def fillImageSpace():
N=512
M=2*N
centered = True
ms = range(0, N)
ss = range(0, N/2)
powerSpect = np.zeros((M,M))
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))
ax[0].imshow(powerSpect)
ax[1].imshow(powerSpect)
fareyImage = np.zeros_like(powerSpect)
maxLines = len(ms)
for i,m in enumerate(ms):
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
ax[0].plot(u, v, '.r', markersize=1)
u, v = radon.getSliceCoordinates2(M-m, powerSpect, centered, M)
ax[0].plot(u, v, '.r', markersize=1)
#ax[1].plot(u, v, '.r',markersize=1)
fareyImage[u,v] = 255
if i == maxLines:
break
maxLines = len(ss)
for i,s in enumerate(ss):
u, v = radon.getSliceCoordinates2(s, powerSpect, centered, M)
ax[0].plot(u, v, '.r', markersize=1)
ax[1].plot(u, v, '.r',markersize=1)
u, v = radon.getSliceCoordinates2(M-s, powerSpect, centered, M)
ax[0].plot(u, v, '.r', markersize=1)
ax[1].plot(u, v, '.r',markersize=1)
fareyImage[u,v] = 255
if i == maxLines:
break
plt.show()
print("Non-zero elements without holes: ", np.count_nonzero(fareyImage)/float(M*M) * 100)
return
def computeLines(kSpace, angles, centered=True, twoQuads=False):
'''
compute finite lines coordinates
Returns a list or list of slice 2-tuples and corresponding list of m values
'''
p, s = kSpace.shape
lines = []
mValues = []
for angle in angles:
m, inv = farey.toFinite(angle, p)
u, v = radon.getSliceCoordinates2(m, kSpace, centered, p)
lines.append((u, v))
mValues.append(m)
#second quadrant
if twoQuads:
if m != 0 and m != p: #dont repeat these
m = p - m
u, v = radon.getSliceCoordinates2(m, kSpace, centered, p)
lines.append((u, v))
mValues.append(m)
return lines, mValues
def createFractal4(reduction, N, proportion):
#parameters
M = 2*N
twoQuads = True
angles, lengths = mojette.angleSet_Symmetric(N,N,1,True,50)
perpAngle = farey.farey(1,0)
angles.append(perpAngle)
powerSpect = np.zeros((M,M))
#compute lines
centered = True
mLines = []
sLines = []
mValues = []
sValues = []
pValues = []
qValues = []
for angle in angles:
m, s, p, q, inv = farey.toFinite(angle, M)
pValues.append(p)
qValues.append(q)
if m not in mValues and m < M:
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
mLines.append((u,v))
mValues.append(m)
#second quadrant
if twoQuads:
if m != 0 and m != M: #dont repeat these
m = M-m
if m not in mValues and m < M:
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
mLines.append((u,v))
mValues.append(m)
i = (len(mValues)+len(sValues))/float(M)
if i >= 1:
break
ss = []
ss.append(M)
ss.extend(range(0, N/2))
maxLines = len(ss)
for i,s in enumerate(ss):
u, v = radon.getSliceCoordinates2(s, powerSpect, centered, M)
sLines.append((u,v))
sValues.append(s)
i = (len(mValues)+len(sValues))/float(M)
if i >= 1.5:
break
length = 0
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))
plt.gray()
plt.tight_layout()
maxLines = len(sLines+mLines)
i = 0
ax[0].imshow(powerSpect)
ax[1].imshow(powerSpect)
color=iter(cm.jet(np.linspace(0,1,maxLines+1)))
fareyImage = np.zeros_like(powerSpect)
fareyImage1 = np.zeros_like(powerSpect)
for i, sLine in enumerate(sLines):
u, v = sLine
ax[1].plot(u, v, '.w',markersize=1)
fareyImage[u,v] = 1
length = length + 1
i = np.count_nonzero(fareyImage)/float((M*M))
if i >= reduction*proportion:
break
maxLines = len(mLines)
for i, mLine in enumerate(mLines):
u, v = mLine
ax[0].plot(u, v, '.r', markersize=1)
ax[1].plot(u, v, '.r',markersize=1)
fareyImage[u,v] = 1
fareyImage1[u,v] = 1
length = length + 1
i = np.count_nonzero(fareyImage)/float((M*M))
if i >= reduction:
break
print("Proportion of M:", (length/float(M)))
print("Non-zero elements with holes: ", np.count_nonzero(fareyImage1)/float((M*M)) * 100)
print("Non-zero elements without holes: ", np.count_nonzero(fareyImage)/float((M*M)) * 100)
print("Absolute difference percentage extra filled in is ", (np.count_nonzero(fareyImage)- np.count_nonzero(fareyImage1))/float((M*M)) *100)
withHoles = np.count_nonzero(fareyImage1)/float((M*M)) * 100
withoutHoles = np.count_nonzero(fareyImage)/float((M*M)) * 100
percentage = (withoutHoles - withHoles)/float(withHoles) * 100
print("Percentage difference percentage extra filled in is ", percentage)
ax[0].set_title('Sampling (colour per line) for dyadic size:'+str(M))
ax[1].set_title('Sampling (same colour per line) for dyadic size:'+str(M))
imageio.imsave("farey_image_"+str(M)+"_"+".png", fareyImage)
plt.show()
lines = mLines + sLines
return fareyImage, lines
#np.set_printoptions(threshold=np.nan)
#compute lines
print("Computing Finite lines...")
centered = True
lines = []
mValues = []
pValues = []
qValues = []
z=25
for angle in angles:
#m, inv = farey.toFinite(angle, p)
#u, v = radon.getSliceCoordinates2(m, powerSpect, centered, p)
m, p, q, inv = farey.toFinite(angle, M)
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
lines.append((u,v))
mValues.append(m)
pValues.append(p)
qValues.append(q)
#second quadrant
if twoQuads:
#if m != 0 and m != p: #dont repeat these
if m != 0 and m != M: #dont repeat these
#m = p-m
#u, v = radon.getSliceCoordinates2(m, powerSpect, centered, p)
m = M-m
z = M-2*z
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, M)
lines.append((u,v))
print("Number of Angles:", len(angles))
print("angles:", angles)
powerSpect = np.zeros((p, p))
#compute lines
print("Computing Finite lines...")
centered = True
lines = []
mValues = []
pValues = []
qValues = []
for angle in angles:
m, p1, q, inv = farey.toFinite(angle, p)
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, p)
lines.append((u, v))
mValues.append(m)
pValues.append(p1)
qValues.append(q)
#second quadrant
if twoQuads:
if m != 0 and m != p: #dont repeat these
m = p - m
u, v = radon.getSliceCoordinates2(m, powerSpect, centered, p)
lines.append((u, v))
mValues.append(m)
mu = len(lines)
print("Number of lines:", len(lines))
print("Proportion of p:", len(lines) / float(p))
print("Proportion of 2D space:", 2.0 - len(lines) / float(p))
psnr = imageio.impsnr(lena, np.abs(reconLena))
print("Acutal RMSE:", math.sqrt(mse))
print("Acutal SSIM:", ssim)
print("Acutal PSNR:", psnr)
#compute lines
centered = True
subsetsLines = []
subsetsMValues = []
mu = 0
for angles in subsetsAngles:
lines = []
mValues = []
for angle in angles:
m, inv = farey.toFinite(angle, p)
u, v = radon.getSliceCoordinates2(m, powSpectLena, centered, p)
lines.append((u, v))
mValues.append(m)
#second quadrant
if twoQuads:
if m != 0 and m != p: #dont repeat these
m = p - m
u, v = radon.getSliceCoordinates2(m, powSpectLena, centered, p)
lines.append((u, v))
mValues.append(m)
subsetsLines.append(lines)
subsetsMValues.append(mValues)
mu += len(lines)
print("Number of lines:", mu)
print(subsetsMValues)