def fit_spheroid_shape_pearson(img, msk, diameter_a, diameter_c, phi, intensity, wavelength, pixel_size, detector_distance, full_output=False, x0=0, y0=0, detector_adu_photon=1, detector_quantum_efficiency=1, material='water', rmax=None, downsampling=1, do_brute_evals=0, maxfev=1000, do_photon_counting=False, deltab=0.5, force_prolate=True):
"""
Fit the shape of a spheroid using pearson correlation.
"""
Xmc, Ymc, img, msk = _prepare_for_fitting(img, msk, x0, y0, rmax, downsampling, detector_adu_photon, do_photon_counting, pixel_size, detector_distance)
diameter = (diameter_a**2*diameter_c)**(1/3.)
S = sphere_model_convert_intensity_to_scaling(intensity, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, 1, material)
size = lambda d: sphere_model_convert_diameter_to_size(d, wavelength, pixel_size, detector_distance)
I_fit_m = lambda da,dc,p: I_spheroid_diffraction(S,Xmc,Ymc,size(da),size(dc),0.,p)
def E_fit_m(p):
if not (img[msk].std() and I_fit_m(p[0],p[1],p[2]).std()): return numpy.ones(len(p))
else: return 1-scipy.stats.pearsonr(I_fit_m(p[0],p[1],p[2]),img[msk])[0]*numpy.ones(len(p))
# Start with brute force with a sensible range
# We'll assume at least 20x oversampling
if do_brute_evals:
dmin = sphere_model_convert_size_to_diameter(1./(downsampling*img.shape[0]), wavelength, pixel_size, detector_distance)
dmax = dmin*downsampling*img.shape[0]/20
pmin = 0.
pmax = numpy.pi
Ns = do_brute_evals
diameter = scipy.optimize.brute(E_fit_m, [(dmin, dmax),(dmin,dmax),(pmin,pmax)], Ns=Ns)[0]
# End with least square
p0 = numpy.array([diameter_a,diameter_c,phi])
p, cov, infodict, mesg, ier = leastsq(E_fit_m, p0, maxfev=maxfev, xtol=1e-5, full_output=True)
[diameter_a, diameter_c, phi] = p
diameter_a = abs(diameter_a)
diameter_c = abs(diameter_c)
phi = phi % numpy.pi
if force_prolate and diameter_a > diameter_c:
return fit_spheroid_shape_pearson(img, msk, diameter_c, diameter_a, phi+numpy.pi/2., intensity, wavelength, pixel_size, detector_distance, full_output,
x0, y0, detector_adu_photon, detector_quantum_efficiency, material, rmax, downsampling, do_brute_evals, maxfev, do_photon_counting, deltab)
# Reduced Chi-squared and standard error
chisquared = ((I_fit_m(diameter_a, diameter_c, phi) - img[msk])**2).sum()/(img.shape[0]*img.shape[1] - 1)
if cov is not None:
pcov = cov[0,0]*chisquared
else:
pcov = None
if full_output:
infodict['error'] = chisquared
infodict['pcov'] = pcov
return diameter_a, diameter_c, phi, infodict
else:
return diameter_a, diameter_c, phi
def fit_spheroid_intensity_pixelwise(img, msk, diameter_a, diameter_c, phi, intensity, wavelength, pixel_size, detector_distance, full_output=False, x0=0, y0=0, detector_adu_photon=1, detector_quantum_efficiency=1, material='water', rmax=None, downsampling=1, maxfev=1000, do_photon_counting=False):
"""
Fit the intensity [J / m^2] on a spheroid to diffraction data using least square optimization.
The cost function is defined as a pixelwise comparison between model and data.
usage:
======
intensity = fit_spheroid_intensity(img, msk, diameter_a, diameter_c, phi, intensity, pixel_size, detector_distance)
intensity, info = fit_spheroid_intensity(img, msk, diameter_a, diameter_c, phi, intensity, pixel_size, detector_distance, full_output=True)
intensity, info = fit_spheroid_intensity(img, msk, diameter_a, diameter_c, phi, intensity, pixel_size, detector_distance, full_output=True, x0=0, y0=0, adup=1, queff=1, material='water', rmax=None, downsampling=1, maxfev=1000)
Parameters:
===========
...
"""
Xmc, Ymc, img, msk = _prepare_for_fitting(img, msk, x0, y0, rmax, downsampling, detector_adu_photon, do_photon_counting, pixel_size, detector_distance)
size_a = sphere_model_convert_diameter_to_size(diameter_a, wavelength, pixel_size, detector_distance)
size_c = sphere_model_convert_diameter_to_size(diameter_c, wavelength, pixel_size, detector_distance)
diameter = (diameter_a**2*diameter_c)**(1/3.)
scaling = lambda i: sphere_model_convert_intensity_to_scaling(i, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, 1, material)
I_fit_m = lambda i: I_spheroid_diffraction(scaling(i),Xmc,Ymc,size_a,size_c,0.,phi)
E_fit_m = lambda i: I_fit_m(i) - img[msk]
#print(E_fit_m(intensity))
if len(img[msk]):
[intensity], cov, infodict, mesg, ier = leastsq(E_fit_m, intensity, maxfev=maxfev, xtol=1e-3, full_output=True)
# Reduced Chi-squared and standard error
chisquared = (E_fit_m(intensity)**2).sum()/(img.shape[0]*img.shape[1] - 1)
if cov is not None:
pcov = cov[0,0]*chisquared
else:
pcov = None
else:
infodict={}
pcov = None
chisquared = 0
if full_output:
infodict['error'] = chisquared
infodict['pcov'] = pcov
return intensity, infodict
else:
return intensity
def fit_full_spheroid_model(img, msk, diameter_a, diameter_c, phi, intensity, wavelength, pixel_size, detector_distance, full_output=False, x0=0, y0=0, detector_adu_photon=1., detector_quantum_efficiency=1., material='water', rmax=None, downsampling=1, maxfev=1000, deltab=0.2, do_photon_counting=False,n=1):
diameter_a = max(diameter_a, 1.E-9)
diameter_c = max(diameter_c, 1.E-9)
#intensity = max(intensity,1.)
#x0 = min(x0, img.shape[1])
#y0 = min(y0, img.shape[0])
for i in range(n):
Xm, Ym, img, msk = _prepare_for_fitting(img, msk, x0, y0, rmax, downsampling, detector_adu_photon, do_photon_counting, pixel_size, detector_distance)
size = lambda d: sphere_model_convert_diameter_to_size(d, wavelength, pixel_size, detector_distance)
d = lambda da,dc: (da**2*dc)**(1/3.)
scaling = lambda i,da,dc: sphere_model_convert_intensity_to_scaling(i, d(da,dc), wavelength, pixel_size, detector_distance, detector_quantum_efficiency, 1, material)
I_fit_m = lambda dx,dy,da,dc,p,i: I_spheroid_diffraction(scaling(i,da,dc), Xm-dx, Ym-dy, size(da), size(dc), 0., p)
E_fit_m = lambda p: I_fit_m(p[0],p[1],p[2],p[3],p[4],p[5]) - img[msk]
p0 = numpy.array([0,0,diameter_a,diameter_c,phi,intensity])
x0_bound = (None, None)
y0_bound = (None, None)
d_a_bound = ((1-deltab)*diameter_a, (1+deltab)*diameter_a)
d_c_bound = ((1-deltab)*diameter_c, (1+deltab)*diameter_c)
p_bound = (None, None)
i_bound = (None, None)
bounds = numpy.array([x0_bound, y0_bound , d_a_bound, d_c_bound, p_bound, i_bound])
p, cov, info, mesg, ier = spimage.leastsqbound(E_fit_m, p0, maxfev=maxfev, xtol=1e-5, full_output=True, bounds=bounds)
[dx0, dy0, diameter_a, diameter_c, phi, intensity] = p
diameter_a = abs(diameter_a)
diameter_c = abs(diameter_c)
x0 += dx0
y0 += dy0
phi = phi % numpy.pi
if (numpy.isfinite(p) == False).sum() > 0:
break
# Reduced Chi-squared and standard errors
chisquared = (E_fit_m(p)**2).sum()/(img.shape[0]*img.shape[1] - len(p))
#print(cov)
if cov is not None:
pcov = numpy.diag(cov)*chisquared
else:
pcov = numpy.array(len(p)*[None])
if full_output:
info["error"] = chisquared
info["pcov"] = pcov
return x0, y0, diameter_a, diameter_c, phi, intensity, info
else:
return x0, y0, diameter_a, diameter_c, phi, intensity
def fit_spheroid_shape_pearson(img,
msk,
diameter_a,
diameter_c,
phi,
intensity,
wavelength,
pixel_size,
detector_distance,
full_output=False,
x0=0,
y0=0,
detector_adu_photon=1,
detector_quantum_efficiency=1,
material='water',
rmax=None,
downsampling=1,
do_brute_evals=0,
maxfev=1000,
do_photon_counting=False,
deltab=0.5,
force_prolate=True):
"""
Fit the shape of a spheroid using pearson correlation.
"""
Xmc, Ymc, img, msk = _prepare_for_fitting(img, msk, x0, y0, rmax,
downsampling,
detector_adu_photon,
do_photon_counting, pixel_size,
detector_distance)
diameter = (diameter_a**2 * diameter_c)**(1 / 3.)
S = sphere_model_convert_intensity_to_scaling(intensity, diameter,
wavelength, pixel_size,
detector_distance,
detector_quantum_efficiency,
1, material)
size = lambda d: sphere_model_convert_diameter_to_size(
d, wavelength, pixel_size, detector_distance)
I_fit_m = lambda da, dc, p: I_spheroid_diffraction(S, Xmc, Ymc, size(da),
size(dc), 0., p)
def E_fit_m(p):
if not (img[msk].std() and I_fit_m(p[0], p[1], p[2]).std()):
return numpy.ones(len(p))
else:
return 1 - scipy.stats.pearsonr(I_fit_m(p[0], p[1], p[2]),
img[msk])[0] * numpy.ones(len(p))
# Start with brute force with a sensible range
# We'll assume at least 20x oversampling
if do_brute_evals:
dmin = sphere_model_convert_size_to_diameter(
1. / (downsampling * img.shape[0]), wavelength, pixel_size,
detector_distance)
dmax = dmin * downsampling * img.shape[0] / 20
pmin = 0.
pmax = numpy.pi
Ns = do_brute_evals
diameter = scipy.optimize.brute(E_fit_m, [(dmin, dmax), (dmin, dmax),
(pmin, pmax)],
Ns=Ns)[0]
# End with least square
p0 = numpy.array([diameter_a, diameter_c, phi])
p, cov, infodict, mesg, ier = leastsq(E_fit_m,
p0,
maxfev=maxfev,
xtol=1e-5,
full_output=True)
[diameter_a, diameter_c, phi] = p
diameter_a = abs(diameter_a)
diameter_c = abs(diameter_c)
phi = phi % numpy.pi
if force_prolate and diameter_a > diameter_c:
return fit_spheroid_shape_pearson(
img, msk, diameter_c, diameter_a, phi + numpy.pi / 2., intensity,
wavelength, pixel_size, detector_distance, full_output, x0, y0,
detector_adu_photon, detector_quantum_efficiency, material, rmax,
downsampling, do_brute_evals, maxfev, do_photon_counting, deltab)
# Reduced Chi-squared and standard error
chisquared = ((I_fit_m(diameter_a, diameter_c, phi) - img[msk])**
2).sum() / (img.shape[0] * img.shape[1] - 1)
if cov is not None:
pcov = cov[0, 0] * chisquared
else:
pcov = None
if full_output:
infodict['error'] = chisquared
infodict['pcov'] = pcov
return diameter_a, diameter_c, phi, infodict
else:
return diameter_a, diameter_c, phi
def fit_full_spheroid_model(img,
msk,
diameter_a,
diameter_c,
phi,
intensity,
wavelength,
pixel_size,
detector_distance,
full_output=False,
x0=0,
y0=0,
detector_adu_photon=1.,
detector_quantum_efficiency=1.,
material='water',
rmax=None,
downsampling=1,
maxfev=1000,
deltab=0.2,
do_photon_counting=False,
n=1):
diameter_a = max(diameter_a, 1.E-9)
diameter_c = max(diameter_c, 1.E-9)
#intensity = max(intensity,1.)
#x0 = min(x0, img.shape[1])
#y0 = min(y0, img.shape[0])
for i in range(n):
Xm, Ym, img, msk = _prepare_for_fitting(img, msk, x0, y0, rmax,
downsampling,
detector_adu_photon,
do_photon_counting, pixel_size,
detector_distance)
size = lambda d: sphere_model_convert_diameter_to_size(
d, wavelength, pixel_size, detector_distance)
d = lambda da, dc: (da**2 * dc)**(1 / 3.)
scaling = lambda i, da, dc: sphere_model_convert_intensity_to_scaling(
i, d(da, dc), wavelength, pixel_size, detector_distance,
detector_quantum_efficiency, 1, material)
I_fit_m = lambda dx, dy, da, dc, p, i: I_spheroid_diffraction(
scaling(i, da, dc), Xm - dx, Ym - dy, size(da), size(dc), 0., p)
E_fit_m = lambda p: I_fit_m(p[0], p[1], p[2], p[3], p[4], p[5]) - img[
msk]
p0 = numpy.array([0, 0, diameter_a, diameter_c, phi, intensity])
x0_bound = (None, None)
y0_bound = (None, None)
d_a_bound = ((1 - deltab) * diameter_a, (1 + deltab) * diameter_a)
d_c_bound = ((1 - deltab) * diameter_c, (1 + deltab) * diameter_c)
p_bound = (None, None)
i_bound = (None, None)
bounds = numpy.array(
[x0_bound, y0_bound, d_a_bound, d_c_bound, p_bound, i_bound])
p, cov, info, mesg, ier = spimage.leastsqbound(E_fit_m,
p0,
maxfev=maxfev,
xtol=1e-5,
full_output=True,
bounds=bounds)
[dx0, dy0, diameter_a, diameter_c, phi, intensity] = p
diameter_a = abs(diameter_a)
diameter_c = abs(diameter_c)
x0 += dx0
y0 += dy0
phi = phi % numpy.pi
if (numpy.isfinite(p) == False).sum() > 0:
break
# Reduced Chi-squared and standard errors
chisquared = (E_fit_m(p)**2).sum() / (img.shape[0] * img.shape[1] - len(p))
#print(cov)
if cov is not None:
pcov = numpy.diag(cov) * chisquared
else:
pcov = numpy.array(len(p) * [None])
if full_output:
info["error"] = chisquared
info["pcov"] = pcov
return x0, y0, diameter_a, diameter_c, phi, intensity, info
else:
return x0, y0, diameter_a, diameter_c, phi, intensity
def fit_spheroid_intensity_pixelwise(img,
msk,
diameter_a,
diameter_c,
phi,
intensity,
wavelength,
pixel_size,
detector_distance,
full_output=False,
x0=0,
y0=0,
detector_adu_photon=1,
detector_quantum_efficiency=1,
material='water',
rmax=None,
downsampling=1,
maxfev=1000,
do_photon_counting=False):
"""
Fit the intensity [J / m^2] on a spheroid to diffraction data using least square optimization.
The cost function is defined as a pixelwise comparison between model and data.
usage:
======
intensity = fit_spheroid_intensity(img, msk, diameter_a, diameter_c, phi, intensity, pixel_size, detector_distance)
intensity, info = fit_spheroid_intensity(img, msk, diameter_a, diameter_c, phi, intensity, pixel_size, detector_distance, full_output=True)
intensity, info = fit_spheroid_intensity(img, msk, diameter_a, diameter_c, phi, intensity, pixel_size, detector_distance, full_output=True, x0=0, y0=0, adup=1, queff=1, material='water', rmax=None, downsampling=1, maxfev=1000)
Parameters:
===========
...
"""
Xmc, Ymc, img, msk = _prepare_for_fitting(img, msk, x0, y0, rmax,
downsampling,
detector_adu_photon,
do_photon_counting, pixel_size,
detector_distance)
size_a = sphere_model_convert_diameter_to_size(diameter_a, wavelength,
pixel_size,
detector_distance)
size_c = sphere_model_convert_diameter_to_size(diameter_c, wavelength,
pixel_size,
detector_distance)
diameter = (diameter_a**2 * diameter_c)**(1 / 3.)
scaling = lambda i: sphere_model_convert_intensity_to_scaling(
i, diameter, wavelength, pixel_size, detector_distance,
detector_quantum_efficiency, 1, material)
I_fit_m = lambda i: I_spheroid_diffraction(scaling(i), Xmc, Ymc, size_a,
size_c, 0., phi)
E_fit_m = lambda i: I_fit_m(i) - img[msk]
#print(E_fit_m(intensity))
if len(img[msk]):
[intensity], cov, infodict, mesg, ier = leastsq(E_fit_m,
intensity,
maxfev=maxfev,
xtol=1e-3,
full_output=True)
# Reduced Chi-squared and standard error
chisquared = (E_fit_m(intensity)**
2).sum() / (img.shape[0] * img.shape[1] - 1)
if cov is not None:
pcov = cov[0, 0] * chisquared
else:
pcov = None
else:
infodict = {}
pcov = None
chisquared = 0
if full_output:
infodict['error'] = chisquared
infodict['pcov'] = pcov
return intensity, infodict
else:
return intensity
