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steer_wav.py
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import numpy as np
from wavan import uv_plane
def steer_wav(na,nb,Nite=2):
N=11 #Number of directions (odd)
#--------------------Definitions----------------------#
x, y, shiftx, shifty, ishiftx, ishifty = uv_plane(na, nb)
x *= na/2.
y *= nb/2.
rt = np.sqrt(x**2.+y**2.)
x[x == 0] = 1
theta = np.arctan(y/x)
del x, y
#-----------------------------------------
#Angular function
#-----------------------------------------
Gk = np.zeros((N,nb,na))
Gkt = np.zeros((nb,na))
for j in range(N):
AA = 2**(N-1) * np.math.factorial(N-1)/np.sqrt(np.float(N*np.math.factorial(2*(N-1))))
#Condition A
#-------------------
ca = np.where(theta-(np.pi*j)/N < np.pi/2.)
Gkt[ca] = AA * np.cos( theta[ca] - (np.pi*j)/N )**(N-1)
#Condition B
#-------------------
cb = np.where(theta-(np.pi*j)/N >= np.pi/2)
Gkt[cb] = 0.
#Delete reflection
#-------------------
#if (j >= 0) & (j <= 2):
# Gkt[0:nb,0:na/2] = 0.
#if (j > 2) and (j < 9):
# Gkt[0:nb/2,0:na] = 0.
#if j >= 9:
# Gkt[0:nb,(na/2)-1:na] = 0.
#-------------------
Gk[j,:,:] = Gkt
Gkt=0
#-----------------------------------------
#First division uv-plan
#-----------------------------------------
H0 = np.zeros((nb,na))
L0 = np.zeros((nb,na))
max = np.pi/2.
r = rt*max/(na/2.)
#Condition A
#-------------------
ca = np.where((r > np.pi/4.) & (r < np.pi/2.))
H0[ca] = np.cos( np.pi/2. * np.log(2. * r[ca] / np.pi)/np.log(2.) )
L0[ca] = 2.*np.cos( np.pi/2. * np.log(4. * r[ca] / np.pi)/np.log(2.) )
#Condition B
#-------------------
cb = np.where(r <= np.pi/4.)
H0[cb] = 0.
L0[cb] = 2.
#Condition C
#-------------------
cc = np.where(r >= np.pi/2.)
H0[cc] = 1.
L0[cc] = 0.
#-----------------------------------------
#Iterative division uv-plan
#-----------------------------------------
Hi = np.zeros((Nite,nb,na))
Li = np.zeros((Nite,nb,na))
Hit = np.zeros((nb,na))
Lit = np.zeros((nb,na))
for ite in range(Nite):
max = np.pi/2.
r = (rt*max)/(na/(2.**(ite+1.)))
#Condition A
#-------------------
ca = np.where((r > np.pi/4.) & (r < np.pi/2.))
Hit[ca] = np.cos( np.pi/2. * np.log(2. * r[ca] / np.pi)/np.log(2.) )
Lit[ca] = 2.*np.cos( np.pi/2. * np.log(4. * r[ca] / np.pi)/np.log(2.) )
#Condition B
#-------------------
cb = np.where(r <= np.pi/4)
Hit[cb] = 0.
Lit[cb] = 2.
#Condition C
#-------------------
cc = np.where(r >= np.pi/2)
Hit[cc] = 1.
Lit[cc] = 0.
#-------------------
Li[ite,:,:] = Lit
Hi[ite,:,:] = Hit
Lit = Lit * 0.
Hit = Hit * 0.
return H0, L0, Hi, Li, Gk
###############################################
def steer_trans(im,Nite=2):
N=10 #Number of directions (odd)
na = im.shape[1]
nb = im.shape[0]
imFT = np.fft.fft2(im)
x, y, shiftx, shifty, ishiftx, ishifty = uv_plane(na, nb)
del x, y, shiftx, shifty
#Create steerable filters
H0, L0, Hi, Li, Gk = steer_wav(na,nb,Nite=Nite)
#High-pass filter
#--------------------
uvWav = np.copy(H0)
uvplan = np.roll(uvWav,int(ishiftx), axis=1)
uvplan = np.roll(uvplan,int(ishifty), axis=0)
WimFT = imFT*np.conj(uvplan)
Him = np.fft.ifft2(WimFT)
#Scaling filter
#--------------------
Scal = Li[Nite-1,:,:]
uvWav = Scal/2.
uvplan = np.roll(uvWav,int(ishiftx), axis=1)
uvplan = np.roll(uvplan,int(ishifty), axis=0)
WimFT = imFT * np.conj(uvplan)
Sclim = np.fft.ifft2(WimFT)
#Steerable wavelets
#--------------------
steer = np.zeros((Nite,N,nb,na), dtype=complex)
for ite in range(Nite):
for j in range(N):
if ite == 0:
Bp = Hi[0,:,:] * L0/2.
else:
Bp = Hi[ite,:,:] * Li[ite-1,:,:]
uvWav = Bp * Gk[j,:,:]
uvplan = np.roll(uvWav,int(ishiftx), axis=1)
uvplan = np.roll(uvplan,int(ishifty), axis=0)
WimFT = imFT * np.conj(uvplan)
steer[ite,j,:,:] = np.fft.ifft2(WimFT)
return steer,Him,Sclim
###############################################
def steer_inv(steer,Him,Sclim):
N=10 #Number of directions (odd)
na = Him.shape[1]
nb = Him.shape[0]
Nite = steer.shape[0]
imagetot = np.zeros((nb,na), dtype=complex)
x, y, shiftx, shifty, ishiftx, ishifty = uv_plane(na, nb)
del x, y, shiftx, shifty
#Create steerable filters
H0, L0, Hi, Li, Gk = steer_wav(na,nb,Nite=Nite)
#High-pass filter
#--------------------
uvWav = np.copy(H0)
imFT = np.fft.fft2(Him)
uvplan = np.roll(uvWav,int(ishiftx), axis=1)
uvplan = np.roll(uvplan,int(ishifty), axis=0)
Himconv = imFT * uvplan
imagetot = Himconv
#Scaling filter
#--------------------
Scal = Li[Nite-1,:,:]
uvWav = Scal/2.
imFT = np.fft.fft2(Sclim)
uvplan = np.roll(uvWav,int(ishiftx), axis=1)
uvplan = np.roll(uvplan,int(ishifty), axis=0)
Sclimconv = imFT * uvplan
imagetot += Sclimconv
#Steerable wavelets
#--------------------
for ite in range(Nite):
for j in range(N):
if ite == 0:
Bp = Hi[0,:,:] * L0
else:
Bp = Hi[ite,:,:] * Li[ite-1,:,:]/2.
uvWav = Bp * Gk[j,:,:]
imFT = np.fft.fft2(steer[ite,j,:,:])
uvplan = np.roll(uvWav,int(ishiftx), axis=1)
uvplan = np.roll(uvplan,int(ishifty), axis=0)
steerconv = imFT * uvplan
imagetot += steerconv
imout = np.fft.ifft2(imagetot).real
return imout