def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
# Experiment with combining transformation matrices.
X1_1 = reg.rotate(np.pi / 4).dot(reg.reflect(-1, 1).dot(X))
X1_2 = reg.reflect(-1, 1).dot(reg.rotate(np.pi / 4).dot(X))
X2_1 = reg.shear(0.6, 0.3).dot(reg.reflect(-1, -1).dot(X))
X2_2 = reg.shear(0.6, 0.3).dot(reg.reflect(-1, 1).dot(X))
X3_1 = reg.reflect(-1, 1).dot(reg.shear(0.6, 0.3).dot(X))
X3_2 = reg.shear(0.6, 0.3).dot(reg.reflect(-1, 1).dot(X))
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, X1_1)
util.plot_object(ax2, X1_2)
util.plot_object(ax3, X2_1)
util.plot_object(ax3, X2_2)
util.plot_object(ax4, X3_1)
util.plot_object(ax4, X3_2)
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def combining_transforms():
X = util.test_object(1)
#------------------------------------------------------------------#
# TODO: Experiment with combining transformation matrices.
X_t = reg.reflect(-1, 1).dot(reg.rotate(np.pi / 2)).dot(X)
X_u = reg.shear(2, 1).dot(reg.reflect(1, -1)).dot(X)
X_v = reg.reflect(1, -1).dot(reg.shear(2, 1)).dot(X)
X_w = reg.rotate(np.pi / 2).dot(reg.shear(2, 1)).dot(X)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-8, 8), ylim=(-8, 8))
ax2 = fig.add_subplot(142, xlim=(-8, 8), ylim=(-8, 8))
ax3 = fig.add_subplot(143, xlim=(-8, 8), ylim=(-8, 8))
ax4 = fig.add_subplot(144, xlim=(-8, 8), ylim=(-8, 8))
util.plot_object(ax1, X_t)
util.plot_object(ax2, X_u)
util.plot_object(ax3, X_v)
util.plot_object(ax4, X_w)
ax1.set_title('reflect, rotate')
ax2.set_title('shear, reflect')
ax3.set_title('reflect, shear')
ax4.set_title('rotate, shear')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def combining_transforms():
X = util.test_object(1)
X_rot = reg.rotate(3 * np.pi / 7).dot(X)
X_shear = reg.shear(0.3, 0.22).dot(X)
X_rot_shear = reg.shear(0.1, 0.3).dot(X_rot)
X_shear_reflect = reg.reflect(-1, 1).dot(X_shear)
X_multicom = reg.rotate(np.pi / 3).dot(X_rot_shear)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, X_rot_shear)
util.plot_object(ax3, X_shear_reflect)
util.plot_object(ax4, X_multicom)
ax1.set_title('Original')
ax2.set_title('Combination 1')
ax3.set_title('Combination 2')
ax4.set_title('Combination 3')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def combining_transforms():
X = util.test_object(1)
X_shear_reflect = reg.reflect(-1, 1).dot(reg.shear(0.5, 0.2).dot(X))
X_reflect_shear = reg.shear(0.5, 0.2).dot(reg.reflect(-1, 1).dot(X))
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X)
util.plot_object(ax2, X_shear_reflect)
util.plot_object(ax3, X_reflect_shear)
util.plot_object(ax4, X)
ax1.set_title('Original')
ax2.set_title('shear_reflect')
ax3.set_title('reflect_shear')
ax4.set_title('Original')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
fig.show()
def combining_transforms():
X = util.test_object(1)
X_combined = (reg.rotate(3 * np.pi / 5) * reg.shear(0.2, 0.2) * reg.shear(2, 8)).dot(X)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X_combined)
def transforms_test():
X = util.test_object(1)
X_rot = reg.rotate(3*np.pi/4).dot(X)
X_shear = reg.shear(0.1, 0.2).dot(X)
X_reflect = reg.reflect(-1, -1).dot(X)
fig = plt.figure(figsize=(12,5))
ax1 = fig.add_subplot(141, xlim=(-4,4), ylim=(-4,4))
ax2 = fig.add_subplot(142, xlim=(-4,4), ylim=(-4,4))
ax3 = fig.add_subplot(143, xlim=(-4,4), ylim=(-4,4))
ax4 = fig.add_subplot(144, xlim=(-4,4), ylim=(-4,4))
util.plot_object(ax1, X)
util.plot_object(ax2, X_rot)
util.plot_object(ax3, X_shear)
util.plot_object(ax4, X_reflect)
ax1.set_title('Original')
ax2.set_title('Rotation')
ax3.set_title('Shear')
ax4.set_title('Reflection')
ax1.grid()
ax2.grid()
ax3.grid()
ax4.grid()
def combining_transforms():
X = util.test_object(1)
X_1 = X
X_2 = reg.rotate(3 * np.pi / 4).dot(X)
X_3 = reg.reflect(-1, 1).dot(reg.rotate(3 * np.pi / 4).dot(X))
X_4 = reg.shear(0.1, 0.2).dot(
reg.reflect(-1, 1).dot(reg.rotate(3 * np.pi / 4).dot(X)))
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(141, xlim=(-4, 4), ylim=(-4, 4))
ax2 = fig.add_subplot(142, xlim=(-4, 4), ylim=(-4, 4))
ax3 = fig.add_subplot(143, xlim=(-4, 4), ylim=(-4, 4))
ax4 = fig.add_subplot(144, xlim=(-4, 4), ylim=(-4, 4))
util.plot_object(ax1, X_1)
util.plot_object(ax2, X_2)
util.plot_object(ax3, X_3)
util.plot_object(ax4, X_4)
ax1.set_title('Original')
ax2.set_title('Then rotate')
ax3.set_title('Now reflect over x')
ax4.set_title('Lastly, shear')
for ax_obj in [ax1, ax2, ax3, ax4]:
ax_obj.grid()
def ls_affine_test():
X = util.test_object(1)
# convert to homogeneous coordinates
Xh = util.c2h(X)
T_rot = reg.rotate(np.pi / 4)
T_scale = reg.scale(1.2, 0.9)
T_shear = reg.shear(0.2, 0.1)
T = util.t2h(T_rot.dot(T_scale).dot(T_shear), [10, 20])
Xm = T.dot(Xh)
Te = reg.ls_affine(Xh, Xm)
Xmt = Te.dot(Xm)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(131)
ax2 = fig.add_subplot(132)
ax3 = fig.add_subplot(133)
util.plot_object(ax1, Xh)
util.plot_object(ax2, Xm)
util.plot_object(ax3, Xmt)
ax1.set_title('Test shape')
ax2.set_title('Arbitrary transformation')
ax3.set_title('Retrieved test shape')
ax1.grid()
ax2.grid()
ax3.grid()
def affine_corr(I, Im, x, MI):
# Computes normalized cross-correlation between a fixed and
# a moving image transformed with an affine transformation.
# Input:
# I - fixed image
# Im - moving image
# x - parameters of the rigid transform: the first element
# is the rotation angle, the second and third are the
# scaling parameters, the fourth and fifth are the
# shearing parameters and the remaining two elements
# are the translation
# Output:
# C - normalized cross-correlation between I and T(Im)
# Im_t - transformed moving image T(Im)
Tro = reg.rotate(x[0])
Tsc = reg.scale(x[1], x[2])
Tsh = reg.shear(x[3], x[4])
Trss = Tro.dot(Tsc).dot(Tsh)
Th = util.t2h(Trss, [x[5], x[6]])
Im_t, Xt = reg.image_transform(Im, Th)
if MI:
p = joint_histogram(I, Im_t)
S = reg.mutual_information(p)
else:
S = reg.correlation(I, Im_t)
return S, Im_t, Th
def affine_mi_adapted(I, Im, x):
# Computes mutual information between a fixed and
# a moving image transformed with an affine transformation.
# Input:
# I - fixed image
# Im - moving image
# x - parameters of the rigid transform: the first element
# is the rotation angle, the second and third are the
# scaling parameters, the fourth and fifth are the
# shearing parameters and the remaining two elements
# are the translation
# Output:
# MI - mutual information between I and T(Im)
# Im_t - transformed moving image T(Im)
NUM_BINS = 64
SCALING = 100
#------------------------------------------------------------------#
# TODO: Implement the missing functionality
T_rotate = reg.rotate(x[0])
T_scaled = reg.scale(x[1], x[2])
T_shear = reg.shear(x[3], x[4])
t = np.array(x[5:]) * SCALING
T_total = T_shear.dot((T_scaled).dot(T_rotate))
Th = util.t2h(T_total, t)
Im_t, Xt = reg.image_transform(Im, Th)
p = reg.joint_histogram(Im, Im_t)
MI = reg.mutual_information(p)
#------------------------------------------------------------------#
return MI
def optim_affine_corr(x, I, Im, MI):
# Identical to affine_corr in functionality but the x variable is placed
# in front when calling for use in scipy.optimize function.
# Output is changed to only give the similarity because scipy.optimize
# uses this metric to optimize the parameters
Tro = reg.rotate(x[0])
Tsc = reg.scale(x[1], x[2])
Tsh = reg.shear(x[3], x[4])
Trss = Tro.dot(Tsc).dot(Tsh)
Th = util.t2h(Trss, [x[5], x[6]])
Im_t, Xt = reg.image_transform(Im, Th)
if MI:
p = joint_histogram(I, Im_t)
S = reg.mutual_information(p)
else:
S = reg.correlation(I, Im_t)
return S
def image_transform_test():
I = plt.imread('8dc00-mia/data/cameraman.tif')
# 45 deg. rotation around the image center
T_1 = util.t2h(reg.identity(), 128 * np.ones(2))
T_2 = util.t2h(reg.rotate(np.pi / 4), np.zeros(2))
T_3 = util.t2h(reg.identity(), -128 * np.ones(2))
T_rot = T_1.dot(T_2).dot(T_3)
# 45 deg. rotation around the image center followed by shearing
T_shear = util.t2h(reg.shear(0.0, 0.5), np.zeros(2)).dot(T_rot)
# scaling in the x direction and translation
T_scale = util.t2h(reg.scale(1.5, 1), np.array([10, 20]))
It1, Xt1 = reg.image_transform(I, T_rot)
It2, Xt2 = reg.image_transform(I, T_shear)
It3, Xt3 = reg.image_transform(I, T_scale)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(131)
im11 = ax1.imshow(I)
im12 = ax1.imshow(It1, alpha=0.7)
ax2 = fig.add_subplot(132)
im21 = ax2.imshow(I)
im22 = ax2.imshow(It2, alpha=0.7)
ax3 = fig.add_subplot(133)
im31 = ax3.imshow(I)
im32 = ax3.imshow(It3, alpha=0.7)
ax1.set_title('Rotation')
ax2.set_title('Shearing')
ax3.set_title('Scaling')
plt.show()
def affine_corr_adapted(I, Im, x):
#ADAPTED: In order to determine the gradient of the parameters, you only
#need the correlation value. So, the outputs: Th and Im_t are removed.
#Nothing else is changed.
#Attention this function will be used for ngradient in the function:
#intensity_based_registration_rigid_adapted.
# Computes normalized cross-corrleation between a fixed and
# a moving image transformed with an affine transformation.
# Input:
# I - fixed image
# Im - moving image
# x - parameters of the rigid transform: the first element
# is the roation angle, the second and third are the
# scaling parameters, the fourth and fifth are the
# shearing parameters and the remaining two elements
# are the translation
# Output:
# C - normalized cross-corrleation between I and T(Im)
# Im_t - transformed moving image T(Im)
NUM_BINS = 64
SCALING = 100
#------------------------------------------------------------------#
# TODO: Implement the missing functionality
T_rotate = reg.rotate(x[0]) #make rotation matrix (2x2 matrix)
T_scaled = reg.scale(x[1], x[2]) #make scale matrix (2x2 matrix)
T_shear = reg.shear(x[3], x[4]) # make shear matrix (2x2 matrix)
t = np.array(x[5:]) * SCALING #scale translation vector
T_total = T_shear.dot(
(T_scaled).dot(T_rotate)
) #multiply the matrices to get the transformation matrix (2x2)
Th = util.t2h(
T_total, t) #convert to homogeneous transformation matrix (3x3 matrix)
Im_t, Xt = reg.image_transform(Im,
Th) #apply transformation to moving image
C = reg.correlation(
Im, Im_t
) #determine the correlation between the moving and transformed moving image
#------------------------------------------------------------------#
return C
