def steer(self):
N = self.fixedCL.shape
# Obtain 2D view
SteeringGeneric.update_slices(self)
fixed2D, moving2D = self.get_slices()
fixedV, movingV = self.get_slice_axes()
F = SteeringGeneric.get_frame_matrix(self, fixedV, movingV)
# Perform 2D registration
scale, T2 = self.register_scale2d(fixed2D, moving2D)
print "S = ", scale
S = np.identity(3, np.single) * scale
T = F[:,0] * T2[0] + F[:,1] * T2[1]
C = np.array([N[0]/2, N[1]/2, N[2]/2], np.single)
T += C - np.dot(S,C)
T = np.single(T)
# Subtract identitiy from matrix to match convention for PolyAffineCL
for dim in range(3):
S[dim, dim] -= 1.0
# Return 3D transformation that will be folded into an existing polyaffine
return S, T
def steer(self):
N = self.fixedCL.shape
# Obtain 2D view
SteeringGeneric.update_slices(self)
fixed2D, moving2D = self.get_slices()
fixedV, movingV = self.get_slice_axes()
F = SteeringGeneric.get_frame_matrix(self, fixedV, movingV)
# Perform 2D registration
R2, T2 = self.register_rigid2d(fixed2D, moving2D)
print "R2 = ", R2
print "T2 = ", T2
R = np.identity(3, np.float32)
R[:2,:2] = R2
# Project trafo to 3D, from 2D transform in u,v axes from frame F = [u v w]
# [u v w] [R2 0; 0 0 1] [x; y; 0] = R [u v w] [x; y; 0]
# R = F [R2 0; 0 0 1] inv(F)
R = np.dot(F, np.dot(R, np.linalg.inv(F)))
T = F[:,0] * T2[0] + F[:,1] * T2[1]
C = np.array([N[0]/2, N[1]/2, N[2]/2], np.float32)
T += C - np.dot(R,C)
# Subtract identity from R to follow convention in PolyAffineCL
for dim in range(3):
R[dim, dim] -= 1.0
# Return 3D transformation that will be folded into an existing polyaffine
return R, T
def __init__(self, fixedCL, movingCL, center, radius): SteeringGeneric.__init__(self, fixedCL, movingCL, center, radius)
def register_scale2d(self, fixed, moving):
sizex, sizey = moving.shape
x0, y0 = np.mgrid[0:sizex,0:sizey]
xc = float(sizex) / 2.0
yc = float(sizey) / 2.0
F = fixed
M = moving
G = SteeringGeneric.gaussian2(self, fixed.shape)
D = G * (F - M)
Dnorm = np.linalg.norm(D.ravel())
Dnorm_ref = Dnorm
I = np.identity(2, np.single)
T = np.zeros((2,), np.single)
scale = 1.0
for iter in xrange(20):
#print "2D diff", Dnorm
S = I * scale
dS = I
Dnorm_prev = Dnorm
D = G * (F - M)
Mx, My = np.gradient(M)
dScale = np.sum(D * (x0*Mx + y0*My))
dT = np.zeros((2,), np.single)
dT[0] = np.sum(D * Mx)
dT[1] = np.sum(D * My)
if iter == 0:
stepScale = 0.2 / max(abs(dScale), 1e-5)
stepT = 1.0 / max(np.max(np.abs(dT)), 1e-5)
for sub_iter in xrange(20):
scale_test = scale + dScale * stepScale
T_test = T + dT * stepT
Cx = (1.0 - scale_test) * xc
Cy = (1.0 - scale_test) * yc
x = x0*scale_test + T_test[0] + Cx
y = y0*scale_test + T_test[1] + Cy
M_test = SteeringGeneric.interp2(self, x, y, moving)
D_test = G * (F - M_test)
Dnorm_test = np.linalg.norm(D_test.ravel())
if Dnorm_test < Dnorm_prev:
stepScale *= 1.2
stepT *= 1.2
Dnorm = Dnorm_test
scale = scale_test
T = T_test
M = M_test
break
else:
stepScale *= 0.5
stepT *= 0.5
if abs(Dnorm-Dnorm_prev) < 1e-4 * abs(Dnorm-Dnorm_ref):
break
return scale, T
def register_rigid2d(self, fixed, moving):
sizex, sizey = moving.shape
x0, y0 = np.mgrid[0:sizex,0:sizey]
xc = float(sizex) / 2.0
yc = float(sizey) / 2.0
F = fixed
M = moving
G = SteeringGeneric.gaussian2(self, fixed.shape)
D = G * (F - M)
Dnorm = np.linalg.norm(D.ravel())
Dnorm_ref = Dnorm
R = np.identity(2, np.float32)
T = np.zeros((2,), np.float32)
angle = 0
for iter in range(20):
Dnorm_prev = Dnorm
ca = math.cos(angle)
sa = math.sin(angle)
R = np.array([[ca, -sa], [sa, ca]], np.float32)
dR = np.array([[-sa, -ca], [ca, -sa]], np.float32)
D = G * (F - M)
Mx, My = np.gradient(M)
dRx = dR[0,0]*(x0-xc) + dR[0,1]*(y0-yc)
dRy = dR[1,0]*(x0-xc) + dR[1,1]*(y0-yc)
dAngle = np.sum(G * D * (dRx*Mx + dRy*My))
dT = np.zeros((2,), np.float32)
dT[0] = np.sum(D * Mx)
dT[1] = np.sum(D * My)
if iter == 0:
stepAngle = 0.5 / max(abs(dAngle),1e-5)
stepT = 1.0 / max(np.max(np.abs(dT)), 1e-5)
for sub_iter in range(20):
angle_test = angle + dAngle * stepAngle
ca = math.cos(angle_test)
sa = math.sin(angle_test)
R = np.array([[ca, -sa], [sa, ca]], np.float32)
Cx = xc - (R[0,0]*xc + R[0,1]*yc)
Cy = yc - (R[1,0]*xc + R[1,1]*yc)
T_test = T + dT * stepT
x = R[0,0] * x0 + R[0,1] * y0 + T_test[0] + Cx
y = R[1,0] * x0 + R[1,1] * y0 + T_test[1] + Cy
M_test = SteeringGeneric.interp2(self, x, y, moving)
D_test = G * (F - M_test)
Dnorm_test = np.linalg.norm(D_test.ravel())
if Dnorm_test < Dnorm_prev:
stepAngle *= 1.2
stepT *= 1.2
M = M_test
Dnorm = Dnorm_test
angle = angle_test
T = T_test
break
else:
stepAngle *= 0.5
stepT *= 0.5
if abs(Dnorm-Dnorm_prev) < 1e-4 * abs(Dnorm-Dnorm_ref):
break
return R, T
