def sag_fine_grained_alignment(vf,
wf,
vg,
wg,
max_freq,
ang=[0, 0, 0],
loc=[0, 0, 0],
mask=None,
B,
alpha,
maxIter,
lambda1):
"""SAG-based fine-grained alignment between experimental data and reference data.
Parameters
vf: Experimental data
pytom_volume.vol
wf: Mask of vf in Fourier space.
pytom.basic.structures.Wedge. If none, no missing wedge.
vg: Reference data
pytom_volume.vol
wg: Mask of vg in Fourier space.
pytom.basic.structures.Wedge. If none, no missing wedge.
max_freq: Maximal frequency involved in calculation.
Integer.
ang: Initial rotation angle
loc: Initial translation value
mask: Mask volume in real space.
pytom_volume.vol
B: Batch number
alpha: Step size
maxIter: The max iteration number
lambda1: Regularization parameter
Returns
-------
(Optimal rotation angle and translation value.
(best_translation, best_rotation, correlation_score)
"""
from pytom_volume import vol, rotateSpline, peak, sum, power
from pytom.basic.transformations import shift
from pytom.basic.filter import lowpassFilter
from pytom.basic.structures import Mask, SingleTiltWedge, Rotation
from pytom_volume import initSphere
from pytom_numpy import vol2npy
import math
import random
if vf.sizeX() != vg.sizeX() or vf.sizeY() != vg.sizeY() or vf.sizeZ(
) != vg.sizeZ():
raise RuntimeError('Two volumes must have the same size!')
if wf is None:
wf = SingleTiltWedge(0)
else:
vf = wf.apply(vf)
if wg is None:
wg = SingleTiltWedge(0)
else:
vg = wg.apply(vg)
if mask is None:
m = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(m,
vf.sizeX() / 2, 0, 0,
vf.sizeX() / 2,
vf.sizeY() / 2,
vf.sizeZ() / 2)
mask = m
old_value = -1
max_pos = [-1, -1, -1]
max_ang = None
max_value = -1.0
ang_epsilon = np.ones(3) * (math.pi * (1.0 / 180))
loc_epsilon = np.ones(3) * 1.0
n = vf.sizeX()
vf0_n = vol2npy(vf)
if maxIter is None:
maxIter = n / 2
iVals = np.int32(np.ceil((n - B) * np.random.random(maxIter)))
if lambda1 is None:
lambda1 = 1 / n
eps = np.finfo(np.float32).eps
Lmax = 0.25 * np.max(np.sum(vf0_n**2)) + lambda1
if alpha is None:
alpha = 1 / Lmax
d = np.zeros(6)
g = np.zeros([n, 6])
covered = np.int32(np.zeros(n))
nCovered = 0
grad = np.zeros(6)
deri = np.zeros(6)
vg2 = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
mask2 = vol(mask.sizeX(), mask.sizeY(), mask.sizeZ())
for i in range(n):
if (covered[i] != 0):
nCovered += 1
for k in range(maxIter):
i = iVals[k] - 1
if k == 0:
rotateSpline(vg, vg2, ang[0], ang[1], ang[2])
rotateSpline(mask, mask2, ang[0], ang[1], ang[2])
vg2 = wf.apply(vg2)
vg2 = lowpassFilter(vg2, max_freq, max_freq / 10.)[0]
vg2_s = transform_single_vol(vg2, mask2)
vf2 = shift(vf,
-loc[0] + vf.sizeX() / 2,
-loc[1] + vf.sizeY() / 2,
-loc[2] + vf.sizeZ() / 2,
imethod='spline')
vf2 = lowpassFilter(vf2, max_freq, max_freq / 10.)[0]
vf2 = wg.apply(vf2, Rotation(ang))
vf2_s = transform_single_vol(vf2, mask2)
i = 0
ri = np.sum(
vol2npy(vf2_s)[i:i + B, :, :] - vol2npy(vg2_s)[i:i + B, :, :])
vg2_p = vol(n, n, n)
vg2_m = vol(n, n, n)
mask2_p = vol(n, n, n)
mask2_m = vol(n, n, n)
for dim_i in range(3):
if abs(ang_epsilon[dim_i]) > eps:
ang_epsilon_t = np.zeros(3)
ang_epsilon_t[dim_i] = ang_epsilon[dim_i]
angle = ang + ang_epsilon_t
rotateSpline(vg, vg2_p, angle[0], angle[1], angle[2])
rotateSpline(mask, mask2_p, angle[0], angle[1], angle[2])
vg2_p = wf.apply(vg2_p)
vg2_p = lowpassFilter(vg2_p, max_freq, max_freq / 10.)[0]
vg2_pf = transform_single_vol(vg2_p, mask2_p)
angle = ang - ang_epsilon_t
rotateSpline(vg, vg2_m, angle[0], angle[1], angle[2])
rotateSpline(mask, mask2_m, angle[0], angle[1], angle[2])
vg2_m = wf.apply(vg2_m)
vg2_m = lowpassFilter(vg2_m, max_freq, max_freq / 10.)[0]
vg2_mf = transform_single_vol(vg2_m, mask2_m)
vg2_ang_deri = (vg2_pf - vg2_mf) / (2 * ang_epsilon[dim_i])
vg2_ang_deri_n = vol2npy(vg2_ang_deri)
deri[dim_i] = np.sum(vg2_ang_deri_n[i:i + B, :, :])
del vg2_pf, vg2_mf, vg2_ang_deri, vg2_ang_deri_n, angle
del vg2_p, vg2_m, mask2_p, mask2_m
vf1_ps = vol(n, n, n)
vf1_ms = vol(n, n, n)
ang_f = [ang[0], ang[1], ang[2]]
for dim_i in range(3):
if abs(loc_epsilon[dim_i]) > eps:
loc_epsilon_t = np.zeros(3)
loc_epsilon_t[dim_i] = ang_epsilon[dim_i]
vf1_ps.copyVolume(vf)
vf1_ms.copyVolume(vf)
loc_r = loc + loc_epsilon_t
vf1_tp = shift(vf1_ps, -loc_r[0] + vf1_ps.sizeX() / 2,
-loc_r[1] + vf1_ps.sizeY() / 2,
-loc_r[2] + vf1_ps.sizeZ() / 2, 'spline')
vf1_tp = lowpassFilter(vf1_tp, max_freq, max_freq / 10.)[0]
vf1_tp = wg.apply(vf1_tp, Rotation(ang_f))
loc_r = loc - loc_epsilon_t
vf1_tm = shift(vf1_ms, -loc_r[0] + vf1_ms.sizeX() / 2,
-loc_r[1] + vf1_ms.sizeY() / 2,
-loc_r[2] + vf1_ms.sizeZ() / 2, 'spline')
vf1_tm = lowpassFilter(vf1_tm, max_freq, max_freq / 10.)[0]
vf1_tm = wg.apply(vf1_tm, Rotation(ang_f))
vf1_tpf = transform_single_vol(vf1_tp, mask2)
vf1_tmf = transform_single_vol(vf1_tm, mask2)
vf1_loc_deri = (vf1_tpf - vf1_tmf) / (2 * ang_epsilon[dim_i])
vf1_loc_deri_n = vol2npy(vf1_loc_deri)
deri[dim_i + 3] = np.sum(vf1_loc_deri_n[i:i + B, :, :])
del vf1_tp, vf1_tm, vf1_tpf, vf1_tmf, vf1_loc_deri, vf1_loc_deri_n
del vf1_ps, vf1_ms, ang_f
for dim_i in range(6):
grad[dim_i] = ri * deri[dim_i] / B
for dim_i in range(6):
d[dim_i] += grad[dim_i] - np.sum(g[i:i + B, dim_i])
for dim_i in range(6):
g[i:i + B, dim_i] = grad[dim_i]
for j0 in range(i, i + B + 1):
if (covered[j0] == 0):
covered[j0] = 1
nCovered += 1
for dim_i in range(6):
opt_beta[dim_i] -= alpha * d[dim_i] / nCovered
ang = opt_beta[:3]
loc = opt_beta[3:]
rotateSpline(vg, vg2, ang[0], ang[1], ang[2])
rotateSpline(mask, mask2, ang[0], ang[1], ang[2])
vg2 = wf.apply(vg2)
vg2 = lowpassFilter(vg2, max_freq, max_freq / 10.)[0]
vg2_s = transform_single_vol(vg2, mask2)
vf2 = shift(vf,
-loc[0] + vf.sizeX() / 2,
-loc[1] + vf.sizeY() / 2,
-loc[2] + vf.sizeZ() / 2,
imethod='spline')
vf2 = lowpassFilter(vf2, max_freq, max_freq / 10.)[0]
vf2 = wg.apply(vf2, Rotation(ang))
vf2_s = transform_single_vol(vf2, mask2)
ri = np.sum(
vol2npy(vf2_s)[i:i + B, :, :] - vol2npy(vg2_s)[i:i + B, :, :])
from pytom.basic.correlation import nxcc
val = nxcc(vf2_s, vg2_s, mask)
if val > max_value:
max_pos = loc
max_ang = ang
max_value = val
if abs(max_value - old_value) <= eps:
break
else:
old_value = max_value
del vg2_s, vf2, vf2_s
del d, g, grad, deri
return max_pos, max_ang, max_value
def frm_constrained_align(vf,
wf,
vg,
wg,
b,
max_freq,
peak_offset=None,
mask=None,
constraint=None,
weights=None,
position=None,
num_seeds=5,
pytom_volume=None):
"""Find the best alignment (translation & rotation) of volume vg (reference) to match vf.
For details, please check the paper.
Parameters
----------
vf: Volume Nr. 1
pytom_volume.vol
wf: Mask of vf in Fourier space.
pytom.basic.structures.Wedge. If none, no missing wedge.
vg: Volume Nr. 2 / Reference
pytom_volume.vol
wg: Mask of vg in Fourier space.
pytom.basic.structures.Wedge. If none, no missing wedge.
b: Bandwidth range of spherical harmonics.
None -> [4, 64]
List -> [b_min, b_max]
Integer -> [b, b]
max_freq: Maximal frequency involved in calculation.
Integer.
peak_offset: The maximal offset which allows the peak of the score to be.
Or simply speaking, the maximal distance allowed to shift vg to match vf.
This parameter is needed to prevent shifting the reference volume out of the frame.
pytom_volume.vol / Integer. By default is half of the volume radius.
mask: Mask volume for vg in real space.
pytom_volume.vol
constraint: Angular constraint
sh_alignment.constrained_frm.AngularConstraint
weights: Obsolete.
position: If the translation is already known or not. If provided, no translational search will be conducted.
List: [x,y,z], default None.
num_seeds: Number of threads for the expectation maximization procedure. The more the better, yet slower.
Integer, default is 5.
Returns
-------
(The best translation and rotation (Euler angle, ZXZ convention [Phi, Psi, Theta]) to transform vg to match vf.
(best_translation, best_rotation, correlation_score)
"""
from pytom_volume import vol, rotateSpline, peak
from pytom.basic.transformations import shift
from pytom.basic.correlation import FLCF
from pytom.basic.filter import lowpassFilter
from pytom.basic.structures import Mask, SingleTiltWedge
from pytom_volume import initSphere
from pytom_numpy import vol2npy
if vf.sizeX() != vg.sizeX() or vf.sizeY() != vg.sizeY() or vf.sizeZ(
) != vg.sizeZ():
raise RuntimeError('Two volumes must have the same size!')
if wf is None:
wf = SingleTiltWedge(0)
if wg is None:
wg = SingleTiltWedge(0)
if peak_offset is None:
peak_offset = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(peak_offset,
vf.sizeX() / 4, 0, 0,
vf.sizeX() / 2,
vf.sizeY() / 2,
vf.sizeZ() / 2)
elif peak_offset.__class__ == int:
peak_radius = peak_offset
peak_offset = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(peak_offset, peak_radius, 0, 0,
vf.sizeX() / 2,
vf.sizeY() / 2,
vf.sizeZ() / 2)
elif peak_offset.__class__ == vol:
pass
else:
raise RuntimeError('Peak offset is given wrong!')
# cut out the outer part which normally contains nonsense
m = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(m,
vf.sizeX() / 2, 0, 0,
vf.sizeX() / 2,
vf.sizeY() / 2,
vf.sizeZ() / 2)
vf = vf * m
vg = vg * m
if mask is None:
mask = m
else:
vg = vg * mask
if position is None: # if position is not given, we have to find it ourself
# first roughtly determine the orientation (only according to the energy info)
# get multiple candidate orientations
numerator, denominator1, denominator2 = frm_correlate(
vf, wf, vg, wg, b, max_freq, weights, True, None, None, False)
score = numerator / (denominator1 * denominator2)**0.5
res = frm_find_topn_constrained_angles_interp(
score, num_seeds,
get_adaptive_bw(max_freq, b) / 16., constraint)
else:
# the position is given by the user
vf2 = shift(vf, -position[0] + vf.sizeX() / 2,
-position[1] + vf.sizeY() / 2,
-position[2] + vf.sizeZ() / 2, 'fourier')
score = frm_correlate(vf2, wf, vg, wg, b, max_freq, weights, ps=False)
orientation, max_value = frm_find_best_constrained_angle_interp(
score, constraint=constraint)
return position, orientation, max_value
# iteratively refine the position & orientation
from pytom.tools.maths import euclidianDistance
max_iter = 10 # maximal number of iterations
mask2 = vol(mask.sizeX(), mask.sizeY(),
mask.sizeZ()) # store the rotated mask
vg2 = vol(vg.sizeX(), vg.sizeY(), vg.sizeZ())
lowpass_vf = lowpassFilter(vf, max_freq, max_freq / 10.)[0]
max_position = None
max_orientation = None
max_value = -1.0
for i in xrange(num_seeds):
old_pos = [-1, -1, -1]
lm_pos = [-1, -1, -1]
lm_ang = None
lm_value = -1.0
orientation = res[i][0] # initial orientation
for j in xrange(max_iter):
rotateSpline(vg, vg2, orientation[0], orientation[1],
orientation[2]) # first rotate
rotateSpline(mask, mask2, orientation[0], orientation[1],
orientation[2]) # rotate the mask as well
vg2 = wf.apply(vg2) # then apply the wedge
vg2 = lowpassFilter(vg2, max_freq, max_freq / 10.)[0]
score = FLCF(lowpass_vf, vg2, mask2) # find the position
pos = peak(score, peak_offset)
pos, val = find_subpixel_peak_position(vol2npy(score), pos)
if val > lm_value:
lm_pos = pos
lm_ang = orientation
lm_value = val
if euclidianDistance(lm_pos, old_pos) <= 1.0:
# terminate this thread
if lm_value > max_value:
max_position = lm_pos
max_orientation = lm_ang
max_value = lm_value
break
else:
old_pos = lm_pos
# here we shift the target, not the reference
# if you dont want the shift to change the energy landscape, use fourier shift
vf2 = shift(vf, -lm_pos[0] + vf.sizeX() / 2,
-lm_pos[1] + vf.sizeY() / 2,
-lm_pos[2] + vf.sizeZ() / 2, 'fourier')
score = frm_correlate(vf2, wf, vg, wg, b, max_freq, weights, False,
denominator1, denominator2, True)
orientation, val = frm_find_best_constrained_angle_interp(
score, constraint=constraint)
else: # no converge after the specified iteration, still get the best result as we can
if lm_value > max_value:
max_position = lm_pos
max_orientation = lm_ang
max_value = lm_value
# print max_value # for show the convergence of the algorithm
return max_position, max_orientation, max_value
if len(sys.argv) == 1:
print(helper)
sys.exit()
try:
dir_name, name_prefix, wedge_angle, output, bHelp = parse_script_options(
sys.argv[1:], helper)
except:
sys.exit()
if bHelp is True:
print(helper)
sys.exit()
if name_prefix is None:
name_prefix = ''
wedge_angle = float(wedge_angle)
w = SingleTiltWedge(wedge_angle)
pl = ParticleList()
all_files = os.listdir(dir_name)
for fname in all_files:
p = None
name_suffix = fname.split('.')[-1]
if len(name_prefix):
if name_prefix in fname and name_suffix in ['em', 'mrc']:
p = Particle(dir_name + '/' + fname)
else:
if name_suffix in ['em', 'mrc']:
p = Particle(dir_name + '/' + fname)
if p is not None:
pl.append(p)
from pytom.tools.parse_script_options import parse_script_options
from pytom.basic.structures import ParticleList, SingleTiltWedge
helper = ScriptHelper(sys.argv[0].split('/')[-1], # script name
description='Set the same wedge to all the particles in the particle list.',
authors='Yuxiang Chen',
options=[ScriptOption(['-p'], 'Particle list', True, False),
ScriptOption(['-w'], 'Wedge Angle (degree)', True, False),
ScriptOption(['-o'], 'Output particle list', True, True),
ScriptOption(['-h', '--help'], 'Help.', False, True)])
if len(sys.argv) == 1:
print(helper)
sys.exit()
try:
pl_name, wedge_angle, output, bHelp = parse_script_options(sys.argv[1:], helper)
except:
sys.exit()
if bHelp is True:
print(helper)
sys.exit()
pl = ParticleList()
pl.fromXMLFile(pl_name)
w = SingleTiltWedge(int(wedge_angle))
pl.setWedgeAllParticles(w)
if output is None:
pl.toXMLFile(pl_name)
else:
pl.toXMLFile(output)