def mixingsubband(fimau,fimao):
'''
References
----------
Pierrick Coupe - [email protected]
Jose V. Manjon - [email protected]
Brain Imaging Center, Montreal Neurological Institute.
Mc Gill University
Copyright (C) 2010 Pierrick Coupe and Jose V. Manjon
'''
s=fimau.shape
p0 = 2**(np.ceil(np.log2(s[0])))
p1 = 2**(np.ceil(np.log2(s[1])))
p2 = 2**(np.ceil(np.log2(s[2])))
pad1 = np.zeros((p0,p1,p2));
pad2 = pad1.copy();
pad1[:s[0],:s[1],:s[2]] = fimau[...]
pad2[:s[0],:s[1],:s[2]] = fimao[...]
af = np.array([ [0, -0.01122679215254],
[0, 0.01122679215254],
[-0.08838834764832, 0.08838834764832],
[0.08838834764832, 0.08838834764832],
[0.69587998903400, -0.69587998903400],
[0.69587998903400, 0.69587998903400],
[0.08838834764832, -0.08838834764832],
[-0.08838834764832, -0.08838834764832],
[0.01122679215254, 0],
[0.01122679215254, 0]])
sf=np.array(af[::-1,:])
w1 = dwt3D(pad1,1,af)
w2 = dwt3D(pad2,1,af)
w1[0][2] = w2[0][2]
w1[0][4] = w2[0][4]
w1[0][5] = w2[0][5]
w1[0][6] = w2[0][6]
fima = idwt3D(w1,1,sf)
fima = fima[:s[0],:s[1],:s[2]];
# TO-DO: NAN checking
#ind=np.isnan(fima)
#fima[ind]=fimau[ind];
# negative checking (only for rician noise mixing)
fima[fima<0]=0
return fima
def ascm(ima,fimau,fimao,h):
'''
Adaptive Soft (wavelet) Coefficient Mixing proposed by P. Coupe et al.
Combines two filtered 3D-images at different resolutions and the orginal
image. Returns the resulting combined image.
Parameters
----------
ima: the original (not filtered) image
fimau : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:3x3), which corresponds to a "high resolution" filter.
fimao : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:5x5), which corresponds to a "low resolution" filter.
h: the estimated standard deviation of the Gaussian random variables
that explain the rician noise. Note: In P. Coupe et al. the
rician noise was simulated as sqrt((f+x)^2 + (y)^2) where f is
the pixel value and x and y are independent realizations of a
random variable with Normal distribution, with mean=0 and
standard deviation=h
References
----------
Pierrick Coupe - [email protected]
Jose V. Manjon - [email protected]
Brain Imaging Center, Montreal Neurological Institute.
Mc Gill University
Copyright (C) 2008 Pierrick Coupe and Jose V. Manjon
************************************************************************
* 3D Adaptive Multiresolution Non-Local Means Filter *
* P. Coupe a, J. V. Manjon, M. Robles , D. L. Collin *
************************************************************************
'''
s=fimau.shape;
p=[0,0,0]
p[0]=2**math.ceil(math.log(s[0],2))
p[1]=2**math.ceil(math.log(s[1],2))
p[2]=2**math.ceil(math.log(s[2],2))
pad1=np.zeros((p[0],p[1],p[2]));
pad2=np.zeros((p[0],p[1],p[2]));
pad3=np.zeros((p[0],p[1],p[2]));
pad1[:s[0], :s[1], :s[2]]=fimau[:,:,:]
pad2[:s[0], :s[1], :s[2]]=fimao[:,:,:]
pad3[:s[0], :s[1], :s[2]]=ima[:,:,:]
af = np.array([ [0, -0.01122679215254],
[0, 0.01122679215254],
[-0.08838834764832, 0.08838834764832],
[0.08838834764832, 0.08838834764832],
[0.69587998903400, -0.69587998903400],
[0.69587998903400, 0.69587998903400],
[0.08838834764832, -0.08838834764832],
[-0.08838834764832, -0.08838834764832],
[0.01122679215254, 0],
[0.01122679215254, 0]])
sf=np.array(af[::-1,:])
w1= dwt3D.dwt3D(pad1,1,af)
w2= dwt3D.dwt3D(pad2,1,af)
w3= dwt3D.dwt3D(pad3,1,af)
for i in xrange(7):
tmp = np.array(w3[0][i])
tmp = tmp[:(s[0]//2), :(s[1]//2), :(s[2]//2)]
sigY = np.std(tmp, ddof=1)
sigX = (sigY*sigY) - h*h
if sigX<0:
T=abs(w3[0][i]).max()
else:
T=(h*h)/(sigX**0.5)
w3[0][i]=abs(w3[0][i])
dist=np.array(w3[0][i])-T
dist=np.exp(-0.01*dist)
dist=1./(1+dist)
w3[0][i]=dist*w1[0][i] + (1-dist)*w2[0][i]
w3[1]=w1[1]
fima= idwt3D.idwt3D(w3,1,sf)
fima=fima[:s[0], :s[1], :s[2]]
return fima
def hsm(fimau, fimao):
'''
Hard Subband Mixing algorithm, proposed by P. Coupe et al.
Combines two filtered 3D-images at different resolutions. Returns the
resulting combined image.
Parameters
----------
fimau : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:3x3), which corresponds to a "high resolution" filter.
fimao : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:5x5), which corresponds to a "low resolution" filter.
References
----------
Pierrick Coupe - [email protected]
Jose V. Manjon - [email protected]
Brain Imaging Center, Montreal Neurological Institute.
Mc Gill University
Copyright (C) 2008 Pierrick Coupe and Jose V. Manjon
************************************************************************
* 3D Adaptive Multiresolution Non-Local Means Filter *
* P. Coupe a, J. V. Manjon, M. Robles , D. L. Collin *
************************************************************************
Details on Wavelet mixing
************************************************************************
* The hard wavelet subbands mixing is described in: *
* *
* P. Coupe, S. Prima, P. Hellier, C. Kervrann, C. Barillot. *
* 3D Wavelet Sub-Bands Mixing for Image Denoising *
* International Journal of Biomedical Imaging, 2008 *
************************************************************************
'''
s = fimau.shape
p = [0, 0, 0]
p[0] = 2**math.ceil(math.log(s[0], 2))
p[1] = 2**math.ceil(math.log(s[1], 2))
p[2] = 2**math.ceil(math.log(s[2], 2))
pad1 = np.zeros((p[0], p[1], p[2]))
pad2 = np.zeros((p[0], p[1], p[2]))
pad1[:s[0], :s[1], :s[2]] = fimau
pad2[:s[0], :s[1], :s[2]] = fimao
af = np.array([[0, -0.01122679215254], [0, 0.01122679215254],
[-0.08838834764832, 0.08838834764832],
[0.08838834764832, 0.08838834764832],
[0.69587998903400, -0.69587998903400],
[0.69587998903400, 0.69587998903400],
[0.08838834764832, -0.08838834764832],
[-0.08838834764832, -0.08838834764832],
[0.01122679215254, 0], [0.01122679215254, 0]])
sf = np.array(af[::-1, :])
w1 = dwt3D.dwt3D(pad1, 1, af)
w2 = dwt3D.dwt3D(pad2, 1, af)
#w1[0][2] = (w2[0][2]+w1[0][2])/2;
#w1[0][4] = (w2[0][4]+w1[0][4])/2;
#w1[0][5] = (w2[0][5]+w1[0][5])/2;
#w1[0][6] = (w2[0][6]+w1[0][6])/2;
w1[0][2] = w2[0][2]
w1[0][4] = w2[0][4]
w1[0][5] = w2[0][5]
w1[0][6] = w2[0][6]
fima = idwt3D.idwt3D(w1, 1, sf)
fima = fima[:s[0], :s[1], :s[2]]
return fima
def ascm(ima, fimau, fimao, h):
'''
Adaptive Soft (wavelet) Coefficient Mixing proposed by P. Coupe et al.
Combines two filtered 3D-images at different resolutions and the orginal
image. Returns the resulting combined image.
Parameters
----------
ima: the original (not filtered) image
fimau : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:3x3), which corresponds to a "high resolution" filter.
fimao : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:5x5), which corresponds to a "low resolution" filter.
h: the estimated standard deviation of the Gaussian random variables
that explain the rician noise. Note: In P. Coupe et al. the
rician noise was simulated as sqrt((f+x)^2 + (y)^2) where f is
the pixel value and x and y are independent realizations of a
random variable with Normal distribution, with mean=0 and
standard deviation=h
References
----------
Pierrick Coupe - [email protected]
Jose V. Manjon - [email protected]
Brain Imaging Center, Montreal Neurological Institute.
Mc Gill University
Copyright (C) 2008 Pierrick Coupe and Jose V. Manjon
************************************************************************
* 3D Adaptive Multiresolution Non-Local Means Filter *
* P. Coupe a, J. V. Manjon, M. Robles , D. L. Collin *
************************************************************************
'''
s = fimau.shape
p = [0, 0, 0]
p[0] = 2**math.ceil(math.log(s[0], 2))
p[1] = 2**math.ceil(math.log(s[1], 2))
p[2] = 2**math.ceil(math.log(s[2], 2))
pad1 = np.zeros((p[0], p[1], p[2]))
pad2 = np.zeros((p[0], p[1], p[2]))
pad3 = np.zeros((p[0], p[1], p[2]))
pad1[:s[0], :s[1], :s[2]] = fimau[:, :, :]
pad2[:s[0], :s[1], :s[2]] = fimao[:, :, :]
pad3[:s[0], :s[1], :s[2]] = ima[:, :, :]
af = np.array([[0, -0.01122679215254], [0, 0.01122679215254],
[-0.08838834764832, 0.08838834764832],
[0.08838834764832, 0.08838834764832],
[0.69587998903400, -0.69587998903400],
[0.69587998903400, 0.69587998903400],
[0.08838834764832, -0.08838834764832],
[-0.08838834764832, -0.08838834764832],
[0.01122679215254, 0], [0.01122679215254, 0]])
sf = np.array(af[::-1, :])
w1 = dwt3D.dwt3D(pad1, 1, af)
w2 = dwt3D.dwt3D(pad2, 1, af)
w3 = dwt3D.dwt3D(pad3, 1, af)
for i in xrange(7):
tmp = np.array(w3[0][i])
tmp = tmp[:(s[0] // 2), :(s[1] // 2), :(s[2] // 2)]
sigY = np.std(tmp, ddof=1)
sigX = (sigY * sigY) - h * h
if sigX < 0:
T = abs(w3[0][i]).max()
else:
T = (h * h) / (sigX**0.5)
w3[0][i] = abs(w3[0][i])
dist = np.array(w3[0][i]) - T
dist = np.exp(-0.01 * dist)
dist = 1. / (1 + dist)
w3[0][i] = dist * w1[0][i] + (1 - dist) * w2[0][i]
w3[1] = w1[1]
fima = idwt3D.idwt3D(w3, 1, sf)
fima = fima[:s[0], :s[1], :s[2]]
return fima
def hsm(fimau, fimao):
'''
Hard Subband Mixing algorithm, proposed by P. Coupe et al.
Combines two filtered 3D-images at different resolutions. Returns the
resulting combined image.
Parameters
----------
fimau : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:3x3), which corresponds to a "high resolution" filter.
fimao : 3D double array,
filtered image with optimized non-local means using a small block
(suggested:5x5), which corresponds to a "low resolution" filter.
References
----------
Pierrick Coupe - [email protected]
Jose V. Manjon - [email protected]
Brain Imaging Center, Montreal Neurological Institute.
Mc Gill University
Copyright (C) 2008 Pierrick Coupe and Jose V. Manjon
************************************************************************
* 3D Adaptive Multiresolution Non-Local Means Filter *
* P. Coupe a, J. V. Manjon, M. Robles , D. L. Collin *
************************************************************************
Details on Wavelet mixing
************************************************************************
* The hard wavelet subbands mixing is described in: *
* *
* P. Coupe, S. Prima, P. Hellier, C. Kervrann, C. Barillot. *
* 3D Wavelet Sub-Bands Mixing for Image Denoising *
* International Journal of Biomedical Imaging, 2008 *
************************************************************************
'''
s=fimau.shape;
p=[0,0,0]
p[0]=2**math.ceil(math.log(s[0],2))
p[1]=2**math.ceil(math.log(s[1],2))
p[2]=2**math.ceil(math.log(s[2],2))
pad1=np.zeros((p[0],p[1],p[2]));
pad2=np.zeros((p[0],p[1],p[2]));
pad1[:s[0], :s[1], :s[2]]=fimau;
pad2[:s[0], :s[1], :s[2]]=fimao;
af = np.array([ [0, -0.01122679215254],
[0, 0.01122679215254],
[-0.08838834764832, 0.08838834764832],
[0.08838834764832, 0.08838834764832],
[0.69587998903400, -0.69587998903400],
[0.69587998903400, 0.69587998903400],
[0.08838834764832, -0.08838834764832],
[-0.08838834764832, -0.08838834764832],
[0.01122679215254, 0],
[0.01122679215254, 0]]);
sf=np.array(af[::-1,:])
w1=dwt3D.dwt3D(pad1,1,af);
w2=dwt3D.dwt3D(pad2,1,af);
#w1[0][2] = (w2[0][2]+w1[0][2])/2;
#w1[0][4] = (w2[0][4]+w1[0][4])/2;
#w1[0][5] = (w2[0][5]+w1[0][5])/2;
#w1[0][6] = (w2[0][6]+w1[0][6])/2;
w1[0][2] = w2[0][2]
w1[0][4] = w2[0][4]
w1[0][5] = w2[0][5]
w1[0][6] = w2[0][6]
fima = idwt3D.idwt3D(w1,1,sf);
fima = fima[:s[0],:s[1],:s[2]];
return fima