def distanceOfShifts(self, oldAlignmentList):
"""
distanceOfShifts: Determines distance of current shifts from previous shifts
@param oldAlignmentList:
"""
from pytom.tools.maths import euclidianDistance, listMean, listStd
distance = []
numberResults = len(self)
oldListXML = oldAlignmentList.toXML()
for i in xrange(0, numberResults):
newResult = self[i]
particle = newResult.getParticle()
try:
oldResultXML = oldListXML.xpath(
'/AlignmentList/Result/Particle[@Filename="' +
particle.getFilename() + '"]/..')
oldResult = MaximisationResult()
oldResult.fromXML(oldResultXML[0])
except:
numberResults = numberResults - 1
continue
newShift = newResult.getShift()
oldShift = oldResult.getShift()
d = euclidianDistance(newShift.toVector(), oldShift.toVector())
distance.append(d)
return [listMean(distance), listStd(distance)]
def vector2euler(vec, reference_vec=[0,0,1]):
"""Transform a vector to an Euler angle representation.
Or: find the Euler angle to rotate the reference vector to the given vector.
Note there are infinite possible ways to do this, since the inplane rotation is not specified.
"""
from pytom.tools.maths import euclidianDistance
if(euclidianDistance(vec, [0,0,0]) == 0):
raise RuntimeError("Vector length should be bigger than 0!")
if(euclidianDistance(vec, reference_vec) == 0):
from pytom.basic.structures import Rotation
return Rotation(0,0,0)
import numpy as np
vec = vec/np.linalg.norm(vec)
axis = np.cross(reference_vec, vec)
angle = np.math.acos(np.dot(vec, reference_vec))
mat = axisAngleToMat(axis, angle, True)
rotation = matToZXZ(mat)
return rotation
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
shifty = np.random.randint(-offset, offset)
shiftz = np.random.randint(-offset, offset)
# first rotate and then shift
v2 = fourier_rotate_vol(v, [phi, psi, the])
v2 = shift(v2, shiftx, shifty, shiftz, 'spline')
# add some noise
v2 = add(v2, 0.01)
# finally apply the wedge
v2 = wedge.apply(v2)
t = Timing()
# frm_match
t.start()
pos, ang = frm_align_vol(v2, [-60, 60], v, [8, 32], 10)
t1 = t.end()
dist_old = rotation_distance([phi, psi, the], ang)
diff_old.append(dist_old)
total_time1 += t1
print euclidianDistance([
shiftx + v.sizeX() / 2, shifty + v.sizeY() / 2, shiftz + v.sizeZ() / 2
], pos), dist_old
print
print np.mean(diff_old)
print total_time1 / 100
from frm import frm_align_vol
from pytom.tools.maths import rotation_distance, euclidianDistance
from pytom.tools.timing import Timing
t = Timing()
t.start()
dis_offset = []
ang_offset = []
for pp in pl:
v = read(pp.getFilename())
pos, ang, score = frm_align_vol(v, [-60.0, 60.0], r, [8, 32], 10)
g_pos = pp.getShift().toVector()
g_pos = [g_pos[0] + 50, g_pos[1] + 50, g_pos[2] + 50]
g_ang = [
pp.getRotation().getZ1(),
pp.getRotation().getZ2(),
pp.getRotation().getX()
]
dis_offset.append(euclidianDistance(g_pos, pos))
ang_offset.append(rotation_distance(g_ang, ang))
print euclidianDistance(g_pos, pos), rotation_distance(g_ang, ang)
tt = t.end()
import numpy as np
print tt / 100, np.mean(dis_offset), np.mean(ang_offset)
def frm_align_vol_rscore(vf, wf, vg, wg, b, radius=None, mask=None, peak_offset=None, weights=None, position=None):
"""Obsolete.
"""
from pytom_volume import vol, rotateSpline, peak
from pytom.basic.transformations import shift
from pytom.basic.correlation import xcf
from pytom.basic.filter import lowpassFilter
from pytom.basic.structures import Mask
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 mask is None:
mask = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(mask, vf.sizeX()/2, 0,0, vf.sizeX()/2,vf.sizeY()/2,vf.sizeZ()/2)
elif mask.__class__ == vol:
pass
elif mask.__class__ == Mask:
mask = mask.getVolume()
elif isinstance(mask, int):
mask_radius = mask
mask = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(mask, mask_radius, 0,0, vf.sizeX()/2,vf.sizeY()/2,vf.sizeZ()/2)
else:
raise RuntimeError('Given mask has wrong type!')
if peak_offset is None:
peak_offset = vol(vf.sizeX(), vf.sizeY(), vf.sizeZ())
initSphere(peak_offset, vf.sizeX()/2, 0,0, vf.sizeX()/2,vf.sizeY()/2,vf.sizeZ()/2)
elif isinstance(peak_offset, 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
vf = vf*mask
# # normalize them first
# from pytom.basic.normalise import mean0std1
# mean0std1(vf)
# mean0std1(vg)
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
orientations = frm_determine_orientation_rscore(vf, wf, vg, wg, b, radius, weights)
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, 'spline')
res = frm_fourier_adaptive_wedge_vol_rscore(vf2, wf, vg, wg, b, radius, weights)
orientation, max_value = frm_find_best_angle_interp(res)
return position, orientation, max_value
# iteratively refine the position & orientation
from pytom.basic.structures import WedgeInfo
from pytom.tools.maths import euclidianDistance
max_iter = 10 # maximal number of iterations
wedge = WedgeInfo([90+wf[0], 90-wf[1]])
old_pos = [-1, -1, -1]
vg2 = vol(vg.sizeX(), vg.sizeY(), vg.sizeZ())
lowpass_vf = lowpassFilter(vf, radius, 0)[0]
for i in range(max_iter):
peak_value = 0.0
position = None
for orientation in orientations:
orientation = orientation[0]
rotateSpline(vg, vg2, orientation[0], orientation[1], orientation[2]) # first rotate
vg2 = wedge.apply(vg2) # then apply the wedge
vg2 = lowpassFilter(vg2, radius, 0)[0]
res = xcf(lowpass_vf, vg2) # find the position
pos = peak(res, peak_offset)
# val = res(pos[0], pos[1], pos[2])
pos, val = find_subpixel_peak_position(vol2npy(res), pos)
if val > peak_value:
position = pos
peak_value = val
if euclidianDistance(position, old_pos) <= 1.0:
break
else:
old_pos = position
# 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, -position[0]+vf.sizeX()/2, -position[1]+vf.sizeY()/2, -position[2]+vf.sizeZ()/2, 'fourier')
res = frm_fourier_adaptive_wedge_vol_rscore(vf2, wf, vg, wg, b, radius, weights)
orientations = frm_find_topn_angles_interp(res)
return position, orientations[0][0], orientations[0][1]