import numpy as np
import sys, os
get_ipython().magic('matplotlib inline')
import matplotlib.image as mpimg
import matplotlib.pyplot as plt
ia898path = os.path.abspath('/home/lotufo')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
# ## Atenção, ler com a função ia.nbread
# In[4]:
dt = ia.nbread('/home/lotufo/ia898/data/digits_train.png')
ia.adshow(dt, 'digits_train.png')
# In[5]:
print(dt.shape)
print(dt.dtype)
print(dt[:3, :20])
# ## Visualizando o dataset
# O dataset é composto de 80 amostras. Cada amostra está organizado como: primeira coluna é o rótulo do dígito, de 0 a 9 e seguida 160 atributos (16 linhas e 10 colunas). O típo é uint8.
# In[6]:
nb = ia.nbshow(10)
sys.path.append(ia898path)
import ia898.src as ia
# ## Showing a numerical example
# In[2]:
if testing:
F = ia.circle([5,7], 2, [2,3])
print (F.astype(np.uint8))
# ## Printing the generated image
# In[4]:
if testing:
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
get_ipython().run_line_magic('matplotlib', 'inline')
f = ia.circle([200,300], 90, [100,150])
ia.adshow(f,'circle')
# ## Contributions
#
# Luis Antonio Prado, 1st semester 2017
f = np.arange(24).reshape(2, 3, 4) # original image with generic axis
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')
ia898path = os.path.abspath('../../')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
# ## Examples
#
# ### Example 1
# In[2]:
if testing:
A = ia.hadamardmatrix(128)
ia.adshow(ia.normalize(A, [0, 255]))
# ### Example 2
# In[4]:
if testing:
A = ia.hadamardmatrix(4)
print(A)
print(np.dot(A, np.transpose(A)))
# ## Measuring time:
# In[3]:
if testing:
np.set_printoptions(suppress=True, precision=4)
A = ia.dctmatrix(4)
print('Visualiza matriz DCT 4x4:\n', A)
B = np.dot(A, np.transpose(A))
print("\nVisualiza propriedade A*A'= I:\n", B)
# ### Example 2
# In[4]:
if testing:
get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import sys, os
ia898path = os.path.abspath('/home/lotufo')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
A = ia.dctmatrix(128)
ia.adshow(ia.normalize(A, [0, 255]), 'DCT 128x128')
# In[ ]:
# In[ ]:
import matplotlib.image as mpimg
ia898path = os.path.abspath('../../')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
# ### Example 1
# In[6]:
if testing:
f = ia.circle([120, 150], 6, [60, 75])
F = ia.dft(f)
Fs = ia.dftshift(F)
ia.adshow(ia.dftview(F))
ia.adshow(ia.dftview(Fs))
# In[7]:
if testing:
F = np.array([[10 + 6j, 20 + 5j, 30 + 4j], [40 + 3j, 50 + 2j, 60 + 1j]])
Fs = ia.dftshift(F)
print('Fs=\n', Fs)
# ## Equation
#
# $$ \begin{matrix}
# HS &=& H_{xo,yo} \\xo &=& \lfloor W/2 \rfloor \\yo &=& \lfloor H/2 \rfloor
# \end{matrix} $$
print(np.round(g.real))
# 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
#
# $$ \begin{matrix}
# f(x) &=& \frac{1}{N}\sum_{u=0}^{N-1}F(u)\exp(j2\pi\frac{ux}{N}) \\ & & 0 \leq x < N, 0 \leq u < N \\ \mathbf{f} &=& \frac{1}{\sqrt{N}}(A_N)^* \mathbf{F}
# \end{matrix} $$
# $$ \begin{matrix}
# f(x,y) &=& \frac{1}{NM}\sum_{u=0}^{N-1}\sum_{v=0}^{M-1}F(u,v)\exp(j2\pi(\frac{ux}{N} + \frac{vy}{M})) \\ & & (0,0) \leq (x,y) < (N,M), (0,0) \leq (u,v) < (N,M) \\
# \mathbf{f} &=& \frac{1}{\sqrt{NM}} (A_N)^* \mathbf{F} (A_M)^*
# \end{matrix} $$
if testing:
g = ia.ellipse([16, 16], [2, 4], [8, 8], np.pi * 0.25)
print('g:\n', g.astype(int))
# ## Measuring time:
# In[4]:
if testing:
from time import time
t = time()
g = ia.ellipse([300, 300], [90, 140], [150, 150], np.pi * 0.25)
tend = time()
print('Computational time (10k, 10k) is {0:.2f} seconds.'.format(tend - t))
ia.adshow(g, "Ellipse")
# In[6]:
if testing:
print('Computational time (10k, 10k) is:')
get_ipython().run_line_magic(
'timeit', 'ia.ellipse([300,300], [90,140], [150,150], np.pi * 0.25)')
# ## Equation
#
# $$
# \begin{matrix}
# \frac{((x-center_x)\cos(\theta) - (y-center_y)\sin(\theta))^2}{r_x^2}
# +
# \frac{((x-center_x)\sin(\theta) - (y-center_y)\cos(\theta))^2}{r_y^2} <= 1
if testing:
F = ia.ramp([5, 7], 3, [4, 10])
print(F)
F = ia.ramp((1, 5, 7), (0, 3, 0), [0, 0, 4, 10, 0, 0])
print(F)
F = ia.ramp([1, 5, 7], [3, 0, 0], [4, 10, 0, 0, 0, 0])
print(F)
# - **Image example**
# In[4]:
if testing:
F = ia.ramp([1, 200, 300], [0, 10, 0], [0, 0, 0, 255, 0, 128])
ia.adshow(ia.normalize(F.reshape(200, 300)))
# In[6]:
if testing:
F = ia.ramp([200, 300], 10, [0, 255])
ia.adshow(ia.normalize(F))
# In[7]:
if testing:
F = ia.ramp([1, 200, 300], [10, 0, 0], [0, 255, 0, 0, 0, 0])
ia.adshow(ia.normalize(F.reshape(200, 300)))
# ### Image example - 3D
# In[9]:
if testing:
get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import sys, os
ia898path = os.path.abspath('/home/lotufo')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
r, c = np.indices((256, 256))
f = ((r - 129)**2 + (c - 129)**2 < 10**2) * 255
ia.adshow(ia.normalize(f), 'Imagem original')
F = ia.dct(f)
ia.adshow(ia.normalize(np.log(abs(F) + 1)), 'DCT')
# ### Example 3
# Compare with dft
# In[10]:
if testing:
f = mpimg.imread('../data/cameraman.tif')
nb = ia.nbshow(3)
nb.nbshow(f, 'Imagem original')
# 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))
# ### Exemplo 3
# Show how to perform Template Matching using phase correlation.
# In[ ]:
if testing:
# 2D example
w1 = f1[27:69, 83:147]
h3 = np.zeros_like(f1)
get_ipython().system(' jupyter nbconvert --to python dftmatrix.ipynb')
import numpy as np
import sys, os
import matplotlib.image as mpimg
ia898path = os.path.abspath('../../')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
# ### Example 1
# In[2]:
if testing:
A = ia.dftmatrix(128)
ia.adshow(ia.normalize(A.real), 'A.real')
ia.adshow(ia.normalize(A.imag), 'A.imag')
# Example 2
# ---------
# In[3]:
if testing:
A = ia.dftmatrix(4)
print('A=\n', A.round(1))
print('A-A.T=\n', A - A.T)
print((np.abs(np.linalg.inv(A) - np.conjugate(A))).max() < 10E-15)
# ### Example 3
#
g = f[::4, ::4] nb.nbshow(f, '%s' % (f.shape, )) nb.nbshow(g, '%s' % (g.shape, )) nb.nbshow() # ## Função comb # # Será necessário a função `comb` para poder fazer esta demonstração. # # Será necessário também ver outras propriedades da convolução e do teorema da convolução para poder fazer esta demonstração. Recomendo ler livros ou textos sobre esta explicação da interpretação no domínio da frequência da redução via interpolação. # In[15]: c = ia.comb((f.shape), (4, 4), (0, 0)) ia.adshow(ia.normalize(c)) # In[16]: C = np.fft.fft2(c) F = np.fft.fft2(f) G2 = ia.pconv(F, C) nb = ia.nbshow(3) nb.nbshow(ia.dftview(F), 'Espectro da imagem original') nb.nbshow(ia.dftview(C), 'Espectro do trêm de impulsos') nb.nbshow(ia.dftview(G2), 'Espectro resultante da convolução') nb.nbshow() # In[17]: g2 = np.fft.ifft2(G2)
print(a)
# ### Example 4
# In[5]:
if testing:
get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
f = mpimg.imread('../data/cameraman.tif')
h = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]])
g = ia.conv(f, h)
gn = ia.normalize(g, [0, 255])
ia.adshow(f, title='input')
ia.adshow(gn, title='filtered')
# ## Limitations
#
# Both image and kernel are internally converted to double.
# ## Equation
#
# $$ \begin{matrix}
# (f \ast h)(r,c) &=& \sum_{i=0}^{H-1} \sum_{j=0}^{W-1} f_{e}(i,j) h_{e}(r-i, c-j) \\
# f_{e}(r,c) &=& \left\{ \begin{array}{llcl} f(r,c), & 0 \leq r \leq H_{f}-1 & and & 0 \leq r \leq W_f-1 \\
# 0, & H_f \leq r \leq H-1 & or & W_f \leq c \leq W-1 \end{array}\right.\\
# h_{e}(r,c) &=& \left\{ \begin{array}{llcl} f(r,c), & 0 \leq r \leq H_{h}-1 & and & 0 \leq r \leq W_h-1 \\
# 0, & H_h \leq r \leq H-1 & or & W_h \leq c \leq W-1 \end{array}\right.\\
# H & \geq & H_f + H_h - 1 \\
print('spread factor =', sigma)
print('Laplacian of Gaussian image : \n', F.round(2))
# #### Generating a image 2D 128x128, centered at 64x64 and sigma 4:
# In[5]:
if testing:
s, mu, sigma = [128, 128], [64, 64], 4
F = ia.log(s, mu, sigma)
print('image dimensions = ', s)
print('center of function = ', mu)
print('spread factor =', sigma)
ia.adshow(ia.normalize(F), 'Laplacian of Gaussian')
# #### Generating a image 2D 256x256, centered at 128x128 and sigma 20
# In[6]:
if testing:
s, mu, sigma = [256, 256], [128, 128], 20
F = ia.log(s, mu, sigma)
print('image dimensions = ', s)
print('center of function = ', mu)
print('spread factor =', sigma)
ia.adshow(ia.normalize(F), 'Laplacian of Gaussian')
import sys,os
ia898path = os.path.abspath('../../')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.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
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')
np.set_printoptions(suppress=True, precision=4)
A = ia.haarmatrix(4)
print('Visualiza matriz haar 4x4:\n',A)
B = np.dot(A,np.transpose(A))
print("\nVisualiza propriedade A*A'= I:\n", B)
# ### Example 2
# In[3]:
if testing:
A = ia.haarmatrix(128)
ia.adshow(ia.normalize(A),'Haar matrix 128x128')
# ### Example 3
# In[4]:
if testing:
f = mpimg.imread('../data/cameraman.tif')
A = ia.haarmatrix(f.shape[0])
B = ia.haarmatrix(f.shape[1])
F = np.dot(np.dot(A, f), np.transpose(B))
nb = ia.nbshow(2)
itn = 5 - it # negation
print('itn=', itn)
gn = ia.applylut(f, itn)
print('gn=\n', gn)
# ### Example 2
#
# This example shows the negation operation applying the intensity transform through a negation grayscale table: it = 255 - i.
# In[3]:
if testing:
f = mpimg.imread('../data/cameraman.tif')
it = (255 - np.arange(256)).astype('uint8')
g = ia.applylut(f, it)
ia.adshow(f, 'f')
ia.adshow(g, 'g')
# ### Example 3
#
# In this example, the colortable has 3 columns and the application of the colortable to an scalar image results in an image with 3 bands.
# In[4]:
if testing:
f = np.array([[0, 1, 2], [2, 0, 1]])
ct = np.array([[100, 101, 102], [110, 111, 112], [120, 121, 122]])
#print iaimginfo(ct)
g = ia.applylut(f, ct)
print(g)
# In[2]:
if testing:
F = ia.rectangle([7,9], [3,2], [3,4])
print(F)
# - **Example 2**
# In[3]:
if testing:
F = ia.rectangle([200,300], [90,120], [70,120])
ia.adshow(ia.normalize(F))
# ## Equation
#
# \begin{equation}
# g(x,y)=\begin{cases}
# 1, & \text{if } x_\text{min} \leq x < x_\text{max} \text{ and } y_\text{min} \leq y < y_\text{max}.\\
# 0, & \text{otherwise}.
# \end{cases}
# \end{equation}
# ## Contributions
#
# Lucas de Vasconcellos Teixeira, 1st semester 2017
ia898path = os.path.abspath('../../')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.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:
f = ia.gaussian( (100,), 50, [[10*10]])
g = ia.normalize(f, [0,1])
plt.plot(g)
plt.show()
# ### Example 3 - two-dimensional image
# In[4]:
if testing:
f = ia.gaussian((150,250), np.transpose([[75,100]]), [[40*40,0],[0,30*30]])
g = ia.normalize(f, [0,255]).astype(np.uint8)
ia.adshow(g)
# ## Example 4 - Numeric 3-dimensional
# In[6]:
if testing:
f = ia.gaussian((3,4,5), np.transpose([[1,2,3]]), [[1,0,0],[0,4,0],[0,0,9]])
print('f=\n', np.array2string(f, precision=4, suppress_small=1))
g = ia.normalize(f, [0,255]).astype(np.uint8)
print('g=\n', g)
# ## Equation
#
# $$ f(r,c) = r \ c $$
# $$ \text{para} \ r \in [-75,75] $$
# $$ c \in [-100,100]$$
#
#
# No exemplo a seguir é utilizado a função `arange` para gerar os vetores de coordenadas. Para melhorar
# a visualização foi utilizada a função `ia636:iaisolines iaisolines` que permite visualizar os
# pixels de mesmo valores (isolinhas) da imagem gerada com uma cor destacada.
# In[4]:
r, c = np.meshgrid(np.arange(-75, 75), np.arange(-100, 100), indexing='ij')
f = r * c
fn = ia.normalize(f)
ia.adshow(fn, 'Ponto de sela')
#ia.adshow(ia.iaisolines(fn,9), 'Ponto de sela com isolinhas')
# ## Outras images criadas com matrizes de índices
#
# Implemente alguma das seguintes funções da toolbox `ia636:MainPage` que também foram feitas desta forma:
#
# - [ia636:iacos](http://adessowiki.fee.unicamp.br/adesso-1/wiki/ia636/iacos/view/) - Cossenóide
# - [ia636:iacircle](http://adessowiki.fee.unicamp.br/adesso-1/wiki/ia636/iacircle/view/) - Círculo
# - [ia636:iarectangle](http://adessowiki.fee.unicamp.br/adesso-1/wiki/ia636/iarectangle/view/) - Retângulo
# - [ia636:ialog](http://adessowiki.fee.unicamp.br/adesso-1/wiki/ia636/ialog/view/) - Laplaciano da gaussiana
# ## Atividades
#
# - Faça a seguir um programa qualquer de geração de imagem a partir de uma equação:
[[17, 18, 19], [20, 21, 22], [23, 24, 25]]])
print("\n Image Kernel (H): ")
print(h)
result = ia.pconv(f, h)
print("\n Image Output - (G): ")
print(result)
# ## Example with Image 2D
# In[6]:
if testing:
f = mpimg.imread('../data/cameraman.tif')
ia.adshow(f, title='a) - Original Image')
h = np.array([[-1, -1, -1], [0, 0, 0], [1, 1, 1]])
g = ia.pconv(f, h)
print("\nPrewitt´s Mask")
print(h)
gn = ia.normalize(g, [0, 255])
ia.adshow(gn, title='b) Prewitt´s Mask filtering')
ia.adshow(ia.normalize(abs(g)),
title='c) absolute of Prewitt´s Mask filtering')
# ## Equation
#
# $$ f(i) = f(i + kN), h(i)=h(i+kN)$$
#
import numpy as np
import sys,os
ia898path = os.path.abspath('../..')
if ia898path not in sys.path:
sys.path.append(ia898path)
import ia898.src as ia
dir(ia)
print('file:',ia.__file__)
print(ia.__version__)
# In[3]:
if testing:
A = (np.arange(256*256) % 256).reshape(256,256).astype('uint8')
ia.adshow(A,'teste')
ia.show(A)
# In[6]:
if testing:
R = (np.arange(256*256) % 256).reshape(256,256).astype('uint8')
G = 255-R
B = R[:,::-1]
rgb = np.array((R,G,B))
print(rgb.shape)
ia.adshow(rgb)
ia.show(rgb)
ff = rgb.transpose((1,2,0))
print(ff.shape)
sys.path.append(ia898path)
import ia898.src as ia
get_ipython().run_line_magic('matplotlib', 'inline')
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
# ### Example 1
# In[3]:
if testing:
tables = [ 'gray', 'hsv', 'hot', 'cool', 'copper','pink','bone']
r,f = np.indices((10,256), 'uint8')
ia.adshow(f, 'gray scale')
for table in tables:
cm = ia.colormap(table)
g = ia.applylut(f, cm)
g = g.astype('uint8')
if len(g.shape)==3:
g = g.transpose(1,2,0)
ia.adshow(g, table)
# ### Example 2
#
# Plotting the colormap table
