Args:
a (cupy.ndarray): Array for which to compute percentiles.
q (float, tuple of floats or cupy.ndarray): Percentiles to compute
in the range between 0 and 100 inclusive.
axis (int or tuple of ints): Along which axis or axes to compute the
percentiles. The flattened array is used by default.
out (cupy.ndarray): Output array.
interpolation (str): Interpolation method when a quantile lies between
two data points. ``linear`` interpolation is used by default.
Supported interpolations are``lower``, ``higher``, ``midpoint``,
``nearest`` and ``linear``.
keepdims (bool): If ``True``, the axis is remained as an axis of
size one.
Returns:
cupy.ndarray: The percentiles of ``a``, along the axis if specified.
.. seealso:: :func:`numpy.percentile`
"""
q = cupy.asarray(q, dtype=a.dtype)
if q.ndim == 0:
q = q[None]
zerod = True
else:
zerod = False
if q.ndim > 1:
raise ValueError('Expected q to have a dimension of 1.\n'
'Actual: {0} != 1'.format(q.ndim))
if keepdims:
if axis is None:
keepdim = (1,) * a.ndim
else:
keepdim = list(a.shape)
for ax in axis:
keepdim[ax % a.ndim] = 1
keepdim = tuple(keepdim)
# Copy a since we need it sorted but without modifying the original array
if isinstance(axis, int):
axis = axis,
if axis is None:
ap = a.flatten()
nkeep = 0
else:
# Reduce axes from a and put them last
axis = tuple(ax % a.ndim for ax in axis)
keep = set(range(a.ndim)) - set(axis)
nkeep = len(keep)
for i, s in enumerate(sorted(keep)):
a = a.swapaxes(i, s)
ap = a.reshape(a.shape[:nkeep] + (-1,)).copy()
axis = -1
ap.sort(axis=axis)
Nx = ap.shape[axis]
indices = q * 0.01 * (Nx - 1.) # percents to decimals
if interpolation == 'lower':
indices = cupy.floor(indices).astype(cupy.int32)
elif interpolation == 'higher':
indices = cupy.ceil(indices).astype(cupy.int32)
elif interpolation == 'midpoint':
indices = 0.5 * (cupy.floor(indices) + cupy.ceil(indices))
elif interpolation == 'nearest':
# TODO(hvy): Implement nearest using around
raise ValueError("'nearest' interpolation is not yet supported. "
'Please use any other interpolation method.')
elif interpolation == 'linear':
pass
else:
raise ValueError('Unexpected interpolation method.\n'
"Actual: '{0}' not in ('linear', 'lower', 'higher', "
"'midpoint')".format(interpolation))
if indices.dtype == cupy.int32:
ret = cupy.rollaxis(ap, axis)
ret = ret.take(indices, axis=0, out=out)
else:
if out is None:
ret = cupy.empty(ap.shape[:-1] + q.shape, dtype=cupy.float64)
else:
ret = cupy.rollaxis(out, 0, out.ndim)
cupy.ElementwiseKernel(
'S idx, raw T a, raw int32 offset', 'U ret',
'''
ptrdiff_t idx_below = floor(idx);
U weight_above = idx - idx_below;
ptrdiff_t offset_i = _ind.get()[0] * offset;
ret = a[offset_i + idx_below] * (1.0 - weight_above)
+ a[offset_i + idx_below + 1] * weight_above;
''',
'percentile_weightnening'
)(indices, ap, ap.shape[-1] if ap.ndim > 1 else 0, ret)
ret = cupy.rollaxis(ret, -1) # Roll q dimension back to first axis
if zerod:
ret = ret.squeeze(0)
if keepdims:
if q.size > 1:
keepdim = (-1,) + keepdim
ret = ret.reshape(keepdim)
return cupy.ascontiguousarray(ret)
def test_rollaxis_failure(self):
a = testing.shaped_arange((2, 3, 4))
with self.assertRaises(ValueError):
cupy.rollaxis(a, 3)
def _quantile_unchecked(a, q, axis=None, out=None, interpolation='linear',
keepdims=False):
if q.ndim == 0:
q = q[None]
zerod = True
else:
zerod = False
if q.ndim > 1:
raise ValueError('Expected q to have a dimension of 1.\n'
'Actual: {0} != 1'.format(q.ndim))
if keepdims:
if axis is None:
keepdim = (1,) * a.ndim
else:
keepdim = list(a.shape)
for ax in axis:
keepdim[ax % a.ndim] = 1
keepdim = tuple(keepdim)
# Copy a since we need it sorted but without modifying the original array
if isinstance(axis, int):
axis = axis,
if axis is None:
ap = a.flatten()
nkeep = 0
else:
# Reduce axes from a and put them last
axis = tuple(ax % a.ndim for ax in axis)
keep = set(range(a.ndim)) - set(axis)
nkeep = len(keep)
for i, s in enumerate(sorted(keep)):
a = a.swapaxes(i, s)
ap = a.reshape(a.shape[:nkeep] + (-1,)).copy()
axis = -1
ap.sort(axis=axis)
Nx = ap.shape[axis]
indices = q * (Nx - 1.)
if interpolation == 'lower':
indices = cupy.floor(indices).astype(cupy.int32)
elif interpolation == 'higher':
indices = cupy.ceil(indices).astype(cupy.int32)
elif interpolation == 'midpoint':
indices = 0.5 * (cupy.floor(indices) + cupy.ceil(indices))
elif interpolation == 'nearest':
# TODO(hvy): Implement nearest using around
raise ValueError('\'nearest\' interpolation is not yet supported. '
'Please use any other interpolation method.')
elif interpolation == 'linear':
pass
else:
raise ValueError('Unexpected interpolation method.\n'
'Actual: \'{0}\' not in (\'linear\', \'lower\', '
'\'higher\', \'midpoint\')'.format(interpolation))
if indices.dtype == cupy.int32:
ret = cupy.rollaxis(ap, axis)
ret = ret.take(indices, axis=0, out=out)
else:
if out is None:
ret = cupy.empty(ap.shape[:-1] + q.shape, dtype=cupy.float64)
else:
ret = cupy.rollaxis(out, 0, out.ndim)
cupy.ElementwiseKernel(
'S idx, raw T a, raw int32 offset, raw int32 size', 'U ret',
'''
ptrdiff_t idx_below = floor(idx);
U weight_above = idx - idx_below;
ptrdiff_t max_idx = size - 1;
ptrdiff_t offset_bottom = _ind.get()[0] * offset + idx_below;
ptrdiff_t offset_top = min(offset_bottom + 1, max_idx);
U diff = a[offset_top] - a[offset_bottom];
if (weight_above < 0.5) {
ret = a[offset_bottom] + diff * weight_above;
} else {
ret = a[offset_top] - diff * (1 - weight_above);
}
''',
'percentile_weightnening'
)(indices, ap, ap.shape[-1] if ap.ndim > 1 else 0, ap.size, ret)
ret = cupy.rollaxis(ret, -1) # Roll q dimension back to first axis
if zerod:
ret = ret.squeeze(0)
if keepdims:
if q.size > 1:
keepdim = (-1,) + keepdim
ret = ret.reshape(keepdim)
return _core._internal_ascontiguousarray(ret)
def test_rollaxis_failure(self):
a = testing.shaped_arange((2, 3, 4))
with self.assertRaises(ValueError):
cupy.rollaxis(a, 3)