def generate_image(n,l, N=100):
nmax = max(20,n)
lfg = math.log_factorial_generator(nmax)
#rzfa = math.zernike_2d_radial(n,l,lfg)
#rap = math.zernike_2d_polynome(n,l,rzfa)
rap = math.zernike_2d_polynome(n,l)#,rzfa)
image = flex.vec3_double()
original=open('original.dat','w')
count = 0
for x in range(-N, N+1):
for y in range(-N, N+1):
rr = smath.sqrt(x*x+y*y)/N
if rr>1.0:
value=0.0
else:
tt = smath.atan2(y,x)
value = rap.f(rr,tt)
value = value.real
count = count + 1
image.append([x+N,y+N,value])
print>>original, x+N,y+N, value
original.close()
return image
def tst_2d_zernike_mom(n, l, filename, h5file, flag):
rebuilt = open(filename, 'w')
# image = generate_image()
# image=ImageToDat("/Users/wyf/Desktop/test11.png")
image = preprocess_image(h5file, flag)
# image = ImageToDat('cha.png')
NP = int(smath.sqrt(image.size()))
N = int(NP / 2)
print "=====", NP, N
grid_2d = math.two_d_grid(N, nmax)
grid_2d.clean_space(image)
grid_2d.construct_space_sum()
zernike_2d_mom = math.two_d_zernike_moments(grid_2d, nmax)
moments = zernike_2d_mom.moments()
coefs = flex.real(moments)
nl_array = math.nl_array(nmax)
nls = nl_array.nl()
nl_array.load_coefs(nls, coefs)
lfg = math.log_factorial_generator(nmax)
# print nl_array.get_coef(n,l)*2
for nl, c in zip(nls, moments):
if (abs(c) < 1e-3):
c = 0
print nl, c
reconst = flex.complex_double(NP**2, 0)
for nl, c in zip(nls, moments):
n = nl[0]
l = nl[1]
if (l > 0):
c = c * 2
#rzfa = math.zernike_2d_radial(n,l,lfg)
rap = math.zernike_2d_polynome(n, l) #,rzfa)
i = 0
for x in range(0, NP):
x = x - N
for y in range(0, NP):
y = y - N
rr = smath.sqrt(x * x + y * y) / N
if rr > 1.0:
value = 0.0
else:
tt = smath.atan2(y, x)
value = rap.f(rr, tt)
reconst[i] = reconst[i] + value * c
i = i + 1
i = 0
for x in range(0, NP):
for y in range(0, NP):
value = reconst[i].real
print >> rebuilt, x, y, value
i = i + 1
rebuilt.close()
def evaluate_c2(nls, moments, r, phi):
c2 = 0
two_pi = smath.pi * 2.0
for nl, c in zip(nls, moments):
n = nl[0]
l = nl[1]
if (l / 2 * 2 != l): continue
if (l > 0): c = c * 2.0
rap = math.zernike_2d_polynome(n, l)
for nl1, c1 in zip(nls, moments):
n1 = nl1[0]
l1 = nl1[1]
if (l != l1): continue
if (l1 > 0): c1 = c1 * 2.0
rap1 = math.zernike_2d_polynome(n1, l1)
tmp_c2 = rap.f(r,
phi / 2) # using phi/2 because it will add up later
tmp_c2 = tmp_c2 * rap1.f(r, phi / 2)
c2 = c2 + tmp_c2.real * c * c1
return c2 * two_pi
def generate_image(n, moments, N=100):
# Generate images from the zernike moments, N is the number of points from 0 to 1
nmax = n
image = flex.vec3_double()
NP = 2 * N + 1
reconst = flex.complex_double(NP**2, 0)
nl_array = math.nl_array(nmax)
nls = nl_array.nl()
r_theta = flex.vec2_double()
for x in range(0, NP):
x = x - N
for y in range(0, NP):
y = y - N
rr = smath.sqrt(x * x + y * y) / N
if rr > 1.0:
tt = 0.0
else:
tt = smath.atan2(y, x)
r_theta.append([rr, tt])
for nl, c in zip(nls, moments):
n = nl[0]
l = nl[1]
#if(l/2*2 != l): continue
if (l > 0): c = c * 2.0
rap = math.zernike_2d_polynome(n, l)
i = 0
for pt in r_theta:
rr = pt[0]
if rr > 1.0:
value = 0.0
else:
tt = pt[1]
value = rap.f(rr, tt)
reconst[i] = reconst[i] + value * c
i = i + 1
return reconst
i = 0
for x in range(0, NP):
for y in range(0, NP):
value = reconst[i].real
image.append([x, y, value])
i = i + 1
return image
def tst_2d_poly(n,l): nmax=max(n,20) np=50 x,y=0.1,0.9 r,t=smath.sqrt(x*x+y*y),smath.atan2(y,x) lfg = math.log_factorial_generator(nmax) #rzfa = math.zernike_2d_radial(n,l,lfg) #rap = math.zernike_2d_polynome(n,l,rzfa) rap = math.zernike_2d_polynome(n,l)#,rzfa) rt_value=rap.f(r,t) grid = math.two_d_grid(np, nmax) zm2d = math.two_d_zernike_moments(grid, nmax) xy_value=zm2d.zernike_poly(n,l,x,y) print rt_value, xy_value, abs(rt_value), abs(xy_value)
def compute_c2(nls, moments, r, phi, Nsample=100):
c2 = 0
two_pi = smath.pi * 2.0
sp1 = flex.double(Nsample, 0)
sp2 = flex.double(Nsample, 0)
theta = flex.random_double(Nsample) * two_pi
for nl, c in zip(nls, moments):
n = nl[0]
l = nl[1]
if (l / 2 * 2 != l): continue
if (l > 0): c = c * 2.0
rap = math.zernike_2d_polynome(n, l)
for ii in range(Nsample):
value1 = rap.f(r, theta[ii] + phi).real * c
value2 = rap.f(r, theta[ii]).real * c
sp1[ii] = sp1[ii] + value1
sp2[ii] = sp2[ii] + value2
return flex.sum(sp1 * sp2) / Nsample
def generate_image2(n, moments, template_image, np):
nmax = n
image = flex.vec3_double()
np_tot = template_image.size()
reconst = flex.complex_double(np_tot, 0)
nl_array = math.nl_array(nmax)
nls = nl_array.nl()
r_theta = flex.vec2_double()
for pt in template_image:
x = pt[0] - np
y = pt[1] - np
rr = smath.sqrt(x * x + y * y) / np
if rr > 1.0:
tt = 0.0
else:
tt = smath.atan2(y, x)
r_theta.append([rr, tt])
for nl, c in zip(nls, moments):
n = nl[0]
l = nl[1]
#if(l/2*2 != l): continue
if (l > 0): c = c * 2.0
rap = math.zernike_2d_polynome(n, l)
i = 0
for pt in r_theta:
rr = pt[0]
if rr > 1.0:
value = 0.0
else:
tt = pt[1]
value = rap.f(rr, tt)
reconst[i] = reconst[i] + value * c
i = i + 1
for i in range(np_tot):
x = template_image[i][0]
y = template_image[i][1]
value = reconst[i].real
image.append([x, y, value])
return image
def tst_2d_zernike_mom(n,l, N=100, filename=None):
nmax = max(20,n)
rebuilt=open('rebuilt.dat','w')
tt1=time.time()
if(filename is not None):
image=read_data(filename)
else:
image=generate_image(n,l)
NP=int(smath.sqrt( image.size() ))
N=NP/2
grid_2d = math.two_d_grid(N, nmax)
grid_2d.clean_space( image )
grid_2d.construct_space_sum()
tt2=time.time()
print "time used: ", tt2-tt1
zernike_2d_mom = math.two_d_zernike_moments( grid_2d, nmax )
moments = zernike_2d_mom.moments()
tt2=time.time()
print "time used: ", tt2-tt1
coefs = flex.real( moments )
nl_array = math.nl_array( nmax )
nls = nl_array.nl()
nl_array.load_coefs( nls, coefs )
lfg = math.log_factorial_generator(nmax)
print nl_array.get_coef(n,l)*2
for nl, c in zip( nls, moments):
if(abs(c)<1e-3):
c=0
print nl, c
print
reconst=flex.complex_double(NP**2, 0)
for nl,c in zip( nls, moments):
n=nl[0]
l=nl[1]
if(l>0):
c=c*2
#rzfa = math.zernike_2d_radial(n,l,lfg)
rap = math.zernike_2d_polynome(n,l) #,rzfa)
i=0
for x in range(0,NP):
x=x-N
for y in range(0,NP):
y=y-N
rr = smath.sqrt(x*x+y*y)/N
if rr>1.0:
value=0.0
else:
tt = smath.atan2(y,x)
value = rap.f(rr,tt)
reconst[i]=reconst[i]+value*c
i=i+1
i = 0
for x in range(0,NP):
for y in range(0,NP):
value=reconst[i].real
if(value>0):
print>>rebuilt, x,y,image[i][2],value
i=i+1
rebuilt.close()
def tst_image(n, N=100, filename=None):
nmax = n
nmax0 = 8
nl_array0 = math.nl_array(nmax0)
nls0 = nl_array0.nl()
nl_array = math.nl_array(nmax)
nls = nl_array.nl()
if (filename is not None):
image = read_data(filename)
else:
moments = flex.random_double(nls0.size())
# moments=flex.double(nls.size(),0 )
# moments[3] = 1.0
# moments[7] = 1.0
image = generate_image(n, moments)
orig = open('original.dat', 'w')
for pt in image:
print >> orig, pt[0], pt[1], pt[2]
orig.close()
Nq = 100
Nphi = 100
c2_image = from_I_to_C2(nmax, image, Nq, Nphi)
c2_output = open('c2.dat', 'w')
for pt in c2_image:
print >> c2_output, pt[0], pt[1], pt[2]
c2_output.close()
coef_table = calc_integral_triple_zernike2d(nmax)
moments[0] = 0
new_mom = moments.concatenate(flex.double(nls.size() - nls0.size(), 0))
nmax4c2 = 2 * nmax
Inm = math.nl_c_array(nmax4c2)
Inm.load_coefs(nls, new_mom)
cnm = calc_Cnm_from_Inm(Inm, coef_table, nmax4c2)
cnm_coef = cnm.coefs()
print "#cnm[0]", cnm_coef[0]
# cnm_coef[0]=0
### calculate 2d zernike moments for C2_image ###
image = c2_image
NP = int(smath.sqrt(image.size()))
N = NP / 2
grid_2d = math.two_d_grid(N, nmax)
grid_2d.clean_space(image)
grid_2d.construct_space_sum()
zernike_2d_mom = math.two_d_zernike_moments(grid_2d, nmax)
c2_moments = zernike_2d_mom.moments()
#coefs = flex.real( c2_moments )
#cnm_coef = flex.real( c2_moments )
cnm_coef = c2_moments
c2_reconst = generate_image2(n, cnm_coef, c2_image, Nq)
c2_r = open('c2r.dat', 'w')
for pt in c2_reconst:
print >> c2_r, pt[0], pt[1], pt[2]
c2_r.close()
ls_score = 0
np_tot = c2_image.size()
for p1, p2 in zip(c2_image, c2_reconst):
ls_score += (p1[2] - p2[2])**2.0
print nmax, nls.size(), ls_score, np_tot * smath.log(
ls_score / np_tot), "SUM"
for nl, c2m in zip(nls, cnm_coef):
print nl, c2m
exit() #
### calculate 2d zernike moments for C2_image ###
image = c2_image
NP = int(smath.sqrt(image.size()))
N = NP / 2
grid_2d = math.two_d_grid(N, nmax)
grid_2d.clean_space(image)
grid_2d.construct_space_sum()
tt2 = time.time()
zernike_2d_mom = math.two_d_zernike_moments(grid_2d, nmax)
c2_moments = zernike_2d_mom.moments()
#coefs = flex.real( c2_moments )
coefs = (c2_moments)
for nl, c2m, c2mm in zip(nls, cnm_coef, coefs):
if (nl[0] / 2 * 2 == nl[0]):
print c2m, c2mm
coefs = flex.real(moments)
nl_array.load_coefs(nls, coefs)
for nl, c in zip(nls, moments):
if (abs(c) < 1e-3):
c = 0
print nl, c
print
reconst = flex.complex_double(NP**2, 0)
for nl, c in zip(nls, moments):
n = nl[0]
l = nl[1]
if (l > 0):
c = c * 2.0
rap = math.zernike_2d_polynome(n, l)
i = 0
for x in range(0, NP):
x = x - N
for y in range(0, NP):
y = y - N
rr = smath.sqrt(x * x + y * y) / N
if rr > 1.0:
value = 0.0
else:
tt = smath.atan2(y, x)
value = rap.f(rr, tt)
reconst[i] = reconst[i] + value * c
i = i + 1
rebuilt = open('rebuilt.dat', 'w')
i = 0
for x in range(0, NP):
for y in range(0, NP):
value = reconst[i].real
print >> rebuilt, x, y, image[i][2], value
i = i + 1
rebuilt.close()
