def fast_warp(img, tf, output_shape, mode='constant', mode_cval=0, order=0):
"""Warp an image according to a given coordinate transformation.
This wrapper function is faster than skimage.transform.warp
Args:
img: `ndarray`, input image
tf: For 2-D images, you can directly pass a transformation object
e.g. skimage.transform.SimilarityTransform, or its inverse.
output_shape: tuple, (rows, cols)
mode: mode for transformation
available modes: {`constant`, `edge`, `symmetric`, `reflect`, `wrap`}
mode_cval: float, Used in conjunction with mode `constant`, the value outside the image boundaries
order: int, The order of interpolation. The order has to be in the range 0-5:
0: Nearest-neighbor
1: Bi-linear (default)
2: Bi-quadratic
3: Bi-cubic
4: Bi-quartic
5: Bi-quintic
Returns:
warped, double `ndarray`
"""
m = tf.params
t_img = np.zeros((img.shape[0], ) + output_shape, img.dtype)
for i in range(t_img.shape[0]):
t_img[i] = _warp_fast(img[i],
m,
output_shape=output_shape,
mode=mode,
cval=mode_cval,
order=order)
return t_img
def fast_warp(img, tf, output_shape, mode="constant", order=0):
"""
This wrapper function is faster than skimage.transform.warp
"""
m = tf.params
t_img = np.zeros((img.shape[0],) + output_shape, img.dtype)
for i in range(t_img.shape[0]):
t_img[i] = _warp_fast(img[i], m, output_shape=output_shape, mode=mode, order=order)
return t_img
def fast_warp(img, tf, output_shape, mode='constant', order=0):
"""
This wrapper function is faster than skimage.transform.warp
"""
m = tf.params
t_img = np.zeros((img.shape[0],) + output_shape, img.dtype)
for i in range(t_img.shape[0]):
t_img[i] = _warp_fast(img[i], m, output_shape=output_shape,
mode=mode, order=order)
return t_img
def compute_drt(img, angles=None, n_beams=600):
if (img.ndim != 2):
raise ValueError("Error: Input image must be 2D")
if (angles is None):
angles = np.arange(360) # full 360 degrees for rotational invariance
# Scale image for desired beam count
scale = n_beams / np.ceil(np.sqrt(2) * max(img.shape))
img = rescale(img, scale=scale, mode="reflect")
# Pad image (same as radon_transform.py)
diagonal = np.sqrt(2) * max(img.shape)
pad = [int(np.ceil(diagonal - s)) for s in img.shape]
new_center = [(s + p) // 2 for s, p in zip(img.shape, pad)]
old_center = [s // 2 for s in img.shape]
pad_before = [nc - oc for oc, nc in zip(old_center, new_center)]
pad_width = [(pb, p - pb) for pb, p in zip(pad_before, pad)]
padded_image = np.pad(img, pad_width, mode="constant", constant_values=0)
assert padded_image.shape[0] == padded_image.shape[
1] # assert padded image is square
# Define radon image vars
sinogram = np.zeros((padded_image.shape[0], len(angles)))
center = padded_image.shape[0] // 2
shift0 = np.array([[1, 0, -center], [0, 1, -center], [0, 0, 1]])
shift1 = np.array([[1, 0, center], [0, 1, center], [0, 0, 1]])
# Construct matrix for rotating (beam directions)
def build_rotation(angle):
T = np.deg2rad(angle)
R = np.array([[np.cos(T), np.sin(T), 0], [-np.sin(T),
np.cos(T), 0], [0, 0, 1]])
return shift1.dot(R).dot(shift0)
# Build sinogram
for i in range(len(angles)):
rotated_img = _warp_fast(padded_image, build_rotation(angles[i]))
# Compute ith angle beam sum vector, i.e. all beams on current angle
sinogram[:, i] = rotated_img.sum(0)
return sinogram
def __radon(self, image, theta=None):
if image.ndim != 2:
raise ValueError('The input image must be 2-D')
if theta is None:
raise ValueError('there is no theta in __radon!!!')
height, width = image.shape
diagonal = np.sqrt(height**2 + width**2)
heightpad = np.ceil(diagonal - height)
widthpad = np.ceil(diagonal - width)
#padding image, so whole img is visible to "rays" while rotating
padded_image = np.zeros((int(height + heightpad), int(width + widthpad)))
y0, y1 = int(np.ceil(heightpad / 2)), int((np.ceil(heightpad / 2) + height))
x0, x1 = int((np.ceil(widthpad / 2))), int((np.ceil(widthpad / 2) + width))
padded_image[y0:y1, x0:x1] = image
#plt.imshow(padded_image, cmap=plt.cm.Greys_r)
#plt.show()
if self.__firstGen:
sinogram = np.zeros((padded_image.shape[0], len(theta)))
else:
sinogram = np.zeros((self.__detNum, len(theta)))
h, w = padded_image.shape
dh, dw = h // 2, w // 2
for i in xrange(len(theta)):
# apply transformation matrix to img, requires inverse of transformation matrix
rotated = _warp_fast(padded_image, np.linalg.inv(self.__build_rotation(-theta[i], dw, dh)), mode="wrap")
#rotated = warp(padded_image, np.linalg.inv(self.__build_rotation(-theta[i], dw, dh)))
if not self.__firstGen:
sinogram[:, i] = self.__radon_view(rotated)
else:
sinogram[:, i] = rotated.sum(0)[::-1]
return sinogram
def fast_warp(img, tf, mode='constant', order=0):
m = tf.params
t_img = np.zeros(img.shape, img.dtype)
for i in range(t_img.shape[0]):
t_img[i] = _warp_fast(img[i], m, mode=mode, order=order)
return t_img
def perform(self, node, inputs, out_storage):
x, rot, shear, scale, trans, oshape = inputs
#foobar.append_ndarray_signature(x, 'AffineImageWarp x')
aff = AffineTransform(rotation=rot, shear=shear, scale=scale,
translation=trans)
if str(x.dtype) != node.inputs[0].dtype:
raise TypeError("Wrong dtype argument to AffineImageWarp", x.dtype)
if np.any(x < 0):
raise ValueError('X should be positive')
if np.any(x > 1.0):
raise ValueError('X should be less than 1')
N, C, H, W = x.shape
rows, cols = oshape
rval = out_storage[0][0]
rval_shape = (N, C, rows, cols)
if ((rval is None)
or (rval.dtype != x.dtype)
or rval.shape != rval_shape):
rval3 = np.empty((N * C, rows, cols), dtype=x.dtype)
bg_check = True
else:
rval3 = rval.reshape((N * C, rows, cols))
bg_check = False
xx = x.reshape(N * C, H, W)
# -- a small exactly-representable float for out-of-bounds pixels
oob = -1.0 / 2 ** 16
order = 1 # TODO: TRY ORDER=2 (WHY DOES RANGE GET LARGER?)
tform = np.linalg.inv(aff._matrix)
for i in xrange(N * C):
if bg_check and i == 0:
rval3[i] = _warp_fast(xx[i], tform,
output_shape=oshape, order=order,
cval=oob)
oob_ratio = np.mean(rval3[i] == oob)
if oob_ratio > 0.5:
raise InvalidDescription('too much background', oob_ratio)
rval3[i] = np.maximum(0, rval3[i])
else:
rval3[i] = _warp_fast(xx[i], np.linalg.inv(aff._matrix),
output_shape=oshape, order=order,
cval=0)
if 0 and i == 0:
print 'Debugprint from AffineImageWarp...'
for sym in 'rot', 'shear', 'scale', 'trans', 'oshape':
print sym, ':', locals()[sym]
import matplotlib.pyplot as pl
pl.subplot(2, 1, 1)
pl.imshow(xx[i], cmap=pl.cm.gray)
pl.subplot(2, 1, 2)
pl.imshow(rval3[i], cmap=pl.cm.gray)
pl.show()
time.sleep(2) # -- give some time to ctrl-C
if np.any(rval3 > 1.001) or np.any(rval3 < 0.0):
min3 = np.min(rval3)
max3 = np.max(rval3)
raise ValueError('interpolated pixel values out of range',
(min3, max3))
out_storage[0][0] = rval3.reshape(rval_shape)
def fast_warp(img, tf, mode='constant', order=0):
m = tf.params
t_img = np.zeros(img.shape, img.dtype)
for i in range(t_img.shape[0]):
t_img[i] = _warp_fast(img[i], m, mode=mode, order=order)
return t_img
def __iradon(self, radon_image, theta=None, output_size=None, fft_filter=False, filter="ramp"):
th = (np.pi / 180.0) * theta
n = radon_image.shape[0]
img = radon_image.copy()
if fft_filter: #fft filter
# resize image to next power of two for fourier analysis
# speeds up fourier and lessens artifacts
order = max(64., 2**np.ceil(np.log(2 * n) / np.log(2)))
# zero pad input image
img.resize((order, img.shape[1]))
#construct the fourier filter
f = fftshift(abs(np.mgrid[-1:1:2 / order])).reshape(-1, 1)
w = 2 * np.pi * f
# start from first element to avoid divide by zero
if filter == "ramp":
pass
elif filter == "shepp-logan":
f[1:] = f[1:] * np.sin(w[1:] / 2) / (w[1:] / 2)
elif filter == "cosine":
f[1:] = f[1:] * np.cos(w[1:] / 2)
elif filter == "hamming":
f[1:] = f[1:] * (0.54 + 0.46 * np.cos(w[1:]))
elif filter == "hann":
f[1:] = f[1:] * (1 + np.cos(w[1:])) / 2
elif filter == None:
f[1:] = 1
else:
raise ValueError("Unknown filter: %s" % filter)
filter_ft = np.tile(f, (1, len(theta)))
# apply filter in fourier domain
projection = fft(img, axis=0) * filter_ft
radon_filtered = np.real(ifft(projection, axis=0))
else: #normal filter
filter_size = 10
filter_tab = np.zeros((2*filter_size+1))
for k in xrange(-filter_size,filter_size):
if(k%2!=0):
filter_tab[k+filter_size] = -4.0 / (np.pi**2 * k**2)
filter_tab[filter_size]=1
radon_filtered = np.zeros((img.shape[0], img.shape[1]))
for i in xrange(img.shape[1]):
radon_filtered[:,i] = np.convolve(img[:,i],filter_tab, mode='same')
# resize filtered image back to original size
radon_filtered = radon_filtered[:radon_image.shape[0], :]
reconstructed = np.zeros((output_size, output_size))
mid_index = np.ceil(n / 2.0)
x = output_size
y = output_size
[X, Y] = np.mgrid[0.0:x, 0.0:y]
xpr = X - int(output_size) // 2
ypr = Y - int(output_size) // 2
# reconstruct image by interpolation
for i in xrange(len(theta)):
t = xpr * np.sin(th[i]) - ypr * np.cos(th[i])
a = np.floor(t)
b = mid_index + a
b0 = ((((b + 1 > 0) & (b + 1 < n)) * (b + 1)) - 1).astype(np.int)
b1 = ((((b > 0) & (b < n)) * b) - 1).astype(np.int)
reconstructed += (t - a) * radon_filtered[b0, i] + (a - t + 1) * radon_filtered[b1, i]
#debug
#print b0
#print i
#print b1
#plt.subplot(221)
#plt.imshow(reconstructed, cmap=plt.cm.Greys_r)
#plt.subplot(222)
#plt.imshow((t - a) * radon_filtered[b0, i], cmap=plt.cm.Greys_r)
#plt.subplot(223)
#plt.imshow((a - t + 1) * radon_filtered[b1, i], cmap=plt.cm.Greys_r)
#plt.show()
h, w = reconstructed.shape
dh, dw = h // 2, w // 2
if not self.__firstGen:
rotated = _warp_fast(reconstructed, np.linalg.inv(self.__build_rotation(90, dw, dh)))
#rotated = warp(reconstructed, np.linalg.inv(self.__build_rotation(-90, dw, dh)))
result = self.normalize_array(rotated * np.pi / (2 * len(th)) )
else:
result = self.normalize_array(reconstructed * np.pi / (2 * len(th)) )
return result
#print("A %d %d") % (result.shape[0], result.shape[1])
if(self.__firstGen==0):
scale = 1/self.__detSize * (self.__emmiterDistance + output_size+self.__detectorsDistance)/(self.__emmiterDistance + output_size/2)
#print("scale %f") % (scale)
margin = (output_size-output_size*scale)/2
if(margin != 0):
result = result[margin:-margin , margin:-margin]
#print("B %d %d") % (result.shape[0], result.shape[1])
result = rescale(result, (1/scale, 1/scale))
#print("C %d %d") % (result.shape[0], result.shape[1])
result = result[0:output_size, 0:output_size]
return result
def radon_real_geom(image, theta=None, circle=True, noise=1):
def build_rotation(theta):
T = np.deg2rad(theta)
R = np.array([[np.cos(T), np.sin(T), 0], [-np.sin(T),
np.cos(T), 0], [0, 0, 1]])
return shift1.dot(R).dot(shift0)
if image.ndim != 2:
raise ValueError('The input image must be 2-D!')
if theta is None:
theta = np.arange(180)
else:
# Pad the image so when it's rotated, nothing relevant gets cut out
diagonal = np.sqrt(2) * max(image.shape)
pad = [int(np.ceil(diagonal - s)) for s in image.shape]
new_center = [(s + p) // 2 for s, p in zip(image.shape, pad)]
old_center = [s // 2 for s in image.shape]
pad_before = [nc - oc for oc, nc in zip(old_center, new_center)]
pad_width = [(pb, p - pb) for pb, p in zip(pad_before, pad)]
padded_image = np.pad(image,
pad_width,
mode='constant',
constant_values=0)
# padded_image should be square
assert padded_image.shape[0] == padded_image.shape[1]
radon_image = np.zeros((padded_image.shape[0], len(theta)))
# For later comparison
radon_image_unaltered = np.zeros((2 * padded_image.shape[0], len(theta)))
# Upscale padded image with nearest neighbour filtering
padded_image = np.array(
Image.fromarray(padded_image).resize(
(2 * padded_image.shape[0], 2 * padded_image.shape[1])))
center = padded_image.shape[0] // 2
shift0 = np.array([[1, 0, -center], [0, 1, -center], [0, 0, 1]])
shift1 = np.array([[1, 0, center], [0, 1, center], [0, 0, 1]])
for i in range(len(theta)):
rotated = _warp_fast(padded_image, build_rotation(theta[i]))
measurement = rotated.sum(0)
# Coordinates of the projection pixels
xp = np.arange(0, np.shape(measurement)[0])
xp = xp - np.shape(measurement)[0] / 2 + 0.5
# Translate and scale coordinates
xr = (xp - np.sin(np.pi * theta[i] / 180) * np.shape(image)[0] /
2) / np.cos(np.pi * theta[i] / 180)
# Get values at new coordinates
f = interpolate.interp1d(xr,
measurement,
bounds_error=False,
fill_value=0)
measurement_new = f(xp)
# Downscale measurement_new to correct size
measurement_new = np.reshape(measurement_new,
(1, np.shape(measurement_new)[0]))
measurement_new = np.array(
Image.fromarray(measurement_new).resize(
(int(np.shape(measurement_new)[1] / 2), 1),
resample=Image.BILINEAR))
# For comparison
radon_image_unaltered[:, i] = measurement
radon_image[:, i] = measurement_new
if noise == 1:
# Add 5% measurement noise
noise = np.random.normal(1,
0.05,
size=(radon_image.shape[0],
radon_image.shape[1]))
radon_image = radon_image * noise
# Visualisation
#radon_image_unaltered = np.array(Image.fromarray(radon_image_unaltered).resize((13, 272), resample=Image.BILINEAR))
#plt.figure()
#plt.subplot(2, 1, 1)
#plt.imshow(np.transpose(radon_image_unaltered))
#plt.subplot(2, 1, 2)
#plt.imshow(np.transpose(radon_image))
return radon_image
def perform(self, node, inputs, out_storage):
x, rot, shear, scale, trans, oshape = inputs
#foobar.append_ndarray_signature(x, 'AffineImageWarp x')
aff = AffineTransform(rotation=rot,
shear=shear,
scale=scale,
translation=trans)
if str(x.dtype) != node.inputs[0].dtype:
raise TypeError("Wrong dtype argument to AffineImageWarp", x.dtype)
if np.any(x < 0):
raise ValueError('X should be positive')
if np.any(x > 1.0):
raise ValueError('X should be less than 1')
N, C, H, W = x.shape
rows, cols = oshape
rval = out_storage[0][0]
rval_shape = (N, C, rows, cols)
if ((rval is None) or (rval.dtype != x.dtype)
or rval.shape != rval_shape):
rval3 = np.empty((N * C, rows, cols), dtype=x.dtype)
bg_check = True
else:
rval3 = rval.reshape((N * C, rows, cols))
bg_check = False
xx = x.reshape(N * C, H, W)
# -- a small exactly-representable float for out-of-bounds pixels
oob = -1.0 / 2**16
order = 1 # TODO: TRY ORDER=2 (WHY DOES RANGE GET LARGER?)
tform = np.linalg.inv(aff._matrix)
for i in xrange(N * C):
if bg_check and i == 0:
rval3[i] = _warp_fast(xx[i],
tform,
output_shape=oshape,
order=order,
cval=oob)
oob_ratio = np.mean(rval3[i] == oob)
if oob_ratio > 0.5:
raise InvalidDescription('too much background', oob_ratio)
rval3[i] = np.maximum(0, rval3[i])
else:
rval3[i] = _warp_fast(xx[i],
np.linalg.inv(aff._matrix),
output_shape=oshape,
order=order,
cval=0)
if 0 and i == 0:
print 'Debugprint from AffineImageWarp...'
for sym in 'rot', 'shear', 'scale', 'trans', 'oshape':
print sym, ':', locals()[sym]
import matplotlib.pyplot as pl
pl.subplot(2, 1, 1)
pl.imshow(xx[i], cmap=pl.cm.gray)
pl.subplot(2, 1, 2)
pl.imshow(rval3[i], cmap=pl.cm.gray)
pl.show()
time.sleep(2) # -- give some time to ctrl-C
if np.any(rval3 > 1.001) or np.any(rval3 < 0.0):
min3 = np.min(rval3)
max3 = np.max(rval3)
raise ValueError('interpolated pixel values out of range',
(min3, max3))
out_storage[0][0] = rval3.reshape(rval_shape)