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# This file is part of the Astrometry.net suite.
# Licensed under a 3-clause BSD style license - see LICENSE
from __future__ import print_function
import sys
import matplotlib
matplotlib.use('Agg')
from math import pi
from pylab import *
from numpy import *
from numpy.random import *
try:
import pyfits
except ImportError:
try:
from astropy.io import fits as pyfits
except ImportError:
raise ImportError("Cannot import either pyfits or astropy.io.fits")
# Given an image and an xylist (including estimated image sigma),
# look at a cutout around each source position, add noise, and recompute
# dcen3x3 to find the noisy peak.
def dcen3a(f0, f1, f2):
s = 0.5 * (f2 - f0)
d = 2. * f1 - (f0 + f2)
if (d <= 1.e-10*f0):
return None
aa = f1 + 0.5 * s * s / d
sod = s / d
return sod * (1. + (4./3.) * (0.25 * d / aa) * (1. - 4. * sod * sod)) + 1.
def dcen3b(f0, f1, f2):
a = 0.5 * (f2 - 2*f1 + f0)
b = f1 - a - f0
xc = -0.5 * b / a
if not (0.0 < xc < 2.0):
return None
return xc
def dcen3(f0, f1, f2):
return dcen3a(f0,f1,f2)
def dcen3x3(image):
my0 = dcen3(image[0,0], image[1,0], image[2,0])
my1 = dcen3(image[0,1], image[1,1], image[2,1])
my2 = dcen3(image[0,2], image[1,2], image[2,2])
mx0 = dcen3(image[0,0], image[0,1], image[0,2])
mx1 = dcen3(image[1,0], image[1,1], image[1,2])
mx2 = dcen3(image[2,0], image[2,1], image[2,2])
if None in [ mx0, mx1, mx2, my0, my1, my2 ]:
return None
# x = (y-1) mx + bx
bx = (mx0 + mx1 + mx2) / 3.
mx = (mx2 - mx0) / 2.
# y = (x-1) my + by
by = (my0 + my1 + my2) / 3.
my = (my2 - my0) / 2.;
# find intersection
xc = (mx * (by - my - 1.) + bx) / (1. + mx * my)
yc = (xc - 1.) * my + by
# check that we are in the box
if not ((0.0 < xc < 2.0) and (0.0 < yc < 2.0)):
return None
return (xc,yc)
if __name__ == '__main__':
imgfn = sys.argv[1]
xyfn = sys.argv[2]
print('FITS Image', imgfn)
print('xylist', xyfn)
p = pyfits.open(imgfn)
I = p[0].data
print('Image is', I.shape)
p = pyfits.open(xyfn)
xy = p[1].data
x = xy.field('X')
y = xy.field('Y')
flux = xy.field('FLUX')
print('Sources:', len(x))
hdr = p[1].header
sigma = hdr['ESTSIGMA']
print('Estimated sigma', sigma)
N = 100
dx = []
dy = []
dx2 = []
dy2 = []
fluxes = []
fluxes2 = []
Nout = 0
Nout2 = 0
for i in range(len(x)):
#print 'peak',i
ix = round(x[i]) - 1
iy = round(y[i]) - 1
cutout = I[iy-1:iy+2, ix-1:ix+2]
if cutout.shape != (3,3):
print('cutout is', cutout.shape)
continue
#cutout5 = I[range(iy-2, iy+3, 2), range(ix-2, ix+3, 2)]
cutout5 = array([ I[range(iy-2, iy+3, 2), ix-2],
I[range(iy-2, iy+3, 2), ix ],
I[range(iy-2, iy+3, 2), ix+2], ])
if cutout5.shape != (3,3):
print('cutout5 has shape', cutout5.shape)
print('yrange', range(iy-2, iy+3, 2))
print('xrange', range(ix-2, ix+3, 2))
print('cutout5', cutout5)
continue
for j in xrange(N):
noise = normal(0, sigma, size=(3,3))
img = cutout + noise
cen = dcen3x3(img)
# original center:
xx = x[i] - ix
yy = y[i] - iy
if cen is not None:
(cx,cy) = cen
dx.append(cx - xx)
dy.append(cy - yy)
fluxes.append(flux[i])
else:
Nout += 1
noise5 = normal(0, sigma, size=(3,3))
cen2 = dcen3x3(cutout5 + noise5)
if cen2 is None:
Nout2 += 1
continue
(cx2, cy2) = cen2
cx = 1. + (cx2-1.) * 2.
cy = 1. + (cy2-1.) * 2.
dx2.append(cx - xx)
dy2.append(cy - yy)
fluxes2.append(flux[i])
dx = array(dx)
dy = array(dy)
dx2 = array(dx2)
dy2 = array(dy2)
print('A total of', Nout, 'of', (N*len(x)), '(%i %%)' % int(round(Nout*100./float(N*len(x)))), 'peaks moved outside the 3x3 box.')
print('A total of', Nout2, 'of', (N*len(x)), '(%i %%)' % int(round(Nout2*100./float(N*len(x)))), 'peaks moved outside the 5x5 box.')
figure()
clf()
subplot(1,2,1)
plot(dx, dy, 'r.')
axis('equal')
ylim(-3,3)
a=axis()
axhline(0)
axvline(0)
axis(a)
title('3x3 centroid error')
xlabel('distance (pixels)')
subplot(1,2,2)
plot(dx2, dy2, 'b.')
axis('equal')
ylim(-3,3)
axhline(0)
axvline(0)
axis(a)
title('5x5 centroid error')
xlabel('distance (pixels)')
savefig('dxdy.png', dpi=75)
subplot(111)
dist = sqrt(dx**2 + dy**2)
dist2 = sqrt(dx2**2 + dy2**2)
clf()
subplot(2,1,1)
(nb,bins,patches) = hist(dist, 40)
xlim(0,bins[-1])
title('3x3 centroid error distance')
#xlabel('pixels')
subplot(2,1,2)
hist(dist2, bins=bins)
xlim(0,bins[-1])
title('5x5 centroid error distance')
xlabel('pixels')
savefig('dists.png', dpi=75)
clf()
dboth = hstack((dx,dy))
sigd = std(dboth)
md = mean(dboth)
xx = arange(dboth.min(), dboth.max(), 0.01)
yy = (len(dboth)*(xx.max()-xx.min())/40) / (sigd * sqrt(2. * pi)) * exp(-((xx-md)**2)/(2*sigd**2))
subplot(2,1,1)
(n,bins,patches) = hist(dboth, 40)
plot(xx, yy, 'r-')
title('3x3 centroid coordinate errors (std=%g)' % sigd)
#xlabel('pixels')
dboth2 = hstack((dx2,dy2))
sigd2 = std(dboth2)
md2 = mean(dboth2)
if len(dboth2):
xx2 = arange(dboth2.min(), dboth2.max(), 0.01)
yy2 = (len(dboth2)*(xx2.max()-xx2.min())/40) / (sigd2 * sqrt(2. * pi)) * exp(-((xx2-md2)**2)/(2*sigd2**2))
else:
xx2 = []
yy2 = []
subplot(2,1,2)
hist(dboth2, bins=bins)
plot(xx2, yy2, 'r-')
title('5x5 centroid coordinate errors (std=%g)' % sigd2)
xlabel('pixels')
savefig('dboth.png', dpi=75)
clf()
subplot(2,1,1)
plot(fluxes, dist, 'r.')
ylabel('pixel distance')
#xlabel('flux')
title('3x3 centroid')
subplot(2,1,2)
plot(fluxes2, dist2, 'b.')
ylabel('pixel distance')
xlabel('flux')
title('5x5 centroid')
savefig('fluxdist.png', dpi=75)
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