-
Notifications
You must be signed in to change notification settings - Fork 0
/
tre3d.py
366 lines (322 loc) · 14 KB
/
tre3d.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
import numpy as np
class params:
def __init__(self):
self.LENGTH = 168
self.HEIGHT = 168
self.WIDTH = 168
def rotation_by_any_axis_theta2(u_start, u_end, theta):
"""
For some applications, it is helpful to be able to make a rotation with a given axis.
Given a unit vector u = (a,b,c),
the matrix for a rotation by an angle of theta about an axis in the direction of u.
:param : u_start is (a1, b1, c1), u_end is (a2, b2, c2)
:return: the matrix
"""
a1, b1, c1 = u_start
a2, b2, c2 = u_end
a, b, c = a2 - a1, b2 - b1, c2 - c1
# (1) shift the vector u to the origin
M1 = np.array([[1, 0, 0, -a1],
[0, 1, 0, -b1],
[0, 0, 1, -c1],
[0, 0, 0, 1]])
M1_inv = np.array([[1, 0, 0, a1],
[0, 1, 0, b1],
[0, 0, 1, c1],
[0, 0, 0, 1]])
# parallel to the x-axis
if b == 0 and c == 0:
Mx = np.array([[1, 0, 0, 0],
[0, np.cos(theta), np.sin(theta), 0],
[0, -np.sin(theta), np.cos(theta), 0],
[0, 0, 0, 1]])
return M1_inv.dot(Mx).dot(M1)
# parallel to the y-axis
elif a == 0 and c == 0:
My = np.array([[np.cos(theta), 0, -np.sin(theta), 0],
[0, 1, 0, 0],
[np.sin(theta), 0, np.cos(theta), 0],
[0, 0, 0, 1]])
return M1_inv.dot(My).dot(M1)
# parallel to the z-axis
elif b == 0 and a == 0:
Mz = np.array([[np.cos(theta), np.sin(theta), 0, 0],
[-np.sin(theta), np.cos(theta), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
return M1_inv.dot(Mz).dot(M1)
else:
cos_alpha = c / np.sqrt(b * b + c * c)
sin_alpha = b / np.sqrt(b * b + c * c)
M2 = np.array([[1, 0, 0, 0],
[0, cos_alpha, sin_alpha, 0],
[0, -sin_alpha, cos_alpha, 0],
[0, 0, 0, 1]])
M2_inv = np.array([[1, 0, 0, 0],
[0, cos_alpha, -sin_alpha, 0],
[0, sin_alpha, cos_alpha, 0],
[0, 0, 0, 1]])
cos_beta = np.sqrt(b * b + c * c) / np.sqrt(a * a + b * b + c * c)
sin_beta = -a / np.sqrt(a * a + b * b + c * c)
M3 = np.array([[cos_beta, 0, -sin_beta, 0],
[0, 1, 0, 0],
[sin_beta, 0, cos_beta, 0],
[0, 0, 0, 1]])
M3_inv = np.array([[cos_beta, 0, sin_beta, 0],
[0, 1, 0, 0],
[-sin_beta, 0, cos_beta, 0],
[0, 0, 0, 1]])
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
M4 = np.array([[cos_theta, sin_theta, 0, 0],
[-sin_theta, cos_theta, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
return M1.dot(M2).dot(M3).dot(M4).dot(M3_inv).dot(M2_inv).dot(M1_inv)
def rotation_by_any_axis_theta(u_start, u_end, theta):
"""
For some applications, it is helpful to be able to make a rotation with a given axis.
Given a unit vector u = (a,b,c),
the matrix for a rotation by an angle of theta about an axis in the direction of u.
:param : u_start is (a1, b1, c1), u_end is (a2, b2, c2)
:return: the matrix
"""
a1, b1, c1 = u_start
a2, b2, c2 = u_end
a, b, c = a2 - a1, b2 - b1, c2 - c1
# (1) shift the vector u to the origin
M1 = np.array([[1, 0, 0, -a1],
[0, 1, 0, -b1],
[0, 0, 1, -c1],
[0, 0, 0, 1]])
# (2) rotation alpha degrees around the X-axis
if b == 0 and c == 0:
cos_alpha = 1
sin_alpha = 0
else:
cos_alpha = c / np.sqrt(b * b + c * c)
sin_alpha = b / np.sqrt(b * b + c * c)
M2 = np.array([[1, 0, 0, 0],
[0, cos_alpha, sin_alpha, 0],
[0, -sin_alpha, cos_alpha, 0],
[0, 0, 0, 1]])
# (3) rotation beta degrees around the Y-axis, u-axis and z-axis is overlapped
cos_beta = np.sqrt(b * b + c * c) / np.sqrt(a * a + b * b + c * c)
sin_beta = a / np.sqrt(a * a + b * b + c * c)
M3 = np.array([[cos_beta, 0, -sin_beta, 0],
[0, 1, 0, 0],
[sin_beta, 0, cos_beta, 0],
[0, 0, 0, 1]])
# (4) rotation theta degrees around the Z-axis
# theta = np.radians(theta)
cos_theta = np.cos(theta)
sin_theta = np.sin(theta)
M4 = np.array([[cos_theta, sin_theta, 0, 0],
[-sin_theta, cos_theta, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
# (5) reverse rotation beta degrees around the Y-axis
M5 = np.array([[cos_beta, 0, sin_beta, 0],
[0, 1, 0, 0],
[-sin_beta, 0, cos_beta, 0],
[0, 0, 0, 1]])
# (6) reverse rotation alpha degrees around the X-axis
M6 = np.array([[1, 0, 0, 0],
[0, cos_alpha, -sin_alpha, 0],
[0, sin_alpha, cos_alpha, 0],
[0, 0, 0, 1]])
# (7) reverse shift the vector u to the origin
M7 = np.array([[1, 0, 0, a1],
[0, 1, 0, b1],
[0, 0, 1, c1],
[0, 0, 0, 1]])
M = M7.dot(M6).dot(M5).dot(M4).dot(M3).dot(M2).dot(M1)
return M
def get_transform_matrix(paras, order=0):
# order default 0:ground to moving 1:moving to fixed
tx, ty, tz, theta_x, theta_y, theta_z, scale = paras
theta_x, theta_y, theta_z = np.radians(theta_x), np.radians(theta_y), np.radians(theta_z)
"""
# T is combining translation, rotation and scale
# (x', y', z', 1).T = T * (x, y, z, 1).T
# T: the order of operations
(1) rotation about the x axis
R(theta_x) = [
[1, 0, 0, 0],
[0, cos(theta_x), -sin(theta_x), 0],
[0, sin(theta_x), cos(theta_x), 0],
[0 , 0, 0, 1]
]
(2) rotation about the y axis
R(thata_y) = [
[cos(theta_y), 0, sin(theta_y), 0],
[0, 1, 0, 0],
[-sin(theta_y), 0, cos(theta_y), 0],
[0, 0, 0, 1]
]
(3) rotation about the z axis
R(theta_z) = [
[cos(theta_z), -sin(theta_z), 0, 0],
[sin(theta_z), cos(theta_z), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]
]
(4) translate by tx, ty, tz
R(tx,ty,tz) = [
[1, 0, 0, tx],
[0, 1, 0, ty],
[0, 0, 1, tz],
[0, 0, 0, 1 ]
]
# T = R(tx,ty,tz) x R(theta_z) x R(theta_y) x R(theta_x)
# scale is equal 1.
# T = np.array([[scale * np.cos(theta_z) * np.cos(theta_y),
# np.cos(theta_z) * np.sin(theta_y) * np.sin(theta_x) - np.sin(theta_z) * np.cos(theta_x),
# np.cos(theta_z) * np.sin(theta_y) * np.cos(theta_x) + np.sin(theta_z) * np.sin(theta_x), tx],
# [np.sin(theta_z) * np.cos(theta_y),
# scale * np.sin(theta_z) * np.sin(theta_y) * np.sin(theta_x) + np.cos(theta_z) * np.cos(theta_x),
# np.sin(theta_z) * np.sin(theta_y) * np.cos(theta_x) - np.cos(theta_z) * np.sin(theta_x), ty],
# [-np.sin(theta_y), np.cos(theta_y) * np.sin(theta_x), scale * np.cos(theta_y) * np.cos(theta_x), tz],
# [0, 0, 0, 1]])
"""
# sin_x, cos_x = np.sin(theta_x), np.cos(theta_x)
# sin_y, cos_y = np.sin(theta_y), np.cos(theta_y)
# sin_z, cos_z = np.sin(theta_z), np.cos(theta_z)
# M = np.zeros((4, 4))
# M[0, 0] = scale * cos_z * cos_y
# M[0, 1] = cos_z * sin_y * sin_x - sin_z * cos_x
# M[0, 2] = cos_z * sin_y * cos_x + sin_z * sin_x
# M[0, 3] = tx
#
# M[1, 0] = sin_z * cos_y
# M[1, 1] = scale * sin_z * sin_y * sin_x + cos_z * cos_x
# M[1, 2] = sin_z * sin_y * cos_x - cos_z * sin_x
# M[1, 3] = ty
#
# M[2, 0] = -sin_y
# M[2, 1] = cos_y * sin_x
# M[2, 2] = scale * cos_y * cos_x
# M[2, 3] = tz
#
# M[3, 3] = 1
# rotation around the center of 3D image (LENGTH/2, WIDTH/2, HEIGHT/2)
pa = params()
u_end = np.array([pa.LENGTH // 2, pa.WIDTH // 2, pa.HEIGHT // 2])
# step 1: rotation around (u_start(0, WIDTH/2, HEIGHT/2), u_end(LENGTH/2, WIDTH/2, HEIGHT/2)) x-axis
# u_start = np.array([0, pa.WIDTH/2, pa.HEIGHT/2])
Mx = rotation_by_any_axis_theta(np.array([0, pa.WIDTH // 2, pa.HEIGHT // 2]), u_end, theta_x)
My = rotation_by_any_axis_theta(np.array([pa.LENGTH // 2, 0, pa.HEIGHT // 2]), u_end, theta_y)
Mz = rotation_by_any_axis_theta(np.array([pa.LENGTH // 2, pa.WIDTH // 2, 0]), u_end, theta_z)
Ms = np.array([[1 * scale, 0, 0, tx],
[0, 1 * scale, 0, ty],
[0, 0, 1 * scale, tz],
[0, 0, 0, 1]])
if order==0:
M = Ms.dot(Mz).dot(My).dot(Mx)
else:
M = Mx.dot(My).dot(Mz).dot(Ms)
# M = Mz.dot(My).dot(Mx).dot(Ms)
return M
def cal_tre_3d(im_shape, matrix_ground2moving, pre_matrix_moving2fixed, SIFT_POINTS_LIMIT_PER_IMAGE = 100):
"""
:param im_shape: (length, width, high) // eg.64x64x64
:param matrix_ground2moving: (shift_x, shift_y, shift_z, rotation_x, rotation_y, rotation_z, scale=1)
:param pre_matrix_moving2fixed: (shift_x, shift_y, shift_z, rotation_x, rotation_y, rotation_z, scale=1)
:param SIFT_POINTS_LIMIT_PER_IMAGE: the number of points
:return: one pair of registration( TRE result)
"""
# step 1: random choice some points in ground truth
detect_points = np.random.randint(1, min(im_shape), size=[SIFT_POINTS_LIMIT_PER_IMAGE, 3])
keypoints_in = []
for point in detect_points:
# print(point)
keypoints_in.append(np.array([point[0], point[1], point[2], 1]))
keypoints_in = np.array(keypoints_in)
# step 2: points will transform from ground truth to moving by matrix_ground2moving
# paras : ground_im --> moving_im
M = get_transform_matrix(matrix_ground2moving, 0)
m_keypoints = np.dot(keypoints_in, M.T)
# step 3: points transform from moving to fixed by pre_matrix_moving2fixed
pre_M = get_transform_matrix(pre_matrix_moving2fixed, 1)
# pre_M = np.linalg.inv(M)
pt_points = np.dot(m_keypoints, pre_M.T)
print('------------------------------------')
print(M, '\n', np.linalg.inv(M), '\n', pre_M)
print('------------------------------------')
print(keypoints_in[:2], '\n', pt_points[:2])
# step 4: calculate the distance of points between origin points and transformed points
# eu_dist = np.sqrt(np.sum(np.square(keypoints_in - pt_points), axis=1))
# tre_dist = np.mean(eu_dist)
eu_dist = np.sqrt(np.sum(np.square(keypoints_in - pt_points), axis=1))
# print(eu_dist)
tre_dist = np.sqrt(np.mean(eu_dist))
return tre_dist
def testinv():
theta = np.radians(30)
# x
Mx = np.array([[1, 0, 0, 0],
[0, np.cos(theta), np.sin(theta), 0],
[0, -np.sin(theta), np.cos(theta), 0],
[0, 0, 0, 1]])
Mx_inv = np.array([[1, 0, 0, 0],
[0, np.cos(theta), -np.sin(theta), 0],
[0, np.sin(theta), np.cos(theta), 0],
[0, 0, 0, 1]])
# y
My = np.array([[np.cos(theta), 0, -np.sin(theta), 0],
[0, 1, 0, 0],
[np.sin(theta), 0, np.cos(theta), 0],
[0, 0, 0, 1]])
My_inv = np.array([[np.cos(theta), 0, np.sin(theta), 0],
[0, 1, 0, 0],
[-np.sin(theta), 0, np.cos(theta), 0],
[0, 0, 0, 1]])
#z
Mz = np.array([[np.cos(theta), np.sin(theta), 0, 0],
[-np.sin(theta), np.cos(theta), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
Mz_inv = np.array([[np.cos(theta), -np.sin(theta), 0, 0],
[np.sin(theta), np.cos(theta), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
Mz_ne = np.array([[np.cos(-theta), np.sin(-theta), 0, 0],
[-np.sin(-theta), np.cos(-theta), 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]])
print(Mx.dot(Mx_inv))
print(My.dot(My_inv))
print(Mz.dot(Mz_inv))
loc = np.array([2, 3, 4, 1])
Mt = np.array([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[-2, -3, -4, 1]])
print(loc.dot(Mt))
print(Mz, '\n', Mz_ne)
if __name__ == '__main__':
import matplotlib.pyplot as plt
y1, y2, y3, y4, y5, y6 = [], [], [], [], [], []
x = []
pa = params()
shape = (pa.LENGTH, pa.HEIGHT, pa.WIDTH)
for i in range(1, 31):
y1.append(cal_tre_3d(shape, [i, 0, 0, 0, 0, 0, 1], [-i, 0, 0, 0, 0, 0, 1]))
y2.append(cal_tre_3d(shape, [i, i, 0, 0, 0, 0, 1], [-i, -i, 0, 0, 0, 0, 1]))
y3.append(cal_tre_3d(shape, [i, i, i, 0, 0, 0, 1], [-i, -i, -i, 0, 0, 0, 1]))
y4.append(cal_tre_3d(shape, [i, i, i, i, 0, 0, 1], [-i, -i, -i, -i, 0, 0, 1]))
y5.append(cal_tre_3d(shape, [i, i, i, i, i, 0, 1], [-i, -i, -i, -i, -i, 0, 1]))
y6.append(cal_tre_3d(shape, [i, i, i, i, i, i, 1], [-i, -i, -i, -i, -i, -i, 1]))
x.append(i)
# print(i, res)
print(y6)
plt.axis([0, 31, 0, 1])
plt.plot(x, y1, color="c", linestyle="-", marker="^", linewidth=1, label='y1')
plt.plot(x, y2, color="b", linestyle="-", marker="s", linewidth=1, label='y2')
plt.plot(x, y3, color="y", linestyle="-", marker="*", linewidth=1, label='y3')
plt.plot(x, y4, color="g", linestyle="-", marker="o", linewidth=1, label='y4')
plt.plot(x, y5, color="r", linestyle="-", marker="d", linewidth=1, label='y5')
plt.plot(x, y6, color="k", linestyle="-", marker="+", linewidth=1, label='y6')
plt.legend(loc='upper left')
plt.show()
# testinv()