def create_sphere(size,
radius=-1,
sigma=0,
num_sigma=2,
center=None,
gpu=False):
"""Create a 3D sphere volume.
@param size: size of the resulting volume.
@param radius: radius of the sphere inside the volume.
@param sigma: sigma of the Gaussian.
@param center: center of the sphere.
@return: sphere inside a volume.
"""
if size.__class__ == float or len(size) == 1:
size = (size, size, size)
assert len(size) == 3
if center is None:
center = [size[0] // 2, size[1] // 2, size[2] // 2]
if radius == -1:
radius = xp.min(size) // 2
sphere = xp.zeros(size, dtype=xp.float32)
[x, y, z] = xp.mgrid[0:size[0], 0:size[1], 0:size[2]]
r = xp.sqrt((x - center[0])**2 + (y - center[1])**2 + (z - center[2])**2)
sphere[r <= radius] = 1
if sigma > 0:
ind = xp.logical_and(r > radius, r < radius + num_sigma * sigma)
sphere[ind] = xp.exp(-((r[ind] - radius) / sigma)**2 / 2)
return sphere
def add_noise(data, snr=0.1, m=0):
"""Add gaussian noise to the given volume.
@param data: input volume.
@param snr: SNR of the added noise.
@param m: mean of the added noise.
@return The image with gaussian noise
"""
vs = xp.var(data)
vn = vs / snr
sd = xp.sqrt(vn)
s = xp.ndarray(data.shape)
noise = sd * standard_normal(s.shape) + m
t = data + noise
return t
def circle_filter(sizeX, sizeY, radiusCutoff):
"""
circleFilter: NEEDS Documentation
@param sizeX: NEEDS Documentation
@param sizeY: NEEDS Documentation
@param radiusCutoff: NEEDS Documentation
"""
X, Y = xp.meshgrid(
xp.arange(-sizeX // 2 + sizeX % 2, sizeX // 2 + sizeX % 2),
xp.arange(-sizeY // 2 + sizeY % 2, sizeY // 2 + sizeY % 2))
R = xp.sqrt(X**2 + Y**2)
filter = xp.zeros((sizeX, sizeY), dtype=xp.float32)
filter[R <= radiusCutoff] = 1
return filter
def ellipse_filter(sizeX, sizeY, radiusCutoffX, radiusCutoffY):
"""
circleFilter: NEEDS Documentation
@param sizeX: NEEDS Documentation
@param sizeY: NEEDS Documentation
@param radiusCutoff: NEEDS Documentation
"""
X, Y = xp.meshgrid(
xp.arange(-sizeY // 2 + sizeY % 2, sizeY // 2 + sizeY % 2),
xp.arange(-sizeX // 2 + sizeX % 2, sizeX // 2 + sizeX % 2))
R = xp.sqrt((X / radiusCutoffX)**2 + (Y / radiusCutoffY)**2)
filter = xp.zeros((sizeX, sizeY), dtype=xp.float32)
#print(filter.shape, R.shape)
filter[R <= 1] = 1
return filter
def invert_WedgeSum(invol, r_max=None, lowlimit=0., lowval=0.):
"""
invert wedge sum - avoid division by zero and boost of high frequencies
@param invol: input volume
@type invol: L{pytom_volume.vol} or L{pytom_volume.vol_comp}
@param r_max: radius
@type r_max: L{int}
@param lowlimit: lower limit - all values below this value that lie in the specified radius will be replaced \
by lowval
@type lowlimit: L{float}
@param lowval: replacement value
@type lowval: L{float}
@author: FF
"""
from math import sqrt
if not r_max:
r_max = invol.shape[1] // 2 - 1
dx, dy, dz = invol.shape
if dz != dx:
X, Y, Z = xp.meshgrid(xp.arange(-dx // 2, dx // 2 + dx % 2),
xp.arange(-dy // 2, dy // 2 + dy % 2),
xp.arange(0, dz))
invol = xp.fft.fftshift(invol, axes=(0, 1))
else:
X, Y, Z = xp.meshgrid(xp.arange(-dx // 2, dx // 2 + dx % 2),
xp.arange(-dy // 2, dy // 2 + dy % 2),
xp.arange(-dz // 2, dz // 2 + dz % 2))
R = xp.sqrt(X**2 + Y**2 + Z**2).astype(xp.int32)
invol_out = invol.copy().astype(xp.float32)
invol_out[invol < lowlimit] = lowval
invol_out = 1. / invol_out
invol_out[R >= r_max] = 0
if dx != dz:
invol_out = xp.fft.fftshift(invol_out, axes=(0, 1))
return invol_out
def norm_inside_mask(inp, mask):
"""
To normalise a 2D array within a mask
@param inp: A 2D array to be normalized.
@type inp: numpy array 2D
@param mask: A 2D array of the same size as the input to mask of parts of the ixp.
@type mask: numpy array 2D
@return: A normalized 2D array.
@returntype: numpy array 2D
@requires: the shape of inp to be equal to the shape of the mask
"""
# assert ixp.shape == mask.shape
# assert len(ixp.shape) == 2
mea = xp.divide(xp.sum(xp.multiply(inp, mask)), xp.sum(mask))
st = xp.sqrt(
xp.sum((xp.multiply(mask, mea) + xp.multiply(inp, mask) - mea)**2) /
xp.sum(mask))
return xp.multiply((inp - mea) / st, mask)
def profile2FourierVol(profile, dim=None, reduced=False):
"""
create Volume from 1d radial profile, e.g., to modulate signal with \
specific function such as CTF or FSC. Simple linear interpolation is used\
for sampling.
@param profile: profile
@type profile: 1-d L{pytom_volume.vol} or 1-d python array
@param dim: dimension of (cubic) output
@type dim: L{int}
@param reduced: If true reduced Fourier representation (N/2+1, N, N) is generated.
@type reduced: L{bool}
@return: 3-dim complex volume with spherically symmetrical profile
@rtype: L{pytom_volume.vol}
@author: FF
"""
if dim is None:
try:
dim = [
2 * profile.shape[0],
] * 3
except:
dim = [
2 * len(profile),
] * 3
is3D = (len(dim) == 3)
nx, ny = dim[:2]
if reduced:
if is3D:
nz = int(dim[2] // 2) + 1
else:
ny = int(ny // 2) + 1
else:
if is3D:
nz = dim[2]
try:
r_max = profile.shape[0] - 1
except:
r_max = len(profile) - 1
if len(dim) == 3:
if reduced:
X, Y, Z = xp.meshgrid(xp.arange(-nx // 2, nx // 2 + nx % 2),
xp.arange(-ny // 2, ny // 2 + ny % 2),
xp.arange(0, nz))
else:
X, Y, Z = xp.meshgrid(xp.arange(-nx // 2, nx // 2 + nx % 2),
xp.arange(-ny // 2, ny // 2 + ny % 2),
xp.arange(-nz // 2, nz // 2 + nz % 2))
R = xp.sqrt(X**2 + Y**2 + Z**2)
else:
if reduced:
X, Y = xp.meshgrid(xp.arange(-nx // 2, ny // 2 + ny % 2),
xp.arange(0, ny))
else:
X, Y = xp.meshgrid(xp.arange(-nx // 2, nx // 2 + nx % 2),
xp.arange(-ny // 2, ny // 2 + ny % 2))
R = xp.sqrt(X**2 + Y**2)
IR = xp.floor(R).astype(xp.int64)
valIR_l1 = IR.copy()
valIR_l2 = valIR_l1 + 1
val_l1, val_l2 = xp.zeros_like(X, dtype=xp.float64), xp.zeros_like(
X, dtype=xp.float64)
l1 = R - IR.astype(xp.float32)
l2 = 1 - l1
try:
profile = xp.array(profile)
except:
import numpy
profile = xp.array(numpy.array(profile))
for n in xp.arange(r_max):
val_l1[valIR_l1 == n] = profile[n]
val_l2[valIR_l2 == n + 1] = profile[n + 1]
val_l1[IR == r_max] = profile[n + 1]
val_l2[IR == r_max] = profile[n + 1]
val_l1[R > r_max] = 0
val_l2[R > r_max] = 0
fkernel = l2 * val_l1 + l1 * val_l2
if reduced:
fkernel = xp.fft.fftshift(fkernel, axes=(0, 1))
else:
fkernel = xp.fft.fftshift(fkernel)
return fkernel
def create_asymmetric_wedge(angle1,
angle2,
cutoffRadius,
sizeX,
sizeY,
sizeZ,
smooth,
rotation=None):
'''This function returns an asymmetric wedge object.
@param angle1: angle of wedge1 in degrees
@type angle1: int
@param angle2: angle of wedge2 in degrees
@type angle2: int
@param cutOffRadius: radius from center beyond which the wedge is set to zero.
@type cutOffRadius: int
@param sizeX: the size of the box in x-direction.
@type sizeX: int
@param sizeY: the size of the box in y-direction.
@type sizeY: int
@param sizeZ: the size of the box in z-direction.
@type sizeZ: int
@param smooth: smoothing parameter that defines the amount of smoothing at the edge of the wedge.
@type smooth: float
@return: 3D array determining the wedge object.
@rtype: ndarray of xp.float64'''
range_angle1Smooth = smooth / xp.sin(angle1 * xp.pi / 180.)
range_angle2Smooth = smooth / xp.sin(angle2 * xp.pi / 180.)
wedge = xp.zeros((sizeX, sizeY, sizeZ // 2 + 1))
if rotation is None:
z, y, x = xp.meshgrid(
xp.arange(-sizeX // 2 + sizeX % 2, sizeX // 2 + sizeX % 2),
xp.arange(-sizeY // 2 + sizeY % 2, sizeY // 2 + sizeY % 2),
xp.arange(0, sizeZ // 2 + 1))
else:
cx, cy, cz = [s // 2 for s in (sizeX, sizeY, sizeZ)]
grid = xp.mgrid[-cx:sizeX - cx, -cy:sizeY - cy, :sizeZ // 2 + 1]
phi, the, psi = rotation
phi = -float(phi) * xp.pi / 180.0
the = -float(the) * xp.pi / 180.0
psi = -float(psi) * xp.pi / 180.0
sin_alpha = xp.sin(phi)
cos_alpha = xp.cos(phi)
sin_beta = xp.sin(the)
cos_beta = xp.cos(the)
sin_gamma = xp.sin(psi)
cos_gamma = xp.cos(psi)
# Calculate inverse rotation matrix
Inv_R = xp.zeros((3, 3), dtype='float32')
Inv_R[0, 0] = cos_alpha * cos_gamma - cos_beta * sin_alpha \
* sin_gamma
Inv_R[0, 1] = -cos_alpha * sin_gamma - cos_beta * sin_alpha \
* cos_gamma
Inv_R[0, 2] = sin_beta * sin_alpha
Inv_R[1, 0] = sin_alpha * cos_gamma + cos_beta * cos_alpha \
* sin_gamma
Inv_R[1, 1] = -sin_alpha * sin_gamma + cos_beta * cos_alpha \
* cos_gamma
Inv_R[1, 2] = -sin_beta * cos_alpha
Inv_R[2, 0] = sin_beta * sin_gamma
Inv_R[2, 1] = sin_beta * cos_gamma
Inv_R[2, 2] = cos_beta
temp = grid.reshape((3, grid.size // 3))
temp = xp.dot(Inv_R, temp)
grid = xp.reshape(temp, grid.shape)
y = grid[0, :, :, :]
z = grid[1, :, :, :]
x = grid[2, :, :, :]
r = xp.sqrt(x**2 + y**2 + z**2)
wedge[xp.tan(angle1 * xp.pi / 180) < y / x] = 1
wedge[xp.tan(-angle2 * xp.pi / 180) > y / x] = 1
wedge[sizeX // 2, :, 0] = 1
if smooth:
area = xp.abs(x -
(y / xp.tan(angle1 * xp.pi / 180))) <= range_angle1Smooth
strip = 1 - (xp.abs(x - (y / xp.tan(angle1 * xp.pi / 180.))) *
xp.sin(angle1 * xp.pi / 180.) / smooth)
wedge += (strip * area * (1 - wedge) * (y > 0))
area2 = xp.abs(x +
(y /
xp.tan(angle2 * xp.pi / 180))) <= range_angle2Smooth
strip2 = 1 - (xp.abs(x + (y / xp.tan(angle2 * xp.pi / 180.))) *
xp.sin(angle2 * xp.pi / 180.) / smooth)
wedge += (strip2 * area2 * (1 - wedge) * (y <= 0))
wedge[r > cutoffRadius] = 0
return xp.fft.fftshift(wedge, axes=(0, 1))
def weightedXCF(volume, reference, numberOfBands, wedgeAngle=-1, gpu=False):
"""
weightedXCF: Determines the weighted correlation function for volume and reference
@param volume: A volume
@param reference: A reference
@param numberOfBands:Number of bands
@param wedgeAngle: A optional wedge angle
@return: The weighted correlation function
@rtype: L{pytom_volume.vol}
@author: Thomas Hrabe
@todo: does not work yet -> test is disabled
"""
if gpu:
import cupy as xp
else:
import numpy as xp
from pytom.tompy.correlation import bandCF
from pytom.tompy.transforms import fourier_reduced2full
from math import sqrt
import pytom_freqweight
result = xp.zeros_like(volume)
q = 0
if wedgeAngle >= 0:
wedgeFilter = pytom_freqweight.weight(wedgeAngle, 0, volume.sizeX(),
volume.sizeY(), volume.sizeZ())
wedgeVolume = wedgeFilter.getWeightVolume(True)
else:
wedgeVolume = xp.ones_like(volume)
w = xp.sqrt(1 / float(volume.size))
numberVoxels = 0
for i in range(numberOfBands):
"""
notation according Steward/Grigorieff paper
"""
band = [0, 0]
band[0] = i * volume.shape[0] / numberOfBands
band[1] = (i + 1) * volume.shape[0] / numberOfBands
r = bandCF(volume, reference, band, gpu=gpu)
cc = r[0]
filter = r[1]
#get bandVolume
bandVolume = filter.getWeightVolume(True)
filterVolumeReduced = bandVolume * wedgeVolume
filterVolume = fourier_reduced2full(filterVolumeReduced)
#determine number of voxels != 0
N = filterVolume[abs(filterVolume) < 1].sum()
#add to number of total voxels
numberVoxels = numberVoxels + N
cc2 = r[0].copy()
cc2 = cc2**2
cc = shiftscale(cc, w, 1)
ccdiv = cc2 / (cc)
ccdiv = ccdiv**3
#abs(ccdiv); as suggested by grigorief
ccdiv = shiftscale(ccdiv, 0, N)
result = result + ccdiv
result = shiftscale(result, 0, 1 / float(numberVoxels))
return result
def weightedXCC(volume, reference, numberOfBands, wedgeAngle=-1, gpu=False):
"""
weightedXCC: Determines the band weighted correlation coefficient for a volume and reference. Notation according Steward/Grigorieff paper
@param volume: A volume
@type volume: L{pytom_volume.vol}
@param reference: A reference of same size as volume
@type reference: L{pytom_volume.vol}
@param numberOfBands: Number of bands
@param wedgeAngle: A optional wedge angle
@return: The weighted correlation coefficient
@rtype: float
@author: Thomas Hrabe
"""
if gpu:
import cupy as xp
else:
import numpy as xp
from pytom.tompy.transform import fft, fourier_reduced2full
from pytom.basic.structures import WedgeInfo
result = 0
numberVoxels = 0
#volume.write('vol.em');
#reference.write('ref.em');
wedge = WedgeInfo(wedgeAngle)
wedgeVolume = wedge.returnWedgeVolume(volume.shape[0], volume.shape[1],
volume.shape[2])
increment = int(volume.shape[0] / 2 * 1 / numberOfBands)
band = [0, 100]
for i in range(0, volume.shape[0] / 2, increment):
band[0] = i
band[1] = i + increment
r = bandCC(volume, reference, band, gpu=gpu)
cc = r[0]
#print cc;
filter = r[1]
#get bandVolume
bandVolume = filter.getWeightVolume(True)
filterVolumeReduced = bandVolume * wedgeVolume
filterVolume = fourier_reduced2full(filterVolumeReduced)
#determine number of voxels != 0
N = (filterVolume != 0).sum()
w = xp.sqrt(1 / float(N))
#add to number of total voxels
numberVoxels = numberVoxels + N
#print 'w',w;
#print 'cc',cc;
#print 'N',N;
cc2 = cc * cc
#print 'cc2',cc2;
if cc <= 0.0:
cc = cc2
else:
cc = cc2 / (cc + w)
#print 'cc',cc;
cc = cc * cc * cc
#no abs
#print 'cc',cc;
#add up result
result = result + cc * N
return result * (1 / float(numberVoxels))
def bandCC(volume, reference, band, verbose=False, shared=None, index=None):
"""
bandCC: Determines the normalised correlation coefficient within a band
@param volume: The volume
@type volume: L{pytom_volume.vol}
@param reference: The reference
@type reference: L{pytom_volume.vol}
@param band: [a,b] - specify the lower and upper end of band.
@return: First parameter - The correlation of the two volumes in the specified band.
Second parameter - The bandpass filter used.
@rtype: List - [float,L{pytom_freqweight.weight}]
@author: Thomas Hrabe
"""
if not index is None: print(index)
from pytom.tompy.filter import bandpass
from pytom.tompy.correlation import xcf
#from pytom.tompy.filter import vol_comp
if verbose:
print('lowest freq : ', band[0], ' highest freq', band[1])
vf, m = bandpass(volume,
band[0],
band[1],
returnMask=True,
fourierOnly=True)
rf = bandpass(reference, band[0], band[1], mask=m,
fourierOnly=True) #,vf[1])
#ccVolume = vol_comp(rf[0].shape[0],rf[0].shape[1],rf[0].shape[2])
#ccVolume.copyVolume(rf[0])
vf = vf.astype(xp.complex128)
ccVolume = rf.astype(vf.dtype)
ccVolume = ccVolume * xp.conj(vf)
#pytom_volume.conj_mult(ccVolume,vf[0])
cc = ccVolume.sum()
cc = cc.real
v = vf
r = rf
absV = xp.abs(v)
absR = xp.abs(r)
sumV = xp.sum(absV**2)
sumR = xp.sum(absR**2)
sumV = xp.abs(sumV)
sumR = xp.abs(sumR)
if sumV == 0:
sumV = 1
if sumR == 0:
sumR = 1
cc = cc / (xp.sqrt(sumV * sumR))
#numerical errors will be punished with nan
if abs(cc) > 1.1:
cc = float('nan')
return float(cc)
def randomizePhaseBeyondFreq(volume, frequency):
'''This function randomizes the phases beyond a given frequency, while preserving the Friedel symmetry.
@param volume: target volume
@type volume: 3d ndarray
@param frequency: frequency in pixel beyond which phases are randomized.
@type frequency: int
@return: 3d volume.
@rtype: 3d ndarray
@author: GvdS'''
from numpy.fft import ifftn, fftshift, fftn, rfftn, irfftn
from numpy import angle, abs, exp, meshgrid, arange, sqrt, pi, rot90
threeD = len(volume.shape) == 3
twoD = len(volume.shape) == 2
if not twoD and not threeD:
raise Exception(
'Invalid volume dimensions: either supply 3D or 2D ndarray')
if twoD:
dx, dy = volume.shape
else:
dx, dy, dz = volume.shape
ft = xp.fft.rfftn(volume)
phase = xp.angle(ft)
amplitude = xp.abs(ft)
rnda = generate_random_phases_3d(
amplitude.shape,
reduced_complex=True) # (ranf((dx,dy,dz//2+1)) * pi * 2) - pi
if twoD:
X, Y = xp.meshgrid(xp.arange(-dx // 2, dx // 2 + dx % 2),
xp.arange(-dy // 2, dy // 2 + dy % 2))
RF = xp.sqrt(X**2 + Y**2).astype(int)
R = xp.fft.fftshift(RF)[:, :dy // 2 + 1]
else:
X, Y, Z = xp.meshgrid(xp.arange(-dx // 2, dx // 2),
xp.arange(-dy // 2, dy // 2),
xp.arange(-dz // 2, dz // 2))
RF = xp.sqrt(X**2 + Y**2 + Z**2) # .astype(int)
R = xp.fft.fftshift(RF)[:, :, :dz // 2 + 1]
# centralslice = fftshift(rnda[:,:,0])
# cc = dx//2
# ccc= (dx-1)//2
# centralslice[cc, cc-ccc:cc] = centralslice[cc,-ccc:][::-1]*-1
# centralslice[cc-ccc:cc,cc-ccc:] = rot90(centralslice[-ccc:,cc-ccc:],2)*-1
# rnda[:,:,0] = fftshift(centralslice)
rnda[R <= frequency] = 0
phase[R > frequency] = 0
phase += rnda
image = xp.fft.irfftn((amplitude * xp.exp(1j * phase)), s=volume.shape)
if xp.abs(image.imag).sum() > 1E-8:
raise Exception(
'Imaginary part is non-zero. Failed to centro-summetrize the phases.'
)
return image.real
