def isccsym(F):
import ea979.src as ia
if len(F.shape) == 1: F = F[np.newaxis, np.newaxis, :]
if len(F.shape) == 2: F = F[np.newaxis, :, :]
n, m, p = F.shape
return (abs(F - np.conjugate(ia.ptrans(F[::-1, ::-1, ::-1], (1, 1, 1)))) <
10E-4).all()
get_ipython().magic('timeit ptrans(l,3)')
get_ipython().magic('timeit ia.ptrans(l,3)')
print('teste 2 d')
get_ipython().magic('timeit ptrans(x,[1,2])')
get_ipython().magic('timeit ia.ptrans(x,[1,2])')
print('teste 3 d')
get_ipython().magic('timeit ptrans(x3d,[1,2,1])')
get_ipython().magic('timeit ia.ptrans(x3d,[1,2,1])')
# In[50]:
if testing:
f = mpimg.imread('../data/cameraman.tif')
g1= ptrans(f, np.array(f.shape)//3)
g2 =ia.ptrans(f, np.array(f.shape)//3)
nb = ia.nbshow(2)
nb.nbshow(g1,title='ptrans')
nb.nbshow(g2,title='ia.ptrans')
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)
# ### Example 3
# Compare with dft
# In[3]:
if testing:
f = mpimg.imread('../data/cameraman.tif')
nb = ia.nbshow(3)
nb.nbshow(f, 'Imagem original')
F1 = np.fft.fft2(f)
F2 = ia.dct(f)
nb.nbshow(
ia.normalize(
np.log(
np.abs(ia.ptrans(F1, (f.shape[0] // 2, f.shape[1] // 2)) +
1))), 'DFT')
nb.nbshow(ia.normalize(np.log(abs(F2) + 1)), 'DCT')
nb.nbshow()
print('Tempo de execução DFT:')
get_ipython().magic('%timeit F1 = np.fft.fft2(f)')
print('\nTempo de execução DCT:')
get_ipython().magic('%timeit F2 = ia.dct(f)')
# ### Example 4
# Compare with scipy function
# In[4]:
if testing:
sys.path.append(ea979path)
import ea979.src as ia
# ### Example 1
#
# Numeric examples in 2D and 3D.
# In[3]:
if testing:
# 2D example
f = np.arange(15).reshape(3, 5)
print("Original 2D image:\n", f, "\n\n")
print("Image translated by (0,0):\n",
ia.ptrans(f, (0, 0)).astype(int), "\n\n")
print("Image translated by (0,1):\n",
ia.ptrans(f, (0, 1)).astype(int), "\n\n")
print("Image translated by (-1,2):\n",
ia.ptrans(f, (-1, 2)).astype(int), "\n\n")
# In[4]:
if testing:
# 3D example
f1 = np.arange(60).reshape(3, 4, 5)
print("Original 3D image:\n", f1, "\n\n")
print("Image translated by (0,0,0):\n",
ia.ptrans(f1, (0, 0, 0)).astype(int), "\n\n")
print("Image translated by (0,1,0):\n",
def dftshift(f):
import ea979.src as ia
return ia.ptrans(f, np.array(f.shape) // 2)
if testing:
print('Is this function symmetric?')
print(ia.isccsym(np.fft.fft2(np.random.rand(100,
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')
get_ipython().magic('matplotlib inline')
import matplotlib.image as mpimg
# ### Example 1
# Show that the point of maximum correlation for two equal images is the origin.
#
#
# In[4]:
if testing:
# 2D example
f1 = mpimg.imread("../data/cameraman.tif")
noise = np.random.rand(f1.shape[0], f1.shape[1])
f2 = ia.normalize(ia.ptrans(f1, (-1, 50)) + 300 * noise)
g1 = ia.phasecorr(f1, f2)
i = np.argmax(g1)
row, col = np.unravel_index(i, g1.shape)
v = g1[row, col]
print(np.array(f1.shape) - np.array((row, col)))
# In[ ]:
if testing:
print('max at:(%d, %d)' % (row, col))
ia.adshow(ia.normalize(f1), "input image")
ia.adshow(ia.normalize(f2), "input image")
ia.adshow(ia.normalize(g1),
"Correlation peak at (%d,%d) with %d" % (row, col, v))