def correlation_test():
I = plt.imread('../data/t1_demo.tif')
Th = util.t2h(reg.identity(), np.array([10, 20]))
J, _ = reg.image_transform(I, Th)
K, _ = reg.image_transform(J, Th)
C1 = reg.correlation(I, I)
C2 = reg.correlation(J, J)
# the self correlation should be very close to 1
assert abs(
C1 - 1
) < 10e-10, "Correlation function is incorrectly implemented (self correlation test)"
assert abs(
C2 - 1
) < 10e-10, "Correlation function is incorrectly implemented (self correlation test)"
C3 = reg.correlation(I, J)
C4 = reg.correlation(I, K)
print("Correlation between images with slight translocation:", C3)
print("Correlation between images with big translocation:", C4, "\n")
print('Test successful!')
########
print("\n\nAnd now for a test on the joint probability histogram: \n")
p = reg.joint_histogram(I, J)
assert abs(1 -
float(np.sum(p))) < 0.01, "Mass probability function error..."
print("Test successful!")
def correlation_test():
I = plt.imread('../data/cameraman.tif')
Th = util.t2h(reg.identity(), np.array([10, 20]))
J, _ = reg.image_transform(I, Th)
C1 = reg.correlation(I, I)
# the self correlation should be very close to 1
assert abs(C1 - 1) < 10e-10, "Correlation function is incorrectly implemented (self correlation test)"
inv_lin_tr = np.array([[0,1],[1,0]])
T = util.t2h(reg.identity(),np.array([0,0]))
K,_ = reg.image_transform(I,T)
C2 = reg.correlation(I,K)
assert abs(C2-1) < 10e-10, "Correlation function is incorrectly implemented (self correlation test)"
print('Test successful!')
def pbr(I_path, Im_path):
I = plt.imread(I_path)
Im = plt.imread(Im_path)
X, Xm = util.my_cpselect(I_path, Im_path)
if len(X[1]) == 1:
print('x must be larger than 1')
return
X = util.c2h(X)
Xm = util.c2h(Xm)
T = reg.ls_affine(X, Xm)
It, Xt = reg.image_transform(Im, T)
fig = plt.figure(figsize=(30, 30))
ax1 = fig.add_subplot(121)
ax1.set_title('Overlay of original images', fontsize=35)
ax1.axis('off')
im11 = ax1.imshow(I)
im12 = ax1.imshow(Im, alpha=0.7)
ax2 = fig.add_subplot(122)
ax2.set_title('Overlay transformed image over the fixed image',
fontsize=35)
ax2.axis('off')
im21 = ax2.imshow(I)
im22 = ax2.imshow(It, alpha=0.7)
return I, Im, It
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 rigid_corr(I, Im, x, MI):
# Computes normalized cross-correlation between a fixed and
# a moving image transformed with a rigid transformation.
# Input:
# I - fixed image
# Im - moving image
# x - parameters of the rigid transform: the first element
# is the rotation angle 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)
SCALING = 100
# the first element is the rotation angle
T = reg.rotate(x[0])
Th = util.t2h(T, x[1:] * SCALING)
# transform the moving image
Im_t, Xt = reg.image_transform(Im, Th)
# compute the similarity between the fixed and transformed moving image
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 correlation_test():
I = plt.imread('../data/cameraman.tif')
Th = util.t2h(reg.identity(), np.array([10, 20]))
J, _ = reg.image_transform(I, Th)
C1 = reg.correlation(I, I)
# the self correlation should be very close to 1
assert abs(
C1 - 1
) < 10e-10, "Correlation function is incorrectly implemented (self correlation test)"
#------------------------------------------------------------------#
# TODO: Implement a few more tests of the correlation definition
#correlation when two signals are exaclty opposite should be very close to -1
C2 = reg.correlation(I, -I)
assert abs(
C2 + 1
) < 10e-10, "Correlation function is incorrectly implemented (opposite self correlation test)"
#detect corrrelation of two signals with different amplitudes should be 1
C3 = reg.correlation(I, I / 2)
assert abs(
C3 - 1
) < 10e-10, "Correlation function is incorrectly implemented (different amplitude self correlation test)"
C4 = reg.correlation(I, J)
print(C4)
assert abs(
C4 - 1
) < 10e-1, "Correlation function is incorrectly implemented (two diff images no correlation)"
#------------------------------------------------------------------#
print('Test successful!')
def point_based_registration(I_path, Im_path, X, Xm):
#read/load the images I and Im
imageI = plt.imread(I_path)
imageIm = plt.imread(Im_path)
#convert to homogenous coordinates using c2h
X_h = util.c2h(X)
Xm_h = util.c2h(Xm)
#compute affine transformation and make a homogenous transformation matrix
Th = reg.ls_affine(X_h, Xm_h)
#transfrom the moving image using the transformation matrix
It, Xt = reg.image_transform(imageIm, Th)
#plotting the results
fig = plt.figure(figsize=(20, 30))
ax1 = fig.add_subplot(131)
im1 = ax1.imshow(imageI) #plot first image (fixed or T1) image
ax2 = fig.add_subplot(132)
im2 = ax2.imshow(imageIm) #plot second image (moving or T2) image
ax3 = fig.add_subplot(133)
im3 = ax3.imshow(It) #plot (T1 moving or T2) transformed image
ax1.set_title('T1 (fixed)')
ax2.set_title('T1 moving or T2')
ax3.set_title('Transformed (T1 moving or T2) image')
return 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 point_based_affine_registration(I, Im):
# let the user selecte points
X, Xm = util.my_cpselect(I, Im)
# find affine transformation matrix
T, reg_error = reg.ls_affine(util.c2h(X), util.c2h(Xm))
# transform the moving image according to T
Im = plt.imread(Im)
It, _ = reg.image_transform(Im, T)
return It, reg_error
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 point_based_registration_demo():
# ---------------------------------
# Append the following code in jupiter to run:
# %matplotlib inline
# import sys
# sys.path.append("C:/Users/s163666/Documents/2019-2020/Medical Image Analysis/Mini_project_mia")
# from project_fout import point_based_registration_demo
# point_based_registration_demo()
# ---------------------------------
# read the fixed and moving images, 2x T1 or T1&T2
# change these in order to read different images
I_path = './data/image_data/3_1_t1.tif'
Im_path = './data/image_data/3_1_t2.tif'
#Select set of corresponding points using my_cpselect
X0, Xm0 = util.my_cpselect(I_path, Im_path)
#Compute the affine transformation between the pair of images
Xm = np.ones((3, Xm0.shape[1]))
Xm[0, :] = Xm0[0, :]
Xm[1, :] = Xm0[1, :]
X = np.ones((3, X0.shape[1]))
X[0, :] = X0[0, :]
X[1, :] = X0[1, :]
T, Etrain = reg.ls_affine(X, Xm)
Etest = reg.point_based_error(I_path, Im_path, T)
#read image
Im = plt.imread(Im_path)
#Apply the affine transformation to the moving image
It, Xt = reg.image_transform(Im, T)
#plot figure
fig = plt.figure(figsize=(12, 5))
#fig, ax = plt.subplots()
ax = fig.add_subplot(121)
im = ax.imshow(It)
ax.set_title("Transformed image")
ax.set_xlabel('x')
ax.set_ylabel('y')
print(Etrain)
print(Etest)
display(fig)
fig.savefig('./data/image_results/3_1_t1 + 3_1_t2.png')
def mutual_information_test():
I = plt.imread('../data/cameraman.tif')
I_mirror, _ = reg.image_transform(I, util.t2h(reg.reflect(-1, 1)))
error_msg = "Mutual Information function is incorrectly implemented"
# mutual information of an image with itself
p1 = reg.joint_histogram(I, I)
p2 = reg.joint_histogram(I, I_mirror)
MI1 = reg.mutual_information(p1)
MI2 = reg.mutual_information(p2)
assert 1 - MI1 < 10e-10, error_msg + " (self MI should be 1)"
assert MI2 < 0.8, error_msg + " (mirrored image gives MI above 0.8 (strange))"
print('MI test successful!')
def correlation_test():
I = plt.imread('../data/cameraman.tif')
Th = util.t2h(reg.identity(), np.array([10,20]))
J, _ = reg.image_transform(I, Th)
C1 = reg.correlation(I, I)
# the self correlation should be very close to 1
assert abs(C1 - 1) < 10e-10, "Correlation function is incorrectly implemented (self correlation test)"
#------------------------------------------------------------------#
# TODO: Implement a few more tests of the correlation definition
#------------------------------------------------------------------#
print('Test successful!')
def my_point_based_registration():
I = '../data/image_data/3_2_t1.tif'
I_d = '../data/image_data/3_2_t1_d.tif'
I_plt = plt.imread('../data/image_data/3_2_t1.tif')
I_d_plt = plt.imread('../data/image_data/3_2_t1_d.tif')
X, Xm = util.my_cpselect(I, I_d)
affine_transformation = reg.ls_affine(X, Xm)
transformed_moving_image, transformed_vector = reg.image_transform(
I_d_plt, affine_transformation)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(131)
Im1 = ax1.imshow(I_plt) # Fixed image or Transformed image
Im2 = ax1.imshow(transformed_moving_image,
alpha=0.7) # Transformed image or Fixed image
def correlation_test():
I = plt.imread('../data/cameraman.tif')
Th = util.t2h(reg.identity(), np.array([10, 20]))
J, _ = reg.image_transform(I, Th)
error_msg = "Correlation function is incorrectly implemented"
C1 = reg.correlation(I, I)
C2 = reg.correlation(I, J)
C3 = reg.correlation(I, np.ones_like(I))
# the self correlation should be very close to 1
assert abs(C1 - 1) < 10e-10, error_msg + " (self correlation should be 1)"
assert C1 >= -1, error_msg + " (self correlation is should be more than -1)"
assert C2 <= 1, error_msg + " (translation correlation should be less than 1)"
assert C2 >= -1, error_msg + " (translation correlation should be more than -1)"
print('Correlation test successful!')
def my_point_based_registration_2():
I2 = '../data/image_data/3_2_t1.tif' # Tweede opdracht T1 slide
I_d_2 = '../data/image_data/3_2_t2.tif' # T2 slice
I_plt_2 = plt.imread('../data/image_data/3_2_t1.tif')
I_d_plt_2 = plt.imread('../data/image_data/3_2_t1_d.tif')
X2, Xm2 = util.my_cpselect(I2, I_d_2)
affine_transformation_2 = reg.ls_affine(X2, Xm2)
transformed_moving_image_2, transformed_vector_2 = reg.image_transform(
I_d_plt_2, affine_transformation_2)
fig = plt.figure(figsize=(12, 5))
ax1 = fig.add_subplot(131)
Im1 = ax1.imshow(
I_plt_2) # Fixed image or Transformed image, Je mag wisselen
Im2 = ax1.imshow(
transformed_moving_image_2,
alpha=0.7) # Transformed image or Fixed image Mag wisselen
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 optim_rigid_corr(x, I, Im, MI):
# Identical to rigid_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
SCALING = 100
# the first element is the rotation angle
T = reg.rotate(x[0])
Th = util.t2h(T, x[1:] * SCALING)
# transform the moving image
Im_t, Xt = reg.image_transform(Im, Th)
# compute the similarity between the fixed and transformed moving image
if MI:
p = joint_histogram(I, Im_t)
S = reg.mutual_information(p)
else:
S = reg.correlation(I, Im_t)
return S
def registration_metrics_demo(use_t2=False):
# read a T1 image
I = plt.imread('../data/t1_demo.tif')
if use_t2:
# read the corresponding T2 image
# note that the T1 and T2 images are already registered
I_t2 = plt.imread('../data/t2_demo.tif')
# create a linear space of rotation angles - 101 angles between 0 and 360 deg.
angles = np.linspace(-np.pi, np.pi, 101, endpoint=True)
CC = np.full(angles.shape, np.nan)
MI = np.full(angles.shape, np.nan)
# visualization
fig = plt.figure(figsize=(14,6))
# correlation
ax1 = fig.add_subplot(131, xlim=(-np.pi, np.pi), ylim=(-1.1, 1.1))
line1, = ax1.plot(angles, CC, lw=2)
ax1.set_xlabel('Rotation angle')
ax1.set_ylabel('Correlation coefficient')
ax1.grid()
# mutual mutual_information
ax2 = fig.add_subplot(132, xlim=(-np.pi, np.pi), ylim=(0, 2))
line2, = ax2.plot(angles, MI, lw=2)
ax2.set_xlabel('Rotation angle')
ax2.set_ylabel('Mutual information')
ax2.grid()
# images
ax3 = fig.add_subplot(133)
im1 = ax3.imshow(I)
im2 = ax3.imshow(I, alpha=0.7)
# used for rotation around image center
t = np.array([I.shape[0], I.shape[1]])/2 + 0.5
T_1 = util.t2h(reg.identity(), t)
T_3 = util.t2h(reg.identity(), -t)
# loop over the rotation angles
for k, ang in enumerate(angles):
# transformation matrix for rotating the image
# I by angles(k) around its center point
T_2 = util.t2h(reg.rotate(ang), np.zeros(2))
T_rot = T_1.dot(T_2).dot(T_3)
if use_t2:
# rotate the T2 image
J, Xt = reg.image_transform(I_t2, T_rot)
else:
# rotate the T1 image
J, Xt = reg.image_transform(I, T_rot)
# compute the joint histogram with 16 bins
p = reg.joint_histogram(I, J, 16, [0, 255])
CC[k] = reg.correlation(I, J)
MI[k] = reg.mutual_information(p)
clear_output(wait = True)
# visualize the results
line1.set_ydata(CC)
line2.set_ydata(MI)
im2.set_data(J)
display(fig)
full_path = path+"/transformation_matrix_T1_and_T1_moving_"+str(numberofpoints)+".npy"
else:
full_path = path+"/transformation_matrix_T1_and_T2_"+str(numberofpoints)+".npy"
#compute affine transformation and make a homogenous transformation matrix
Th = np.load(full_path)
#transfrom the moving image using the transformation matrix
It, Xt = reg.image_transform(imageIm, Th)
#plotting the results
fig = plt.figure(figsize = (20,30))
ax1 = fig.add_subplot(131)
im1 = ax1.imshow(imageI) #plot first image (fixed or T1) image
ax2 = fig.add_subplot(132)
im2 = ax2.imshow(imageIm) #plot second image (moving or T2) image
ax3 = fig.add_subplot(133)
im3 = ax3.imshow(It) #plot (T1 moving or T2) transformed image
if set_of_images == 1:
ax1.set_title('T1')
ax2.set_title('T1 moving')
ax3.set_title('Transformed T1 moving')
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
def rigid_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-correlation between a fixed and
# a moving image transformed with a rigid transformation.
# Input:
# I - fixed image
# Im - moving image
# x - parameters of the rigid transform: the first element
# is the rotation angle 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)
SCALING = 100
# the first element is the rotation angle
T = reg.rotate(x[0])
# the remaining two element are the translation
#
# the gradient ascent/descent method work best when all parameters
# of the function have approximately the same range of values
# this is not the case for the parameters of rigid registration
# where the transformation matrix usually takes much smaller
# values compared to the translation vector this is why we pass a
# scaled down version of the translation vector to this function
# and then scale it up when computing the transformation matrix
Th = util.t2h(T, x[1:] * SCALING)
# transform the moving image
Im_t, Xt = reg.image_transform(Im, Th)
# compute the similarity between the fixed and transformed
# moving image
C = reg.correlation(I, Im_t)
return C
