def fit_pps(hdu=None,
img=None,
header=None,
plot=True,
figure=pylab.figure(1),
return_profile=False,
return_gaussian_profile=False,
verbose=False):
if hdu is not None:
img = hdu[0].data
header = hdu[0].header
img[img != img] = 0
asperpix = -header['CD1_1'] * 3600.0
xx, yy = numpy.indices(img.shape)
# Try to fit, make sure fit is successful
fitloop = 1
while fitloop:
if fitloop == 1:
# this never works for no reason at all
fitpars = gaussfitter.gaussfit(
img,
params=[
0,
img.max(), img.shape[0] / 2, img.shape[1] / 2, 2, 2, 0
],
minpars=[0, img.max() / 50.0, 0, 0, 1, 1, 0],
maxpars=[0, 0, 0, 0, 6, 6, 360],
limitedmin=[False, True, False, False, True, True, True],
limitedmax=[False, False, False, False, True, True, True],
fixed=[1, 0, 0, 0, 0, 0, 0])
elif fitloop == 2:
if verbose:
print "Fitloop 1 failed: ", fitpars, ". Trying fitloop2"
fitpars = gaussfitter.gaussfit(
img,
params=[0, img.max(), 0, 0, 2, 2, 0],
minpars=[0, img.max() / 10.0, 0, 0, 1, 1, 0],
maxpars=[0, 0, 0, 0, 6, 6, 360],
limitedmin=[False, True, False, False, True, True, True],
limitedmax=[False, False, False, False, True, True, True],
fixed=[1, 0, 0, 0, 0, 0, 0],
usemoment=[0, 0, 1, 1, 0, 0, 0])
elif fitloop == 3:
if verbose:
print "Fitloop 2 failed: ", fitpars, ". Trying fitloop3"
fitpars = gaussfitter.gaussfit(
img,
minpars=[0, img.max() / 10.0, 0, 0, 1, 1, 0],
maxpars=[0, 0, 0, 0, 6, 6, 360],
limitedmin=[False, True, False, False, True, True, True],
limitedmax=[False, False, False, False, True, True, True])
elif fitloop == 4:
if verbose:
print "Fitloop 3 failed: ", fitpars, ". Trying fitloop4"
fitpars = gaussfitter.gaussfit(img)
else:
fitpars = numpy.array(gaussfitter.moments(img, 0, 1, 1))
print "Using the parameters you specified: ", fitpars
fitloop = -1
gaussim = gaussfitter.twodgaussian(fitpars)(xx, yy)
wxy = fitpars[4:6] * asperpix * numpy.sqrt(8 * numpy.log(2))
mean_fwhm = wxy.sum() / 2.0
if mean_fwhm > 70:
fitloop += 1
else: # there were other conditions before...
if 1:
if verbose:
print "Success. Fitpars: ", fitpars
fitloop = 0
else:
fitloop += 1
wcs = pywcs.WCS(header)
glon, glat = wcs.wcs_pix2sky(fitpars[2:3], fitpars[3:4], 0)
if plot:
ff = aplpy.FITSFigure(hdu, figure=figure)
ff.show_grayscale()
ff.show_circles([glon], [glat], [1. / 60.], edgecolor='r')
ff.show_circles([glon], [glat], [2. / 60.], edgecolor='b')
if return_gaussian_profile:
return azimuthalAverage(gaussim, center=fitpars[2:4], returnradii=True)
elif return_profile:
return azimuthalAverage(img, center=fitpars[2:4], returnradii=True)
else:
return glon, glat
def cross_correlation_shifts(image1,
image2,
errim1=None,
errim2=None,
maxoff=None,
verbose=False,
gaussfit=False,
return_error=False,
zeromean=True,
**kwargs):
""" Use cross-correlation and a 2nd order taylor expansion to measure the
offset between two images
Given two images, calculate the amount image2 is offset from image1 to
sub-pixel accuracy using 2nd order taylor expansion.
Parameters
----------
image1: np.ndarray
The reference image
image2: np.ndarray
The offset image. Must have the same shape as image1
errim1: np.ndarray [optional]
The pixel-by-pixel error on the reference image
errim2: np.ndarray [optional]
The pixel-by-pixel error on the offset image.
maxoff: int
Maximum allowed offset (in pixels). Useful for low s/n images that you
know are reasonably well-aligned, but might find incorrect offsets due to
edge noise
zeromean : bool
Subtract the mean from each image before performing cross-correlation?
verbose: bool
Print out extra messages?
gaussfit : bool
Use a Gaussian fitter to fit the peak of the cross-correlation?
return_error: bool
Return an estimate of the error on the shifts. WARNING: I still don't
understand how to make these agree with simulations.
The analytic estimate comes from
http://adsabs.harvard.edu/abs/2003MNRAS.342.1291Z
At high signal-to-noise, the analytic version overestimates the error
by a factor of about 1.8, while the gaussian version overestimates
error by about 1.15. At low s/n, they both UNDERestimate the error.
The transition zone occurs at a *total* S/N ~ 1000 (i.e., the total
signal in the map divided by the standard deviation of the map -
it depends on how many pixels have signal)
**kwargs are passed to correlate2d, which in turn passes them to convolve.
The available options include image padding for speed and ignoring NaNs.
References
----------
From http://solarmuri.ssl.berkeley.edu/~welsch/public/software/cross_cor_taylor.pro
Examples
--------
>>> import numpy as np
>>> im1 = np.zeros([10,10])
>>> im2 = np.zeros([10,10])
>>> im1[4,3] = 1
>>> im2[5,5] = 1
>>> import image_registration
>>> yoff,xoff = image_registration.cross_correlation_shifts(im1,im2)
>>> im1_aligned_to_im2 = np.roll(np.roll(im1,int(yoff),1),int(xoff),0)
>>> assert (im1_aligned_to_im2-im2).sum() == 0
"""
if zeromean:
image1 = image1 - (image1[image1 == image1].mean())
image2 = image2 - (image2[image2 == image2].mean())
image1 = np.nan_to_num(image1)
image2 = np.nan_to_num(image2)
quiet = kwargs.pop('quiet') if 'quiet' in kwargs else not verbose
ccorr = (correlate2d(image1, image2, quiet=quiet, **kwargs) / image1.size)
# allow for NaNs set by convolve (i.e., ignored pixels)
ccorr[ccorr != ccorr] = 0
if ccorr.shape != image1.shape:
raise ValueError(
"Cross-correlation image must have same shape as input images. This can only be violated if you pass a strange kwarg to correlate2d."
)
ylen, xlen = image1.shape
xcen = xlen / 2 - (1 - xlen % 2)
ycen = ylen / 2 - (1 - ylen % 2)
if ccorr.max() == 0:
warnings.warn("WARNING: No signal found! Offset is defaulting to 0,0")
return 0, 0
if maxoff is not None:
if verbose: print("Limiting maximum offset to %i" % maxoff)
subccorr = ccorr[ycen - maxoff:ycen + maxoff + 1,
xcen - maxoff:xcen + maxoff + 1]
ymax, xmax = np.unravel_index(subccorr.argmax(), subccorr.shape)
xmax = xmax + xcen - maxoff
ymax = ymax + ycen - maxoff
else:
ymax, xmax = np.unravel_index(ccorr.argmax(), ccorr.shape)
subccorr = ccorr
if return_error:
#if errim1 is None:
# errim1 = np.ones(ccorr.shape) * image1[image1==image1].std()
#if errim2 is None:
# errim2 = np.ones(ccorr.shape) * image2[image2==image2].std()
#eccorr =( (correlate2d(errim1**2, image2**2,quiet=quiet,**kwargs)+
#correlate2d(errim2**2, image1**2,quiet=quiet,**kwargs))**0.5
# / image1.size)
eccorr = (
(correlate2d(
(image1 * 0.15)**2, image2**2, quiet=quiet, **kwargs) +
correlate2d(
(image2 * 0.15)**2, image1**2, quiet=quiet, **kwargs))**0.5 /
image1.size)
if maxoff is not None:
subeccorr = eccorr[ycen - maxoff:ycen + maxoff + 1,
xcen - maxoff:xcen + maxoff + 1]
else:
subeccorr = eccorr
if gaussfit:
try:
from agpy import gaussfitter
except ImportError:
raise ImportError(
"Couldn't import agpy.gaussfitter; try using cross_correlation_shifts with gaussfit=False"
)
if return_error:
pars, epars = gaussfitter.gaussfit(subccorr,
err=subeccorr,
return_all=True)
exshift = epars[2]
eyshift = epars[3]
else:
pars, epars = gaussfitter.gaussfit(subccorr, return_all=True)
xshift = maxoff - pars[2] if maxoff is not None else xcen - pars[2]
yshift = maxoff - pars[3] if maxoff is not None else ycen - pars[3]
if verbose:
print("Gaussian fit pars: ", xshift, yshift, epars[2], epars[3],
pars[4], pars[5], epars[4], epars[5])
else:
xshift_int = xmax - xcen
yshift_int = ymax - ycen
local_values = ccorr[ymax - 1:ymax + 2, xmax - 1:xmax + 2]
d1y, d1x = np.gradient(local_values)
d2y, d2x, dxy = second_derivative(local_values)
fx, fy, fxx, fyy, fxy = d1x[1, 1], d1y[1, 1], d2x[1, 1], d2y[1,
1], dxy[1,
1]
shiftsubx = (fyy * fx - fy * fxy) / (fxy**2 - fxx * fyy)
shiftsuby = (fxx * fy - fx * fxy) / (fxy**2 - fxx * fyy)
xshift = -(xshift_int + shiftsubx)
yshift = -(yshift_int + shiftsuby)
# http://adsabs.harvard.edu/abs/2003MNRAS.342.1291Z
# Zucker error
if return_error:
#acorr1 = (correlate2d(image1,image1,quiet=quiet,**kwargs) / image1.size)
#acorr2 = (correlate2d(image2,image2,quiet=quiet,**kwargs) / image2.size)
#ccorrn = ccorr / eccorr**2 / ccorr.size #/ (errim1.mean()*errim2.mean()) #/ eccorr**2
normalization = 1. / ((image1**2).sum() / image1.size) / (
(image2**2).sum() / image2.size)
ccorrn = ccorr * normalization
exshift = (np.abs(
-1 * ccorrn.size * fxx * normalization / ccorrn[ymax, xmax] *
(ccorrn[ymax, xmax]**2 / (1 - ccorrn[ymax, xmax]**2)))**-0.5)
eyshift = (np.abs(
-1 * ccorrn.size * fyy * normalization / ccorrn[ymax, xmax] *
(ccorrn[ymax, xmax]**2 / (1 - ccorrn[ymax, xmax]**2)))**-0.5)
if np.isnan(exshift):
raise ValueError("Error: NAN error!")
if return_error:
return xshift, yshift, exshift, eyshift
else:
return xshift, yshift
ax2.set_xlim(0, 100)
ax2.set_ylim(0, zzplot[ddplot < 100].max() * 1.1)
pylab.draw()
print >> outf, file, wxarr, wyarr, cx, cy, peak, frac20, frac40, frac60, flux20, flux40, flux60, fluxnb20, fluxnb40, fluxnb60, fluxr20, fluxr40, fluxr60, pflux, meandc, stddc
pylab.savefig(file.replace('fits', 'png'))
print "Completed loop for file %s in %0.1fs" % (file, time.time() - t0)
outf.close()
if sample in ("notmars", "dec2011notmars"):
PSF = numpy.median(imstack, axis=2)[100:200, 100:200]
gf, gg = gaussfitter.gaussfit(PSF,
returnfitimage=True,
limitedmin=[1, 1, 0, 0, 0, 0, 0, 0])
fitsfile[0].data = PSF
fitsfile[0].header['CRVAL1'] = 0
fitsfile[0].header['CRVAL2'] = 0
fitsfile[0].header['CRPIX1'] = 0
fitsfile[0].header['CRPIX2'] = 0
fitsfile[0].header['CD1_1'] = -0.002
fitsfile[0].header['CD2_2'] = 0.002
fitsfile[0].header.update('OBJECT', "Uranus & Neptune")
fitsfile[0].header['BMAJ'] = gf[4] * numpy.sqrt(
8 * numpy.log(2)) * 7.2 / 3600.0
fitsfile[0].header['BMIN'] = gf[5] * numpy.sqrt(
8 * numpy.log(2)) * 7.2 / 3600.0
for key in [
wxarr, wyarr = numpy.zeros(len(filelist)), numpy.zeros(len(filelist))
frac20, frac40, frac60 = numpy.zeros(len(filelist)), numpy.zeros(
len(filelist)), numpy.zeros(len(filelist))
for jj, file in enumerate(filelist):
fitsfile = pyfits.open(file)
img = fitsfile[0].data
header = fitsfile[0].header
img[img != img] = 0
xx, yy = numpy.indices(img.shape)
fitpars = gaussfitter.gaussfit(
img,
params=[img.max(), img.shape[0] / 2, img.shape[1] / 2, 2, 2, 0],
minpars=[0, 0, 0, 0, 1, 1, 0],
vheight=0)
gaussim = gaussfitter.twodgaussian(fitpars)(xx, yy)
asperpix = -header['CD1_1'] * 3600.0
cy, cx = fitpars[2:4]
wxy = fitpars[4:6] * asperpix * numpy.sqrt(8 * numpy.log(2))
wxarr[jj], wyarr[jj] = max(wxy), min(wxy)
rr = (numpy.sqrt((xx - cx)**2 + (yy - cy)**2))
rrs = numpy.argsort(rr.flat)
zz = img.flat[rrs]
zzg = gaussim.flat[rrs]
#dd = numpy.arange(rr.min(),rr.max())
def cross_correlation_shifts(image1, image2, errim1=None, errim2=None,
maxoff=None, verbose=False, gaussfit=False,
return_error=False, zeromean=True, **kwargs):
""" Use cross-correlation and a 2nd order taylor expansion to measure the
offset between two images
Given two images, calculate the amount image2 is offset from image1 to
sub-pixel accuracy using 2nd order taylor expansion.
Parameters
----------
image1: np.ndarray
The reference image
image2: np.ndarray
The offset image. Must have the same shape as image1
errim1: np.ndarray [optional]
The pixel-by-pixel error on the reference image
errim2: np.ndarray [optional]
The pixel-by-pixel error on the offset image.
maxoff: int
Maximum allowed offset (in pixels). Useful for low s/n images that you
know are reasonably well-aligned, but might find incorrect offsets due to
edge noise
zeromean : bool
Subtract the mean from each image before performing cross-correlation?
verbose: bool
Print out extra messages?
gaussfit : bool
Use a Gaussian fitter to fit the peak of the cross-correlation?
return_error: bool
Return an estimate of the error on the shifts. WARNING: I still don't
understand how to make these agree with simulations.
The analytic estimate comes from
http://adsabs.harvard.edu/abs/2003MNRAS.342.1291Z
At high signal-to-noise, the analytic version overestimates the error
by a factor of about 1.8, while the gaussian version overestimates
error by about 1.15. At low s/n, they both UNDERestimate the error.
The transition zone occurs at a *total* S/N ~ 1000 (i.e., the total
signal in the map divided by the standard deviation of the map -
it depends on how many pixels have signal)
**kwargs are passed to correlate2d, which in turn passes them to convolve.
The available options include image padding for speed and ignoring NaNs.
References
----------
From http://solarmuri.ssl.berkeley.edu/~welsch/public/software/cross_cor_taylor.pro
Examples
--------
>>> import numpy as np
>>> im1 = np.zeros([10,10])
>>> im2 = np.zeros([10,10])
>>> im1[4,3] = 1
>>> im2[5,5] = 1
>>> import image_registration
>>> yoff,xoff = image_registration.cross_correlation_shifts(im1,im2)
>>> im1_aligned_to_im2 = np.roll(np.roll(im1,int(yoff),1),int(xoff),0)
>>> assert (im1_aligned_to_im2-im2).sum() == 0
"""
if not image1.shape == image2.shape:
raise ValueError("Images must have same shape.")
if zeromean:
image1 = image1 - (image1[image1==image1].mean())
image2 = image2 - (image2[image2==image2].mean())
image1 = np.nan_to_num(image1)
image2 = np.nan_to_num(image2)
quiet = kwargs.pop('quiet') if 'quiet' in kwargs else not verbose
ccorr = (correlate2d(image1,image2,quiet=quiet,**kwargs) / image1.size)
# allow for NaNs set by convolve (i.e., ignored pixels)
ccorr[ccorr!=ccorr] = 0
if ccorr.shape != image1.shape:
raise ValueError("Cross-correlation image must have same shape as input images. This can only be violated if you pass a strange kwarg to correlate2d.")
ylen,xlen = image1.shape
xcen = xlen/2-(1-xlen%2)
ycen = ylen/2-(1-ylen%2)
if ccorr.max() == 0:
warnings.warn("WARNING: No signal found! Offset is defaulting to 0,0")
return 0,0
if maxoff is not None:
if verbose: print("Limiting maximum offset to %i" % maxoff)
subccorr = ccorr[ycen-maxoff:ycen+maxoff+1,xcen-maxoff:xcen+maxoff+1]
ymax,xmax = np.unravel_index(subccorr.argmax(), subccorr.shape)
xmax = xmax+xcen-maxoff
ymax = ymax+ycen-maxoff
else:
ymax,xmax = np.unravel_index(ccorr.argmax(), ccorr.shape)
subccorr = ccorr
if return_error:
if errim1 is None:
errim1 = np.ones(ccorr.shape) * image1[image1==image1].std()
if errim2 is None:
errim2 = np.ones(ccorr.shape) * image2[image2==image2].std()
eccorr =( (correlate2d(errim1**2, image2**2,quiet=quiet,**kwargs)+
correlate2d(errim2**2, image1**2,quiet=quiet,**kwargs))**0.5
/ image1.size)
if maxoff is not None:
subeccorr = eccorr[ycen-maxoff:ycen+maxoff+1,xcen-maxoff:xcen+maxoff+1]
else:
subeccorr = eccorr
if gaussfit:
try:
from agpy import gaussfitter
except ImportError:
raise ImportError("Couldn't import agpy.gaussfitter; try using cross_correlation_shifts with gaussfit=False")
if return_error:
pars,epars = gaussfitter.gaussfit(subccorr,err=subeccorr,return_all=True)
exshift = epars[2]
eyshift = epars[3]
else:
pars,epars = gaussfitter.gaussfit(subccorr,return_all=True)
xshift = maxoff - pars[2] if maxoff is not None else xcen - pars[2]
yshift = maxoff - pars[3] if maxoff is not None else ycen - pars[3]
if verbose:
print("Gaussian fit pars: ",xshift,yshift,epars[2],epars[3],pars[4],pars[5],epars[4],epars[5])
else:
xshift_int = xmax-xcen
yshift_int = ymax-ycen
local_values = ccorr[ymax-1:ymax+2,xmax-1:xmax+2]
d1y,d1x = np.gradient(local_values)
d2y,d2x,dxy = second_derivative(local_values)
fx,fy,fxx,fyy,fxy = d1x[1,1],d1y[1,1],d2x[1,1],d2y[1,1],dxy[1,1]
shiftsubx=(fyy*fx-fy*fxy)/(fxy**2-fxx*fyy)
shiftsuby=(fxx*fy-fx*fxy)/(fxy**2-fxx*fyy)
xshift = -(xshift_int+shiftsubx)
yshift = -(yshift_int+shiftsuby)
# http://adsabs.harvard.edu/abs/2003MNRAS.342.1291Z
# Zucker error
if return_error:
#acorr1 = (correlate2d(image1,image1,quiet=quiet,**kwargs) / image1.size)
#acorr2 = (correlate2d(image2,image2,quiet=quiet,**kwargs) / image2.size)
#ccorrn = ccorr / eccorr**2 / ccorr.size #/ (errim1.mean()*errim2.mean()) #/ eccorr**2
normalization = 1. / ((image1**2).sum()/image1.size) / ((image2**2).sum()/image2.size)
ccorrn = ccorr * normalization
exshift = (np.abs(-1 * ccorrn.size * fxx*normalization/ccorrn[ymax,xmax] *
(ccorrn[ymax,xmax]**2/(1-ccorrn[ymax,xmax]**2)))**-0.5)
eyshift = (np.abs(-1 * ccorrn.size * fyy*normalization/ccorrn[ymax,xmax] *
(ccorrn[ymax,xmax]**2/(1-ccorrn[ymax,xmax]**2)))**-0.5)
if np.isnan(exshift):
raise ValueError("Error: NAN error!")
if return_error:
return xshift,yshift,exshift,eyshift
else:
return xshift,yshift