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()
fig.show()
def image_transform_test():
I = plt.imread('../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')
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
# -*- coding: utf-8 -*-
"""
Created on Tue Sep 10 15:36:11 2019
@author: 20161879
"""
import sys
sys.path.append("../code")
import numpy as np
import matplotlib.pyplot as plt
import registration as reg
import registration_util as util
X = util.test_object(1)
X_scaled = reg.scale(2, 3).dot(X)
fig = plt.figure(figsize=(5, 5))
ax1 = fig.add_subplot(111)
ax1.grid()
util.plot_object(ax1, X)
util.plot_object(ax1, X_scaled)