Newer
Older
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
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu Aug 29 11:30:17 2019
@author: vand@dtu.dk
"""
import numpy as np
import skimage.io
import matplotlib.pyplot as plt
import st2d
#%% ST AND ORIENTATIONS - VISUALIZATION OPTIONS
plt.close('all')
filename = '../data2D/drawn_fibres_B.png';
sigma = 0.5
rho = 2
image = skimage.io.imread(filename)
S = st2d.structure_tensor(image, sigma, rho)
val,vec = st2d.eig_special(S)
# visualization
figsize = (10,5)
fig, ax = plt.subplots(1, 5, figsize=figsize, sharex=True, sharey=True)
ax[0].imshow(image,cmap=plt.cm.gray)
st2d.plot_orientations(ax[0], image.shape, vec)
ax[0].set_title('Orientation as arrows')
orientation_st_rgba = plt.cm.hsv((np.arctan2(vec[1], vec[0])/np.pi).reshape(image.shape))
ax[1].imshow(plt.cm.gray(image)*orientation_st_rgba)
ax[1].set_title('Orientation as color on image')
ax[2].imshow(orientation_st_rgba)
ax[2].set_title('Orientation as color')
anisotropy = (1-val[0]/val[1]).reshape(image.shape)
ax[3].imshow(anisotropy)
ax[3].set_title('Degree of anisotropy')
ax[4].imshow(plt.cm.gray(anisotropy)*orientation_st_rgba)
ax[4].set_title('Orientation and anisotropy')
plt.show()
#%% ST AND ORIENTATIONS - HISTOGRAMS OPTIONS
filename = '../data2D/10X.png';
sigma = 0.5
rho = 15
N = 180 # number of angle bins for orientation histogram
# computation
image = skimage.io.imread(filename)
image = np.mean(image[:,:,0:3],axis=2).astype(np.uint8)
S = st2d.structure_tensor(image, sigma, rho)
val,vec = st2d.eig_special(S)
angles = np.arctan2(vec[1], vec[0]) # angles from 0 to pi
distribution = np.histogram(angles, bins=N, range=(0.0, np.pi))[0]
# visualization
figsize = (10,5)
fig, ax = plt.subplots(1, 2, figsize=figsize, sharex=True, sharey=True)
ax[0].imshow(image,cmap=plt.cm.gray)
ax[0].set_title('Input image')
orientation_st_rgba = plt.cm.hsv((angles/np.pi).reshape(image.shape))
ax[1].imshow(plt.cm.gray(image)*orientation_st_rgba)
ax[1].set_title('Orientation as color on image')
fig, ax = plt.subplots(1,2, figsize=figsize)
bin_centers = (np.arange(N)+0.5)*np.pi/N # halp circle (180 deg)
colors = plt.cm.hsv(bin_centers/np.pi)
ax[0].bar(bin_centers, distribution, width = np.pi/N, color = colors)
ax[0].set_xlabel('angle')
ax[0].set_xlim([0,np.pi])
ax[0].set_aspect(np.pi/ax[0].get_ylim()[1])
ax[0].set_xticks([0,np.pi/2,np.pi])
ax[0].set_xticklabels(['0','pi/2','pi'])
ax[0].set_ylabel('count')
ax[0].set_title('Histogram over angles')
st2d.polar_histogram(ax[1], distribution)
ax[1].set_title('Polar histogram')
plt.show()
#%% ST AND ORIENTATIONS - HISTOGRAMS OPTIONS
filename = '../data2D/drawn_field.png';
sigma = 0.5
rho = 15
N = 90 # number of angle bins for orientation histogram
# computation
image = skimage.io.imread(filename)
image = np.mean(image[:,:,0:3],axis=2).astype(np.uint8)
S = st2d.structure_tensor(image, sigma, rho)
val,vec = st2d.eig_special(S)
angles = np.arctan2(vec[1], vec[0]) # angles from 0 to pi
distribution = np.histogram(angles, bins=N, range=(0.0, np.pi))[0]
distribution_weighted = np.histogram(angles, bins=N, range=(0.0, np.pi), weights = (image>175).ravel().astype(np.float))[0]
# visualization
figsize = (10,5)
fig, ax = plt.subplots(1, 2, figsize=figsize, sharex=True, sharey=True)
ax[0].imshow(image,cmap=plt.cm.gray)
ax[0].set_title('Input image')
orientation_st_rgba = plt.cm.hsv((angles/np.pi).reshape(image.shape))
ax[1].imshow(plt.cm.gray(image)*orientation_st_rgba)
ax[1].set_title('Orientation as color on image')
fig, ax = plt.subplots(2, 2, figsize=figsize)
bin_centers = (np.arange(N)+0.5)*np.pi/N # halp circle (180 deg)
colors = plt.cm.hsv(bin_centers/np.pi)
ax[0][0].bar(bin_centers, distribution, width = np.pi/N, color = colors)
ax[0][0].set_xlabel('angle')
ax[0][0].set_xlim([0,np.pi])
ax[0][0].set_aspect(np.pi/ax[0][0].get_ylim()[1])
ax[0][0].set_xticks([0,np.pi/2,np.pi])
ax[0][0].set_xticklabels(['0','pi/2','pi'])
ax[0][0].set_ylabel('count')
ax[0][0].set_title('Histogram over angles - all orientations')
st2d.polar_histogram(ax[0][1], distribution)
ax[0][1].set_title('Polar histogram - all orientations')
ax[1][0].bar(bin_centers, distribution_weighted, width = np.pi/N, color = colors)
ax[1][0].set_xlabel('angle')
ax[1][0].set_xlim([0,np.pi])
ax[1][0].set_aspect(np.pi/ax[1][0].get_ylim()[1])
ax[1][0].set_xticks([0,np.pi/2,np.pi])
ax[1][0].set_xticklabels(['0','pi/2','pi'])
ax[1][0].set_ylabel('count')
ax[1][0].set_title('Histogram over angles - orientations at fibres')
st2d.polar_histogram(ax[1][1], distribution_weighted)
ax[1][1].set_title('Polar histogram - orientations at fibres')
plt.show()
#%% YET ANOTHER EXAMPLE
filename = '../data2D/OCT_im_org.png';
sigma = 0.5
rho = 5
N = 180 # number of angle bins for orientation histogram
# computation
image = skimage.io.imread(filename)
S = st2d.structure_tensor(image, sigma, rho)
val,vec = st2d.eig_special(S)
angles = np.arctan2(vec[1], vec[0]) # angles from 0 to pi
distribution = np.histogram(angles, bins=N, range=(0.0, np.pi))[0]
# visualization
figsize = (10,5)
fig, ax = plt.subplots(1, 2, figsize=figsize, sharex=True, sharey=True)
ax[0].imshow(image,cmap=plt.cm.gray)
ax[0].set_title('Input image')
orientation_st_rgba = plt.cm.hsv((angles/np.pi).reshape(image.shape))
ax[1].imshow(plt.cm.gray(image)*orientation_st_rgba)
ax[1].set_title('Orientation as color on image')
fig, ax = plt.subplots(1,2, figsize=figsize)
bin_centers = (np.arange(N)+0.5)*np.pi/N # halp circle (180 deg)
colors = plt.cm.hsv(bin_centers/np.pi)
ax[0].bar(bin_centers, distribution, width = np.pi/N, color = colors)
ax[0].set_xlabel('angle')
ax[0].set_xlim([0,np.pi])
ax[0].set_aspect(np.pi/ax[0].get_ylim()[1])
ax[0].set_xticks([0,np.pi/2,np.pi])
ax[0].set_xticklabels(['0','pi/2','pi'])
ax[0].set_ylabel('count')
ax[0].set_title('Histogram over angles')
st2d.polar_histogram(ax[1], distribution)
ax[1].set_title('Polar histogram')
plt.show()
#%% INVESTIGATING THE EFFECT OF RHO
filename = '../data2D/short_fibres.png'
image = skimage.io.imread(filename)
image = np.mean(image[:,:,0:3],axis=2)
image -= np.min(image)
image /= np.max(image)
s = 128 # quiver arrow spacing
sigma = 0.5
figsize = (10,5)
rhos = [2,10,20,50]
for k in range(4):
# computation
rho = rhos[k] # changing integration radius
S = st2d.structure_tensor(image,sigma,rho)
val,vec = st2d.eig_special(S)
# visualization
fig, ax = plt.subplots(1, 2, figsize=figsize, sharex=True, sharey=True)
ax[0].imshow(image,cmap=plt.cm.gray)
st2d.plot_orientations(ax[0], image.shape, vec, s = s)
ax[0].set_title(f'Rho = {rho}, arrows')
intensity_rgba = plt.cm.gray(image)
orientation_st_rgba = plt.cm.hsv((np.arctan2(vec[1], vec[0])/np.pi).reshape(image.shape))
ax[1].imshow((0.5+0.5*intensity_rgba)*orientation_st_rgba)
ax[1].set_title(f'Rho = {rho}, color')
#basis_filename = filename.split('/')[-1].split('.')[0]
#fig.savefig(basis_filename + '_rho_' + str(rho) + '.png')
plt.show()
#%% INVESTIGATING THE EFFECT OF SCALING + RHO
filename = '../data2D/short_fibres.png'
downsampling_range = 4
figsize = (10,5)
for k in range(downsampling_range):
# downsampling and computation
scale = 2**k
f = 1/scale # image scale factor
s = 128//scale # quiver arrow spacing
sigma = 0.5 # would it make sense to scale this too?
rho = 50/scale # scaling the integration radius
image = skimage.io.imread(filename)
image = np.mean(image[:,:,0:3],axis=2)
image = skimage.transform.rescale(image,f,multichannel=False)
image -= np.min(image)
image /= np.max(image)
S = st2d.structure_tensor(image,sigma,rho)
val,vec = st2d.eig_special(S)
# visualization
fig, ax = plt.subplots(1, 2, figsize=figsize, sharex=True, sharey=True)
ax[0].imshow(image,cmap=plt.cm.gray)
st2d.plot_orientations(ax[0], image.shape, vec, s = s)
ax[0].set_title(f'Downsample = {scale}, arrows')
intensity_rgba = plt.cm.gray(image)
orientation_st_rgba = plt.cm.hsv((np.arctan2(vec[1], vec[0])/np.pi).reshape(image.shape))
ax[1].imshow((0.5+0.5*intensity_rgba)*orientation_st_rgba)
ax[1].set_title(f'Downsample = {scale}, color')
#basis_filename = filename.split('/')[-1].split('.')[0]
#fig.savefig(basis_filename + '_scale_' + str(scale) + '.png')
plt.show()
#%% COMPARING DOMINANT ORIENTATION AND OPTICAL FLOW
image = skimage.io.imread('../data2D/drawn_fibres_B.png');
# computing structure tensor, orientation and optical flow
sigma = 0.5
rho = 5
S = st2d.structure_tensor(image,sigma,rho)
val,vec = st2d.eig_special(S) # dominant orientation
fx = st2d.solve_flow(S) # optical flow
# visualization
figsize = (10,10)
fy = np.ones(image.shape)
fig, ax = plt.subplots(2,2,figsize=figsize)
ax[0][0].imshow(image,cmap=plt.cm.gray)
st2d.plot_orientations(ax[0][0], image.shape, vec)
ax[0][0].set_title('Orientation from structure tensor, arrows')
ax[0][1].imshow(image,cmap=plt.cm.gray)
st2d.plot_orientations(ax[0][1], image.shape, np.r_[fx,np.ones((1,image.size))])
ax[0][1].set_title('Orientation from optical flow, arrows')
intensity_rgba = plt.cm.gray(image)
orientation_st_rgba = plt.cm.hsv((np.arctan2(vec[1],vec[0])/np.pi).reshape(image.shape))
orientation_of_rgba = plt.cm.hsv((np.arctan2(1,fx)/np.pi).reshape(image.shape))
ax[1][0].imshow(intensity_rgba*orientation_st_rgba)
ax[1][0].set_title('Dominant orientation from structure tensor, color')
ax[1][1].imshow(intensity_rgba*orientation_of_rgba)
ax[1][1].set_title('Orientation from optical flow, color')
plt.show()