nb.nbshow()
print('teste')
get_ipython().magic('timeit ptrans(f,np.array(f.shape)//3)')
get_ipython().magic('timeit ia.ptrans(f,np.array(f.shape)//3)')
# In[34]:
def dftshift(f):
return ptrans(f, np.array(f.shape)//2)
# In[49]:
def idftshift(f):
return ptrans(f, np.ceil(-np.array(np.shape(f))/2).astype(np.int))
# In[48]:
f = mpimg.imread('../data/cameraman.tif')
F = ia.dft(f)
Fs = ia.dftshift(F)
Fs1 = dftshift(F)
iFs1 = idftshift(Fs1)
ia.adshow(ia.dftview(F))
ia.adshow(ia.dftview(Fs))
ia.adshow(ia.dftview(Fs1))
ia.adshow(ia.dftview(iFs1))
ea979path = os.path.abspath('../../')
if ea979path not in sys.path:
sys.path.append(ea979path)
import ea979.src as ia
# ### Example 1
# In[2]:
if testing:
import matplotlib.image as mpimg
import numpy.fft as FFT
f = mpimg.imread('../data/cameraman.tif')
ia.adshow(f, "Original 2D image - Cameraman")
F = FFT.fft2(f)
Fv = ia.dftview(F)
ia.adshow(Fv, "Cameraman DFT optical spectrum")
# ## Equation
#
#
# $$ \begin{matrix}
# Gaux &=& \log(|F_{xc,yc}| + 1)\\xc &=& \lfloor W/2 \rfloor \\yc &=& \lfloor H/2 \rfloor\\ G &=& Gaux|_0^{255}
# \end{matrix} $$
# In[3]:
if testing:
print('testing dftview')
print(
repr(
F = ia.dft(f) # proposed dft
F1 = np.fft.fftn(f) # numpy dft
print('ia.dft:', '\n', F.round(2), '\n')
print('fft.fftn:', '\n', F1.round(2), '\n')
print('Equal Results? (max error)', abs(F1 - F).max())
# ### Image example: 2d circle
# In[5]:
if testing:
f = ia.circle([256, 256], 10, [129, 129])
ia.adshow(f)
F = ia.dft(f)
Fv = ia.dftview(F)
ia.adshow(Fv)
# ### Image example: 3d square
# In[6]:
if False: #testing:
f = np.zeros((25, 30, 40))
f[10:15, 20:26, 21:27] = 1
F = ia.dft(f)
ia.adshow(ia.normalize(ia.mosaic(f, 5)), 'Original Image')
ia.adshow(ia.mosaic(ia.dftview(F), 5), 'Fourier Transformation')
# ### Comparison with other implementations
# In[4]:
if False: #testing:
import matplotlib.image as mpimg
f = mpimg.imread('../data/cameraman.tif')
F = ia.dft(f)
print(F.shape)
H = ia.circle(F.shape, 50, [F.shape[0] / 2, F.shape[1] / 2])
H = ia.normalize(H, [0, 1])
FH = F * ia.idftshift(H)
print(ia.isdftsym(FH))
g = ia.idft(FH)
ia.adshow(f)
ia.adshow(ia.dftview(F))
ia.adshow(ia.normalize(H, [0, 255]))
ia.adshow(ia.dftview(FH))
ia.adshow(ia.normalize(abs(g)))
# ## Equation
#
# $$ \begin{matrix}
# f(x) &=& \frac{1}{N}\sum_{u=0}^{N-1}F(u)\exp(j2\pi\frac{ux}{N}) \\ & & 0 \leq x < N, 0 \leq u < N \\ \mathbf{f} &=& \frac{1}{\sqrt{N}}(A_N)^* \mathbf{F}
# \end{matrix} $$
# $$ \begin{matrix}
# f(x,y) &=& \frac{1}{NM}\sum_{u=0}^{N-1}\sum_{v=0}^{M-1}F(u,v)\exp(j2\pi(\frac{ux}{N} + \frac{vy}{M})) \\ & & (0,0) \leq (x,y) < (N,M), (0,0) \leq (u,v) < (N,M) \\
# \mathbf{f} &=& \frac{1}{\sqrt{NM}} (A_N)^* \mathbf{F} (A_M)^*
# \end{matrix} $$
get_ipython().system(' jupyter nbconvert --to python bwlp.ipynb')
import numpy as np
import sys, os
ea979path = os.path.abspath('../../')
if ea979path not in sys.path:
sys.path.append(ea979path)
import ea979.src as ia
# ### Example 1
# In[2]:
if testing:
H2_10 = ia.bwlp([100, 100], 2, 2) # cutoff period: 2 pixels, order: 10
ia.adshow(ia.dftview(H2_10))
# In[3]:
if testing:
H4_1 = ia.bwlp([100, 100], 4, 1) # cutoff period: 4, order: 1
ia.adshow(ia.dftview(H4_1))
# In[4]:
if testing:
H8_100 = ia.bwlp([100, 100], 8, 100) # cutoff period: 8, order: 100
ia.adshow(ia.dftview(H8_100))
# In[5]:
100)))) # dimension variation
print(ia.isccsym(np.fft.fft2(np.random.rand(101, 100))))
print(ia.isccsym(np.fft.fft2(np.random.rand(101, 101))))
# ### Image Example: circular filter
# In[14]:
if testing:
img = mpimg.imread('../data/cameraman.tif')
F = ia.dft(img)
imgc = 1 * ia.circle(img.shape, 50, [img.shape[0] / 2, img.shape[1] / 2])
imgct = ia.ptrans(imgc, np.array(imgc.shape) // 2)
ia.adshow(ia.normalize(imgct), 'circular filter')
res = F * imgct
ia.adshow(ia.dftview(res))
print('Is this filter symmetric?', ia.isccsym(res))
# ### Image Example 2: retangular filter
# In[17]:
if False: # testing:
mquadra = ia.rectangle(img.shape, [50, 50],
[img.shape[0] / 2, img.shape[1] / 2])
ia.adshow(mquadra, 'RETANGULO')
mquadra = ia.ptrans(mquadra, array(mquadra.shape) / 2)
ia.adshow(ia.normalize(mquadra), 'retangular filter')
mfiltrada = F * mquadra
print('Is this filter symmetric?', ia.isccsym(mfiltrada))