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
# Start here to invert from FFT (useI = False, and will get perfect reconstruction). im.invertFft(useI=True) # Use im2 to recalculate 1d PSD/ACovF starting from the reconstructed image, without altering the original. im2 = PImagePlots() im2.setImage(im.imageI.real, copy=True) im2.calcAll(min_dr=1.0, min_npix=2) im2.plotMore() # Now start plotting things, in comparison. clims = im.showImage() #print clims im2.showImage(clims=clims) im2.showImage() im.showFft(clims=clims) im2.showFft(clims=clims) im.showPsd2d() im2.showPsd2d() im.showPhases() im2.showPhases() im.showAcovf2d() im2.showAcovf2d(imag=False) im.showPsd1d(comparison=im2) im.showAcovf1d(comparison=im2) im.showSf(linear=True, comparison=im2) pylab.show() exit()
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
