1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
|
# coding: utf-8
# /*##########################################################################
# Copyright (C) 2017 European Synchrotron Radiation Facility
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
#
# ############################################################################*/
"""
This module contains utilitary functions for tomography
"""
__author__ = ["P. Paleo"]
__license__ = "MIT"
__date__ = "12/09/2017"
import numpy as np
from math import pi
from silx.math.fit import leastsq
def rescale_intensity(img, from_subimg=None, percentiles=None):
"""
clamp intensity into the [2, 98] percentiles
:param img:
:param from_subimg:
:param percentiles:
:return: the rescale intensity
"""
if percentiles is None:
percentiles = [2, 98]
else:
assert type(percentiles) in (tuple, list)
assert(len(percentiles) == 2)
data = from_subimg if from_subimg is not None else img
imin, imax = np.percentile(data, percentiles)
res = np.clip(img, imin, imax)
return res
def calc_center_corr(sino, fullrot=False, props=1):
"""
Compute a guess of the Center of Rotation (CoR) of a given sinogram.
The computation is based on the correlation between the line projections at
angle (theta = 0) and at angle (theta = 180).
Note that for most scans, the (theta=180) angle is not included,
so the CoR might be underestimated.
In a [0, 360[ scan, the projection angle at (theta=180) is exactly in the
middle for odd number of projections.
:param numpy.ndarray sino: Sinogram
:param bool fullrot: optional. If False (default), the scan is assumed to
be [0, 180).
If True, the scan is assumed to be [0, 380).
:param int props: optional. Number of propositions for the CoR
"""
n_a, n_d = sino.shape
first = 0
last = -1 if not(fullrot) else n_a // 2
proj1 = sino[first, :]
proj2 = sino[last, :][::-1]
# Compute the correlation in the Fourier domain
proj1_f = np.fft.fft(proj1, 2 * n_d)
proj2_f = np.fft.fft(proj2, 2 * n_d)
corr = np.abs(np.fft.ifft(proj1_f * proj2_f.conj()))
if props == 1:
pos = np.argmax(corr)
if pos > n_d // 2:
pos -= n_d
return (n_d + pos) / 2.
else:
corr_argsorted = np.argsort(corr)[:props]
corr_argsorted[corr_argsorted > n_d // 2] -= n_d
return (n_d + corr_argsorted) / 2.
def _sine_function(t, offset, amplitude, phase):
"""
Helper function for calc_center_centroid
"""
n_angles = t.shape[0]
res = amplitude * np.sin(2 * pi * (1. / (2 * n_angles)) * t + phase)
return offset + res
def _sine_function_derivative(t, params, eval_idx):
"""
Helper function for calc_center_centroid
"""
offset, amplitude, phase = params
n_angles = t.shape[0]
w = 2.0 * pi * (1. / (2.0 * n_angles)) * t + phase
grad = (1.0, np.sin(w), amplitude*np.cos(w))
return grad[eval_idx]
def calc_center_centroid(sino):
"""
Compute a guess of the Center of Rotation (CoR) of a given sinogram.
The computation is based on the computation of the centroid of each
projection line, which should be a sine function according to the
Helgason-Ludwig condition.
This method is unlikely to work in local tomography.
:param numpy.ndarray sino: Sinogram
"""
n_a, n_d = sino.shape
# Compute the vector of centroids of the sinogram
i = np.arange(n_d)
centroids = np.sum(sino*i, axis=1)/np.sum(sino, axis=1)
# Fit with a sine function : phase, amplitude, offset
# Using non-linear Levenberg–Marquardt algorithm
angles = np.linspace(0, n_a, n_a, True)
# Initial parameter vector
cmax, cmin = centroids.max(), centroids.min()
offs = (cmax + cmin) / 2.
amp = (cmax - cmin) / 2.
phi = 1.1
p0 = (offs, amp, phi)
constraints = np.zeros((3, 3))
popt, _ = leastsq(model=_sine_function,
xdata=angles,
ydata=centroids,
p0=p0,
sigma=None,
constraints=constraints,
model_deriv=None,
epsfcn=None,
deltachi=None,
full_output=0,
check_finite=True,
left_derivative=False,
max_iter=100)
return popt[0]
|