def isccsym(F):
import ia898.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()
def conv_media2(f, window):
H, W = window
f1 = np.empty(((f.shape[0] + H - 1), (f.shape[1] + W - 1)))
f1[(H - 1):, (W - 1):] = f
if H > 1:
f1[:(H - 1), (W - 1):] = f[(f.shape[0] - (H - 1)):, :]
if W > 1:
f1[(H - 1):, :(W - 1)] = f[:, (f.shape[1] - (W - 1)):]
if (H > 1) & (W > 1):
f1[:(H - 1), :(W - 1)] = f[(f.shape[0] - (H - 1)):,
(f.shape[1] - (W - 1)):]
sat = f1.cumsum(1).cumsum(0)
A = np.zeros_like(sat)
B = np.zeros_like(sat)
C = np.zeros_like(sat)
D = np.zeros_like(sat)
A = sat
B[:, W:] = ia.ptrans(sat, (0, W))[:, W:]
C[H:, :] = ia.ptrans(sat, (H, 0))[H:, :]
D[H:, W:] = ia.ptrans(sat, (H, W))[H:, W:]
g = A + D - C - B
g = g[(H - 1):, (W - 1):]
return g
def fp_match(f, f1):
# DFT das imagens
F = np.fft.fft2(f)
F1 = np.fft.fft2(f1)
# Idetificação do ângulo de rotação
F = ia.dftview(F)
F1 = ia.dftview(F1)
Fp = ia.polar(F,F.shape)
F1p = ia.polar(F1,F1.shape)
Pc = ia.phasecorr(Fp,F1p)
peak = np.unravel_index(np.argmax(Pc), Pc.shape)
ang = (float(peak[1])/Pc.shape[1])*360
#Correção de rotação
t1 = np.array([
[1,0,-f1.shape[0]/2.],
[0,1,-f1.shape[1]/2.],
[0,0,1]]);
t2 = np.array([
[1,0,f1.shape[0]/2.],
[0,1,f1.shape[1]/2.],
[0,0,1]]);
theta = np.radians(ang)
r1 = np.array([
[np.cos(theta),-np.sin(theta),0],
[np.sin(theta),np.cos(theta),0],
[0,0,1]]);
T = t2.dot(r1).dot(t1)
f1c = ia.affine(f1,T,0)
#Máxima correlação eentre f e f1
g = ia.phasecorr(f,f1c)
idx = np.argmax(g)
row,col = np.unravel_index(idx,g.shape)
t = np.array(f.shape) - np.array((row,col))
f1rt = ia.ptrans(f1c,-t)
return [g[row,col],f1rt]
# ## Correlação de fase para estimar o deslocamento e a correlação entre as imagens
# In[15]:
g = ia.phasecorr(f,f1c)
idx = np.argmax(g)
row,col = np.unravel_index(idx,g.shape)
vx = g[row,col]
t = np.array(f.shape) - np.array((row,col))
print('deslocamento:',np.array(f.shape) - np.array((row,col)))
print('correlação:',vx)
f1rt = ia.ptrans(f1c,-t)
nb = ia.nbshow(3)
nb.nbshow(f)
nb.nbshow(f1c)
nb.nbshow(f1rt)
nb.nbshow()
# ## Corrigir a translação e sobrepor as duas imagens para verificar se a implementação está funcionando
#
# Existem várias formas de sobrepor as duas imagens para uma melhor visualização:
# - ponderar cada uma
# - combinação no canal de cores, Red, Green, por exemplo
# - combinação geométria (linhas pares e impares ou na forma de xadrez)
# - ou exclusivo abs(f-f1)
def dftshift(f):
import ia898.src as ia
return ia.ptrans(f, np.array(f.shape) // 2)
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)
print('teste 1 d')
get_ipython().run_line_magic('timeit', 'ptrans(l,3)')
get_ipython().run_line_magic('timeit', 'ia.ptrans(l,3)')
print('teste 2 d')
get_ipython().run_line_magic('timeit', 'ptrans(x,[1,2])')
get_ipython().run_line_magic('timeit', 'ia.ptrans(x,[1,2])')
print('teste 3 d')
get_ipython().run_line_magic('timeit', 'ptrans(x3d,[1,2,1])')
get_ipython().run_line_magic('timeit', 'ia.ptrans(x3d,[1,2,1])')
# In[50]:
if testing:
f = mpimg.imread('/home/lotufo/ia898/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().run_line_magic('timeit', 'ptrans(f,np.array(f.shape)//3)')
get_ipython().run_line_magic('timeit', 'ia.ptrans(f,np.array(f.shape)//3)')
# In[34]:
def dftshift(f):
return ptrans(f, np.array(f.shape) // 2)
get_ipython().run_line_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))
# ### Example 3
# Compare with dft
# In[10]:
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().run_line_magic('timeit', 'F1 = np.fft.fft2(f)')
print('\nTempo de execução DCT:')
get_ipython().run_line_magic('timeit', 'F2 = ia.dct(f)')
# ### Example 4
# Compare with scipy function
# In[11]:
if testing:
import ia898.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",ia.ptrans(f1, (0,1,0)).astype(int),"\n\n")
print("Image translated by (-1,3,2):\n",ia.ptrans(f1, (-1,3,2)).astype(int),"\n\n")