def compare1d_psd_acovf():
"""Compare 1d ACovF in physical coordinates to 1d PSD in physical coordinates, for two similar but different images."""
im = TestImage(shift=True, nx=1000, ny=1000)
scale = 100
im.addSin(scale=scale)
im.hanningFilter()
im.zeroPad()
im.calcAll(min_npix=1, min_dr=1)
im.showImage()
pylab.grid()
pylab.savefig('compare1d_image1.%s' %(figformat), format='%s' %(figformat))
im.showPsd2d()
pylab.savefig('compare1d_psd2d1.%s' %(figformat), format='%s' %(figformat))
im.showPsd1d()
pylab.savefig('compare1d_psd1.%s' %(figformat), format='%s' %(figformat))
im.showAcovf1d()
pylab.savefig('compare1d_acovf1.%s' %(figformat), format='%s' %(figformat))
im = TestImage(shift=True, nx=1000, ny=1000)
im.addSin(scale=scale*2)
im.hanningFilter()
im.zeroPad()
im.calcAll(min_npix=1, min_dr=1)
im.showImage()
pylab.grid()
pylab.savefig('compare1d_image2.%s' %(figformat), format='%s' %(figformat))
im.showPsd2d()
pylab.savefig('compare1d_psd2d2.%s' %(figformat), format='%s' %(figformat))
im.showPsd1d()
pylab.savefig('compare1d_psd2.%s' %(figformat), format='%s' %(figformat))
im.showAcovf1d()
pylab.savefig('compare1d_acovf2.%s' %(figformat), format='%s' %(figformat))
pylab.close()
return
def example_lines():
"""Plot for example_lines, illustrating entire forward process both with and without hanning filter."""
im = TestImage(shift=True, nx=1000, ny=1000)
im.addLines(width=10, spacing=75, value=5, angle=45)
im.zeroPad()
im.calcAll()
im.plotMore()
pylab.savefig('example_lines_a.%s' %(figformat), format='%s' %(figformat))
pylab.close()
im = TestImage(shift=True, nx=1000, ny=1000)
im.addLines(width=10, spacing=75, value=5, angle=45)
im.hanningFilter()
im.zeroPad()
im.calcAll()
im.plotMore()
pylab.savefig('example_lines_b.%s' %(figformat), format='%s' %(figformat))
pylab.close()
return
def gaussian_example():
"""Generate the plots for the example gaussian ... a more detailed version of this is walked through in the
testGaussian.py code. """
gauss = TestImage(shift=True, nx=1000, ny=1000)
sigma_x = 10.
gauss.addGaussian(xwidth=sigma_x, ywidth=sigma_x, value=1)
gauss.zeroPad()
gauss.calcAll(min_npix=2, min_dr=1)
gauss.plotMore()
pylab.savefig('gauss_all.%s' %(figformat), format='%s' %(figformat))
# pull slice of image
x = numpy.arange(0, gauss.nx, 1.0)
d = gauss.image[round(gauss.ny/2.0)][:]
mean = gauss.xcen
sigma = sigma_x
fitval, expval = dofit(x, d, mean, sigma)
doplot(x, d, fitval, expval, 'Image slice', xlabel='Pixels')
pylab.savefig('gauss_image.%s' %(figformat), format='%s' %(figformat))
# pull slice of FFT
x = gauss.xfreq
d = fftpack.ifftshift(gauss.fimage)[0][:].real
d = numpy.abs(d)
idx = numpy.argsort(x)
d = d[idx]
x = x[idx]
mean = 0
sigma_fft = 1/(2.0*numpy.pi*sigma_x)
fitval, expval = dofit(x, d, mean, sigma_fft)
doplot(x, d, fitval, expval, 'FFT slice', xlabel='Frequency')
pylab.xlim(-.2, .2)
pylab.savefig('gauss_fft.%s' %(figformat), format='%s' %(figformat))
# pull slice from PSD
d = fftpack.ifftshift(gauss.psd2d)[0][:].real
d = d[idx]
mean = 0
sigma_psd_freq = sigma_fft/numpy.sqrt(2)
fitval, expval = dofit(x, d, mean, sigma_psd_freq)
doplot(x, d, fitval, expval, 'PSD 2-d slice', xlabel='Frequency')
pylab.xlim(-.2, .2)
pylab.savefig('gauss_psd_freq.%s' %(figformat), format='%s' %(figformat))
# and look at slice from PSD in spatial scale
x = numpy.arange(-gauss.xcen, gauss.nx-gauss.xcen, 1.0)
d = gauss.psd2d[round(gauss.ny/2.0)][:].real
mean = 0
sigma_psd_pix = 1/(sigma_x*numpy.sqrt(2))*numpy.sqrt(gauss.nx*gauss.ny)/(2.0*numpy.pi)
fitval, expval = dofit(x, d, mean, sigma_psd_pix)
doplot(x, d, fitval, expval, 'PSD 2-d slice, spatial scale', xlabel='"Pixels"')
pylab.xlim(-200, 200)
pylab.savefig('gauss_psd_x.%s' %(figformat), format='%s' %(figformat))
# Show 1d PSD in both frequency and pixel space
gauss.showPsd1d(linear=True)
pylab.savefig('gauss_psd1d_all.%s' %(figformat), format='%s' %(figformat))
# and check 1d PSD in frequency space (spatial space doesn't work ...)
x = gauss.rfreq
d = gauss.psd1d.real
sigma = sigma_psd_freq
fitval, expval = dofit(x, d, 0., sigma)
doplot(x, d, fitval, expval, 'PSD 1-d', xlabel='Frequency')
pylab.savefig('gauss_psd1d.%s' %(figformat), format='%s' %(figformat))
# pull slice from ACovF
x = numpy.arange(-gauss.xcen, gauss.nx-gauss.xcen, 1.)
d = gauss.acovf.real[round(gauss.ny/2.0)][:]
mean = 0
sigma_acovf = sigma_x*numpy.sqrt(2)
fitval, expval = dofit(x, d, mean, sigma_acovf)
doplot(x, d, fitval, expval, 'ACovF 2-d slice', xlabel='Pixels')
pylab.xlim(-200, 200)
pylab.savefig('gauss_acovf.%s' %(figformat), format='%s' %(figformat))
# and check 1d ACovF
x = gauss.acovfx
d = gauss.acovf1d.real
sigma_acovf = sigma_x*numpy.sqrt(2)
fitval, expval = dofit(x, d, mean, sigma_acovf)
doplot(x, d, fitval, expval, 'ACovF 1-d', xlabel='Pixels')
pylab.savefig('gauss_acovf1d.%s' %(figformat), format='%s' %(figformat))
pylab.close()
return
def inversion():
"""Generate some example images & invert them to reconstruct the original image."""
im = TestImage(shift=True, nx=1000, ny=1000)
#im.addEllipseGrid(gridX=200, gridY=100, semiX=50, semiY=25, value=1)
im.addLines(width=20, spacing=200, value=1, angle=45)
im.addSin(scale=300)
im.hanningFilter()
im.zeroPad()
#cmap = pylab.cm.gray_r
cmap = None
clims = im.showImage(cmap=cmap)
pylab.savefig('invert_image.%s' %(figformat), format='%s' %(figformat))
im.calcAll(min_npix=1, min_dr=1)
# Invert from ACovF and show perfect reconstruction.
im.invertAcovf2d()
im.invertPsd2d(useI=True)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_acovf2d_good.%s' %(figformat), format='%s' %(figformat))
# Invert from ACovF 2d without phases
im.invertAcovf2d(usePhasespec=False, seed=42)
im.invertPsd2d(useI=True)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_acovf2d_nophases.%s' %(figformat), format='%s' %(figformat))
# Invert from ACovF 1d with phases
im.invertAcovf1d(phasespec=im.phasespec)
im.invertAcovf2d(useI=True)
im.invertPsd2d(useI=True)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_acovf1d_phases.%s' %(figformat), format='%s' %(figformat))
# Invert from ACovF 1d without phases
im.invertAcovf1d(seed=42)
im.invertAcovf2d(useI=True)
im.invertPsd2d(useI=True)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_acovf1d_nophases.%s' %(figformat), format='%s' %(figformat))
# Recalculate 1-d PSD and ACovF from this last reconstructed image (ACovF1d no phases)
im2 = PImagePlots()
im2.setImage(im.imageI)
im2.calcAll(min_npix=1, min_dr=1)
legendlabels=['Reconstructed', 'Original']
im2.showPsd1d(comparison=im, legendlabels=legendlabels)
pylab.savefig('invert_recalc_ACovF_Psd1d.%s' %(figformat), format='%s' %(figformat))
im2.showAcovf1d(comparison=im, legendlabels=legendlabels)
pylab.savefig('invert_recalc_ACovF_Acovf1d.%s' %(figformat), format='%s' %(figformat))
# Invert from PSD and show perfect reconstruction.
im.invertPsd2d()
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_psd2d_good.%s' %(figformat), format='%s' %(figformat))
# Invert from PSD 2d without phases
im.invertPsd2d(usePhasespec=False, seed=42)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_psd2d_nophases.%s' %(figformat), format='%s' %(figformat))
# Invert from PSD 1d with phases
im.invertPsd1d(phasespec=im.phasespec)
im.invertPsd2d(useI=True)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_psd1d_phases.%s' %(figformat), format='%s' %(figformat))
# Invert from PSD 1d without phases
im.invertPsd1d(seed=42)
im.invertPsd2d(useI=True)
im.invertFft(useI=True)
im.showImageI(clims=clims, cmap=cmap)
pylab.savefig('invert_psd1d_nophases.%s' %(figformat), format='%s' %(figformat))
# Recalculate 1-d PSD and ACovF from this last reconstructed image (PSD1d no phases)
im2 = PImagePlots()
im2.setImage(im.imageI)
im2.calcAll(min_npix=1, min_dr=1)
im2.showPsd1d(comparison=im, legendlabels=legendlabels)
pylab.savefig('invert_recalc_PSD_Psd1d.%s' %(figformat), format='%s' %(figformat))
im2.showAcovf1d(comparison=im, legendlabels=legendlabels)
pylab.savefig('invert_recalc_PSD_Acovf1d.%s' %(figformat), format='%s' %(figformat))
pylab.close()
return
import pylab from testImage import TestImage # Plain image, with noise im = TestImage() im.addLines(width=10, spacing=50, value=5) #im.addNoise() im.hanningFilter() im.zeroPad() im.calcAll() #im.plotAll(title='Gaussian Noise') im.plotMore(title='Gaussian Noise') pylab.show() exit() # Gaussian image im = TestImage() im.addGaussian(xwidth=20, ywidth=20) im.hanningFilter() im.zeroPad() im.calcAll() im.plotAll(title='Gaussian') # Sin, s=100 im = TestImage() im.addSin(scale=100) im.hanningFilter() im.zeroPad() im.calcAll() im.plotAll(title='Sin, scale=100')