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deblatting_pw.py
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deblatting_pw.py
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import random
import pdb
import os
import cv2 as cv
import matplotlib.pyplot as plt
import numpy as np
from numpy.fft import fft2, ifft2
import scipy.sparse.linalg
from scipy import sparse
from utils import *
from vis import *
from deblatting import *
def estimateFM_pw(I, B, H, M=None, F=None, F_T=None, M_T=None, state=None, params=None):
## Estimate F_i,M_i in FMO equation I = \sum_i H_i*F_i + (1 - \sum_i H_i*M_i)B, where * is convolution
## M is suggested to be specified to know approximate object size, at least as am array of zeros, for speed-up
## F_T, M_T - template for F_i and M_i
if params is None:
params = Params()
if len(H.shape) == 2: ## not piece-wise
H = H[:,:,np.newaxis,np.newaxis]
elif len(H.shape) == 3:
H = H[:,:,np.newaxis,:]
ns = H.shape[3]
if M is None:
if F is not None:
M = np.zeros(F.shape[:2]+(1,1,))
else:
M = np.zeros(I.shape[:2]+(1,1,))
elif len(M.shape) == 2:
M = M[:,:,np.newaxis,np.newaxis]
elif len(M.shape) == 3:
M = M[:,:,np.newaxis,:]
if F is None:
F = np.zeros((M.shape[0],M.shape[1],3,ns))
single_m = (M.shape[3] == 1)
Fshape = F.shape
Mshape = M.shape
f = vec3(F)
m = vec3(M)
if F_T is not None:
F_T = vec3(F_T)
if M_T is not None:
M_T = M_T.flatten('F')
Me = np.zeros(I.shape[:2]+(1,M.shape[3],))
Fe = np.zeros(I.shape+(ns,))
idx_f, idy_f, idz_f, idf_f = psfshift_idx(F.shape, Fe.shape)
idx_m, idy_m, idz_m, idf_m = psfshift_idx(M.shape, Me.shape)
alpha_f = params.alpha_f/ns
beta_f = params.beta_f/ns
lambda_T = params.lambda_T/ns
alpha_cross_f = params.alpha_cross_f/max(1,ns-1)
beta_cross_f = params.beta_cross_f/max(1,ns-1)
alpha_m = params.alpha_f/M.shape[3]
beta_m = params.beta_f/M.shape[3]
alpha_cross_m = params.alpha_cross_f/max(1,M.shape[3]-1)
beta_cross_m = params.beta_cross_f/max(1,M.shape[3]-1)
lambda_R = params.lambda_R/M.shape[3]
lambda_MT = params.lambda_T/M.shape[3]
if single_m:
beta_cross_m = 0
if ns == 1:
beta_cross_f = 0
## init
Dx = None
if state is not None:
Dx = state.Dx; Dy = state.Dy; DTD = state.DTD; Rn = state.Rn
vx = state.vx; vy = state.vy; ax = state.ax; ay = state.ay
vx_m = state.vx_m; vy_m = state.vy_m; ax_m = state.ax_m; ay_m = state.ay_m
vf = state.vf; af = state.af; vm = state.vm; am = state.am
vc = state.vc; ac = state.ac; vc_m = state.vc_m; ac_m = state.ac_m
if Dx is None:
Dx, Dy = createDerivatives0(Fshape)
DTD = (Dx.T @ Dx) + (Dy.T @ Dy)
vx = np.zeros((Dx.shape[0],Fshape[2]))
vy = np.zeros((Dy.shape[0],Fshape[2]))
ay = 0; ax = 0 ## v=Df splitting due to TV and its assoc. Lagr. mult.
vx_m = np.zeros((Dx.shape[0],1))
vy_m = np.zeros((Dy.shape[0],1))
ay_m = 0; ax_m = 0 ## v_m=Dm splitting due to TV (m-part) and its assoc. Lagr. mult.
af = 0; vf = 0 ## vf=f splitting due to positivity and f=0 outside mask constraint
am = 0; vm = 0 ## vm=m splitting due to mask between [0,1]
vc = 0; ac = 0 ## vc=D_cross*f splitting due to cross-image TV and its assoc. Lagr. mult. (TV works along the 3rd dim of 'f', across the different apeparances of the object)
vc_m = 0; ac_m = 0 ## vc_m=D_cross*m splitting due to cross-mask TV and its assoc. Lagr. mult. (TV works along the 3rd dim of 'm', across the different masks of the object)
if lambda_R > 0:
RnA = createRnMatrix(Fshape[:2]).A
Rn = RnA.T @ RnA - RnA.T - RnA + np.eye(RnA.shape[0])
Rn = sparse.csc_matrix(Rn)
## cross-img derivatives and single image (mask) cases
if ns == 1 or beta_cross_f == 0: # single image - disable cross-img derivatives (would cause errors)
crossDf = lambda xx: 0
crossDf_T = lambda xx: 0
crossDf_DTD = lambda xx: 0
else:
crossDf = lambda xx: crossD(xx,Fshape[2])
crossDf_T = lambda xx: crossD_T(xx,Fshape[2])
crossDf_DTD = lambda xx: crossD_DTD(xx,Fshape[2])
if single_m or beta_cross_m == 0:
crossDm = lambda xx: 0
crossDm_T = lambda xx: 0
crossDm_DTD = lambda xx: 0
else:
crossDm = lambda xx: crossD(xx,1)
crossDm_T = lambda xx: crossD_T(xx,1)
crossDm_DTD = lambda xx: crossD_DTD(xx,1)
fH = fft2(H,axes=(0,1)) # precompute FT
HT = np.conj(fH)
HT3 = np.repeat(HT, 3, axis=2)
## precompute const RHS for 'f/m' subproblem
rhs_f = np.real(ifft2(HT3*(fft2(I-B,axes=(0,1))[:,:,:,np.newaxis]),axes=(0,1)))
rhs_f = params.gamma*np.reshape(rhs_f[idx_f,idy_f,idz_f,idf_f], (Fshape[0]*Fshape[1],-1),'F')
if lambda_T > 0 and F_T is not None:
rhs_f += (lambda_T*F_T) ## template matching term lambda_T*|F-F_T|
if single_m:
rhs_m = np.real(ifft2(np.sum(HT,3)*fft2(np.sum(B*(I-B),2),axes=(0,1))[:,:,np.newaxis],axes=(0,1)))[:,:,:,np.newaxis]
else:
rhs_m = np.real(ifft2(HT*fft2(np.sum(B*(I-B),2),axes=(0,1))[:,:,np.newaxis,np.newaxis],axes=(0,1)))
rhs_m = -params.gamma*np.reshape(rhs_m[idx_m,idy_m,idz_m,idf_m],(Fshape[0]*Fshape[1],-1),'F')
if lambda_MT > 0 and M_T is not None:
rhs_m += (lambda_MT*M_T) ## template matching term lambda_MT*|M-M_T|
beta_tv4 = np.r_[np.repeat(beta_f, Fshape[2]*Fshape[3]), np.repeat(beta_m, M.shape[2]*M.shape[3])]
rel_tol2 = params.rel_tol_f**2
## ADMM loop
for iter in range(params.maxiter):
fdx = Dx @ f; fdy = Dy @ f
mdx = Dx @ m; mdy = Dy @ m
fdc = crossDf(f)
mdc = crossDm(m)
f_old = f; m_old = m
## dual/auxiliary var updates, vx/vy minimization (splitting due to TV regularizer)
if alpha_f > 0 and beta_f > 0:
val_x = fdx + ax
val_y = fdy + ay
shrink_factor = lp_proximal_mapping(np.sqrt(val_x**2 + val_y**2), alpha_f/beta_f, params.lp) # isotropic "TV"
vx = val_x*shrink_factor
vy = val_y*shrink_factor
ax = ax + fdx - vx ## 'a' step
ay = ay + fdy - vy
## vx_m/vy_m minimization (splitting due to TV regularizer for the mask)
if alpha_m > 0 and beta_m > 0:
val_x = mdx + ax_m
val_y = mdy + ay_m
shrink_factor = lp_proximal_mapping(np.sqrt(val_x**2 + val_y**2), alpha_m/beta_m, params.lp)
vx_m = val_x*shrink_factor
vy_m = val_y*shrink_factor
ax_m = ax_m + mdx - vx_m
ay_m = ay_m + mdy - vy_m
if beta_cross_f > 0: # cross-image derivative
val = fdc + ac
shrink_factor = lp_proximal_mapping(val, alpha_cross_f/beta_cross_f, 1)
vc = val*shrink_factor
ac = ac + fdc - vc
if beta_cross_m > 0: # cross-mask derivative
val = mdc + ac_m
shrink_factor = lp_proximal_mapping(val, alpha_cross_m/beta_cross_m, 1)
vc_m = val*shrink_factor
ac_m = ac_m + mdc - vc_m
## vf/vm minimization (positivity and and f-m relation so that F is not large where M is small, mostly means F<=M)
if params.beta_fm > 0:
vf = f + af
vm = m + am
if params.pyramid_eps > 0: # (m,f) constrained to convex pyramid-like shape to force f<=const*m where const = 1/eps
if single_m:
vm, vf = project2pyramid(vm, vf, params.pyramid_eps)
else:
for ii in range(ns):
vm[:,ii], vf[:,ii*Fshape[2]:ii*Fshape[2]+3] = project2pyramid(vm[:,ii], vf[:,ii*Fshape[2]:ii*Fshape[2]+3], params.pyramid_eps)
else: # just positivity and m in [0,1]
vf[vf < 0] = 0
vm[vm < 0] = 0
vm[vm > 1] = 1
# lagrange multiplier (dual var) update
af = af + f - vf
am = am + m - vm
## F,M step
rhs1 = rhs_f + beta_f*(Dx.T @ (vx-ax) + Dy.T @ (vy-ay)) + beta_cross_f*crossDf_T(vc-ac) + params.beta_fm*(vf-af) # f-part of RHS
rhs2 = rhs_m + beta_m*(Dx.T @ (vx_m-ax_m) + Dy.T @ (vy_m-ay_m)) + beta_cross_m*crossDm_T(vc_m-ac_m) + params.beta_fm*(vm-am) # m-part of RHS
def estimateFM_cg_Ax(fmfun0):
fmfun = np.reshape(fmfun0, (-1,(f.shape[1]+m.shape[1])),'F')
xf = fmfun[:,:f.shape[1]]
xm = fmfun[:,f.shape[1]:]
Fe[idx_f,idy_f,idz_f,idf_f] = xf.flatten('F')
Me[idx_m,idy_m,idz_m,idf_m] = xm.flatten('F')
HF = np.sum(fH*fft2(Fe,axes=(0,1)),3)
if single_m:
bHM = B*(np.real(ifft2(np.sum(fH,3)*fft2(Me,axes=(0,1))[:,:,:,0],axes=(0,1))))
else:
bHM = B*(np.real(ifft2(np.sum(fH*fft2(Me,axes=(0,1)),3),axes=(0,1))))
yf = np.real(ifft2(HT3*(HF - fft2(bHM,axes=(0,1)))[:,:,:,np.newaxis],axes=(0,1)))
yf = params.gamma*np.reshape(yf[idx_f,idy_f,idz_f,idf_f],(Fshape[0]*Fshape[1],-1),'F')
if single_m:
ym = np.real(ifft2(np.sum(HT,3)*fft2(np.sum(B*(bHM - np.real(ifft2(HF,axes=(0,1)))),2),axes=(0,1))[:,:,np.newaxis],axes=(0,1)))[:,:,:,np.newaxis]
else:
ym = np.real(ifft2(HT*fft2(np.sum(B*(bHM - np.real(ifft2(HF,axes=(0,1)))),2),axes=(0,1))[:,:,np.newaxis,np.newaxis],axes=(0,1)))
ym = params.gamma*np.reshape(ym[idx_m,idy_m,idz_m,idf_m],(Fshape[0]*Fshape[1],-1),'F')
if lambda_T > 0 and F_T is not None:
yf = yf + lambda_T*xf
yf = yf + beta_cross_f*crossDf_DTD(xf)
ym = ym + beta_cross_m*crossDm_DTD(xm)
if lambda_MT > 0 and M_T is not None:
ym = ym + lambda_MT*xm
if lambda_R > 0:
ym = ym + lambda_R*(Rn @ xm) # mask regularizers
res = np.c_[yf,ym] + beta_tv4*(DTD @ fmfun) + params.beta_fm*fmfun # common regularizers/identity terms
return res.flatten('F')
A = scipy.sparse.linalg.LinearOperator([(f.shape[1]+m.shape[1])*f.shape[0]]*2, matvec=estimateFM_cg_Ax)
fm, info = scipy.sparse.linalg.cg(A, np.c_[rhs1,rhs2].flatten('F'), np.c_[f,m].flatten('F'), params.cg_tol, params.cg_maxiter)
fm = np.reshape(fm, (-1,(f.shape[1]+m.shape[1])),'F')
f = fm[:, :f.shape[1]]
m = fm[:, f.shape[1]:]
if state is not None:
continue
ff = f.flatten()
df = ff-f_old.flatten()
mm = m.flatten()
dm = mm-m_old.flatten()
rel_diff2_f = (df @ df)/(ff @ ff)
rel_diff2_m = (dm @ dm)/(mm @ mm)
if params.visualize:
f_img = ivec3(f, Fshape); m_img = ivec3(m, M.shape)
if single_m:
m_img = np.repeat(m_img,ns,axis=3)
fmon = montageF(f_img)
mmon = montageF(m_img)[:,:,0]
imshow_nodestroy(get_visim(montageH(H[:,:,0,:]),fmon,mmon,I), 400/np.max(I.shape))
if params.verbose:
if params.do_cost: # not fully implemented for all terms, e.g. lambda_R
Fe[idx_f,idy_f,idz_f,idf_f] = ff
Me[idx_m,idy_m,idz_m,idf_m] = m
err = np.sum(np.reshape(np.real(ifft2(fH[:,:,np.newaxis]*fft2(Fe,axes=(0,1)),axes=(0,1)))-B*np.real(ifft2(fH*fft2(Me)))[:,:,np.newaxis]-(I-B), (-1,1),'F')**2)
cost = (params.gamma/2)*err + alpha_f*np.sum(np.sqrt(fdx**2+fdy**2))
cost = cost + alpha_m*np.sum(np.sqrt(mdx**2+mdy**2))
if F_T is not None:
cost = cost + lambda_T*np.sum((f-F_T)**2)/2
if M_T is not None:
cost = cost + np.sum(lambda_MT*(m-M_T)**2)/2
print("FM: iter={}, reldiff=({}, {}), err={}, cost={}".format(iter, np.sqrt(rel_diff2_f), np.sqrt(rel_diff2_m),err,cost))
else:
print("FM: iter={}, reldiff=({}, {})".format(iter, np.sqrt(rel_diff2_f), np.sqrt(rel_diff2_m)))
if rel_diff2_f < rel_tol2 and rel_diff2_m < rel_tol2:
break
f_img = ivec3(f, Fshape)
m_img = ivec3(m, Mshape)
if state is None:
return f_img,m_img
else:
state.Dx = Dx; state.Dy = Dy; state.DTD = DTD; state.Rn = Rn
state.vx = vx; state.vy = vy; state.ax = ax; state.ay = ay
state.vx_m = vx_m; state.vy_m = vy_m; state.ax_m = ax_m; state.ay_m = ay_m
state.vf = vf; state.af = af; state.vm = vm; state.am = am
state.vc = vc; state.vc_m = vc_m; state.ac = ac; state.ac_m = ac_m
return f_img,m_img,state
def crossD(xx, num_channels=3):
## cross-image forward derivative (img2-img1); expects input format of 'x' as in 'f' and 'm' in the main function
return (xx[:,num_channels:] - xx[:,:-num_channels])
def crossD_T(xx, num_channels=3):
## transpose of cross-image derivative (img2-img1); expects input format of 'x' as in 'f' and 'm' in the main function but 1 image less (as is output of crossD)
return np.c_[-xx[:,:num_channels], xx[:,:-num_channels]-xx[:,num_channels:], xx[:,-num_channels:]]
def crossD_DTD(xx, num_channels=3):
## short for crossD_T(crossD(x)) (better memory managenemt when written explicitly)
return np.c_[xx[:,:num_channels]-xx[:,num_channels:2*num_channels], 2*xx[:,num_channels:-num_channels]-xx[:,:-2*num_channels]-xx[:,2*num_channels:], xx[:,-num_channels:]-xx[:,-2*num_channels:-num_channels]]
def psfsplit(H, ns):
## very simple version of PSF fitting with splitting
## there are more sophisticated ways to do it with RANSAC
bH = (H/np.max(H) > 0.4)
x, y = np.nonzero(bH)
res1 = np.polyfit(x, y, 3, full=True)
res2 = np.polyfit(y, x, 3, full=True)
if res2[1].shape[0] == 0 or (res1[1].shape[0] != 0 and res1[1][0] < res2[1][0]):
coeffs = res1[0]
xs = [np.min(x), np.max(x)]
poly1d_fn = np.poly1d(coeffs)
ys = poly1d_fn(xs)
else:
coeffs = res2[0]
ys = [np.min(y), np.max(y)]
poly1d_fn = np.poly1d(coeffs)
xs = poly1d_fn(ys)
Hs = np.zeros((H.shape[0],H.shape[1],ns))
stx = (xs[1]-xs[0])/ns
sty = (ys[1]-ys[0])/ns
for ni in range(ns):
pars = np.array([[xs[0]+ni*stx, ys[0]+ni*sty], [stx, sty]]).T
Hs[:,:,ni] = renderTraj(pars, np.zeros(H.shape))
if ni > 0:
Ht = Hs[:,:,ni]
Ht[(Ht*Hs[:,:,ni-1]) > 0] = 0
Hs[:,:,ni] = Ht
Hs /= np.sum(Hs)
return Hs