def psd1d(image,dx,binsize=1.,pad=True):
"""
NAME:
psd1d
PURPOSE:
Calculate the 1D, azimuthally averaged power spectrum of an image
INPUT:
image - the image [NxM]
dx- spacing in X and Y directions
binsize= (1) radial binsize in terms of Nyquist frequency
OUTPUT:
the 1D power spectrum using definitions of NR 13.4 eqn. (13.4.5)
HISTORY:
2014-06-06 - Written - Bovy (IAS)
"""
#First subtract DC component
image-= numpy.mean(image[True-numpy.isnan(image)])
#Calculate the 2D PSD
ret2d= psd2d(image,pad=pad)
nr, radii,ret= azimuthalAverage(ret2d,returnradii=False,binsize=binsize,
dx=1./2./dx/image.shape[0],
dy=1./2./dx/image.shape[1],
interpnan=False,
return_nr=True)
return (radii/2.**pad/dx/(image.shape[0]/2.-0.),ret,ret/numpy.sqrt(nr))
def powerspectrum(f):
ff = np.fft.fftshift(np.fft.fft2(f))
ff = ff / ff.shape[0] / ff.shape[1]
ps2 = np.abs(ff)**2
r, ps = radialprofile.azimuthalAverage(ps2, returnradii=True)
return np.column_stack((r, ps))
def crosspower(f1,f2):
ff1 = np.fft.fftshift(np.fft.fft2(f1))
ff2 = np.fft.fftshift(np.fft.fft2(f2))
ff1 = ff1 / ff1.shape[0] / ff1.shape[1]
ff2 = ff2 / ff2.shape[0] / ff2.shape[1]
ps2 = np.real(ff1 * np.conjugate(ff2))
r, ps = radialprofile.azimuthalAverage(ps2, returnradii = True)
return np.column_stack((r, ps))
def residual_prof(label):
colours = ['r', 'g', 'b']
for i, band in enumerate(bands):
f = 'stackres_%s_%s.fits'%(label, band)
if os.path.exists(f):
res = pyfits.getdata(f)
rad, prof = azimuthalAverage(res, returnradii=True, binsize=1.0)
middle = rad < res.shape[0]/2.0
rad, prof = [x[middle] for x in (rad, prof)]
rad /= scales
pyplot.plot(rad, prof, '-', color=colours[i])
pyplot.axis('on')
else:
pyplot.axis('off')
def reduce(self):
'''convert raw image data to R(Q), also get other terms'''
if self.image is None: # TODO: make this conditional on need to reduce image data
self.read_image_data()
if abs(self.image.xsize - self.image.ysize) > PIXEL_SIZE_TOLERANCE:
raise ValueError('X & Y pixels have different sizes, not prepared for this')
# TODO: construct the image mask
# radial averaging (average around the azimuth at constant radius, repeat at all radii)
with numpy.errstate(invalid='ignore'):
radii, rAvg = azimuthalAverage(self.image.image,
center=(self.image.x0, self.image.y0),
returnradii=True)
# standard deviation results do not look right, skip that in full data reduction
# with numpy.errstate(invalid='ignore'):
# with warnings.catch_warnings():
# # sift out this RuntimeWarning warning from numpy
# warnings.filterwarnings('ignore', r'Degrees of freedom <= 0 for slice')
# rAvgDev = azimuthalAverage(self.image.image,
# center=(self.image.x0, self.image.y0),
# stddev=True)
radii *= self.image.xsize
Q = (4*math.pi / self.image.wavelength) * numpy.sin(0.5*numpy.arctan2(radii, self.image.SDD))
# scale_factor = 1 /self.image.I0_gain / self.image.I0 # TODO: verify the equation
scale_factor = 1 / self.image.I0 # TODO: verify the equation
rAvg = rAvg * scale_factor
# remove NaNs and non-positives from output data
rAvg = numpy.ma.masked_less_equal(rAvg, 0) # mask the non-positives
rAvg = numpy.ma.masked_invalid(rAvg) # mask the NaNs
Q = calc.remove_masked_data(Q, rAvg.mask)
radii = calc.remove_masked_data(radii, rAvg.mask)
# rAvgDev = calc.remove_masked_data(rAvgDev, rAvg.mask)
rAvg = calc.remove_masked_data(rAvg, rAvg.mask) # always remove the masked array last
full = dict(Q=Q, R=rAvg, x=radii)
self.reduced = dict(full = full) # reset the entire dictionary with new "full" reduction
def main(imagefile = "IsoToRaster01_small.jpg"):
image = cv2.imread("./data/"+imagefile)
im_gray = cv2.imread("./data/"+imagefile, cv2.CV_LOAD_IMAGE_GRAYSCALE)
(thresh, im_bw) = cv2.threshold(im_gray, 128, 255, cv2.THRESH_BINARY | cv2.THRESH_OTSU)
# Take the fourier transform of the image.
F1 = fftpack.fft2(im_bw)
#F1 = cv2.dft(np.float32(im_bw),flags = cv2.DFT_COMPLEX_OUTPUT)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = fftpack.fftshift( F1 )
# Calculate a 2D power spectrum
psd2D = np.abs( F2 )**2
# Calculate the azimuthally averaged 1D power spectrum
psd1D = radialprofile.azimuthalAverage(psd2D)
# Now plot up both
py.figure(1)
py.clf()
py.imshow( np.log10( image ), cmap=py.cm.Greys)
py.figure(2)
py.clf()
py.imshow( np.log10( psd2D ))
py.figure(3)
py.clf()
py.semilogy( psd1D )
py.xlabel('Spatial Frequency')
py.ylabel('Power Spectrum')
py.show()
return 0
Z = clip(Z,0,2)
rows,cols = Z.shape
Z[:rows-1,:cols-1]
if fa == 1:
# First for SFR
# Take the fourier transform of the image.
F1 = fftpack.fft2(Z)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = fftpack.fftshift(F1)
# Calculate a 2D power spectrum
psd2D = np.abs( F2 )**2
# Calculate the azimuthally averaged 1D power spectrum
psd1D = radialprofile.azimuthalAverage(psd2D)
#Secondly for Dencity
# Take the fourier transform of the image.
F1den = fftpack.fft2(Zden)
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2den = fftpack.fftshift(F1den)
# Calculate a 2D power spectrum
psd2Dden = np.abs( F2den )**2
# Calculate the azimuthally averaged 1D power spectrum
psd1Dden = radialprofile.azimuthalAverage(psd2Dden)
print 'creating cross power spectrum'
G1 = F2
G2con = np.conjugate(F2den)
def getFreqs(ar):
freqImage = numpy.abs(numpy.fft.fft2(ar))
freqs = azimuthalAverage(freqImage)
return freqs
#img = np.random.randint(0, 255, (100,100))
x, y = np.mgrid[-100:100:200j, -100:100:200j]
dist = np.hypot(x, y) # Linear distance from point 0, 0
img = np.cos(dist / 5 / np.pi)
plt.figure()
plt.imshow(img)
plt.colorbar()
plt.show()
img = convert_to_8bits(img)
plt.figure()
plt.imshow(img, cmap="hot")
plt.colorbar()
plt.show()
# center, radi = find_centroid(img)
center, radi = (100, 100), 5
rad = radial_profile(img, center)
plt.figure("Method 1")
plt.plot(rad[radi:])
#plt.show()
# Other method
az = azimuthalAverage(img)
plt.figure("Method 2")
plt.plot(az)
plt.show()
x, y = np.mgrid[-100:100:200j, -100:100:200j]
dist = np.hypot(x, y) # Linear distance from point 0, 0
img = np.cos( dist/5 / np.pi)
plt.figure()
plt.imshow(img)
plt.colorbar()
plt.show()
img = convert_to_8bits(img)
plt.figure()
plt.imshow(img,cmap="hot")
plt.colorbar()
plt.show()
# center, radi = find_centroid(img)
center, radi = (100, 100), 5
rad = radial_profile(img, center)
plt.figure("Method 1")
plt.plot(rad[radi:])
#plt.show()
# Other method
az = azimuthalAverage(img)
plt.figure("Method 2")
plt.plot(az)
plt.show()
def getFreqs(ar):
freqImage = numpy.abs(numpy.fft.fft2(ar))
freqs = azimuthalAverage(freqImage)
return freqs
rainfieldSmoothed * window) # FFTW implementation
# Turn on the cache for optimum performance
pyfftw.interfaces.cache.enable()
# Shift frequencies
fprecip = np.fft.fftshift(fprecipNoShift)
# Compute 2D power spectrum
psd2d = np.abs(fprecip)**2 / (fftDomainSize *
fftDomainSize)
psd2dNoShift = np.abs(fprecipNoShift)**2 / (fftDomainSize *
fftDomainSize)
# Compute 1D radially averaged power spectrum
bin_size = 1
nr_pixels, bin_centers, psd1d = radialprofile.azimuthalAverage(
psd2d, binsize=bin_size, return_nr=True)
fieldSize = rainrate.shape
minFieldSize = np.min(fieldSize)
# Extract subset of spectrum
validBins = (
bin_centers < minFieldSize / 2
) # takes the minimum dimension of the image and divide it by two
psd1d = psd1d[validBins]
# Compute frequencies
freq = fftpack.fftfreq(minFieldSize, d=float(resKm))
freqAll = np.fft.fftshift(freq)
# Select only positive frequencies
freq = freqAll[len(psd1d):]
fprecipNoShift = np.fft.fft2(rainfieldSmoothed*window) # Numpy implementation
if FFTmod == 'FFTW':
fprecipNoShift = pyfftw.interfaces.numpy_fft.fft2(rainfieldSmoothed*window) # FFTW implementation
# Turn on the cache for optimum performance
pyfftw.interfaces.cache.enable()
# Shift frequencies
fprecip = np.fft.fftshift(fprecipNoShift)
# Compute 2D power spectrum
psd2d = np.abs(fprecip)**2/(fftDomainSize*fftDomainSize)
psd2dNoShift = np.abs(fprecipNoShift)**2/(fftDomainSize*fftDomainSize)
# Compute 1D radially averaged power spectrum
bin_size = 1
nr_pixels, bin_centers, psd1d = radialprofile.azimuthalAverage(psd2d, binsize=bin_size, return_nr=True)
fieldSize = rainrate.shape
minFieldSize = np.min(fieldSize)
# Extract subset of spectrum
validBins = (bin_centers < minFieldSize/2) # takes the minimum dimension of the image and divide it by two
psd1d = psd1d[validBins]
# Compute frequencies
freq = fftpack.fftfreq(minFieldSize, d=float(resKm))
freqAll = np.fft.fftshift(freq)
# Select only positive frequencies
freq = freqAll[len(psd1d):]
# Compute wavelength [km]