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import numpy as np
import unittest
import astra
import math
import pylab
# return length of intersection of the line through points src = (x,y)
# and det (x,y), and the rectangle defined by xmin, ymin, xmax, ymax
#
# TODO: Generalize from 2D to n-dimensional
def intersect_line_rectangle(src, det, xmin, xmax, ymin, ymax):
EPS = 1e-5
if np.abs(src[0] - det[0]) < EPS:
if src[0] >= xmin and src[0] < xmax:
return ymax - ymin
else:
return 0.0
if np.abs(src[1] - det[1]) < EPS:
if src[1] >= ymin and src[1] < ymax:
return xmax - xmin
else:
return 0.0
n = np.sqrt((det[0] - src[0]) ** 2 + (det[1] - src[1]) ** 2)
check = [ (-(xmin - src[0]), -(det[0] - src[0]) / n ),
(xmax - src[0], (det[0] - src[0]) / n ),
(-(ymin - src[1]), -(det[1] - src[1]) / n ),
(ymax - src[1], (det[1] - src[1]) / n ) ]
pre = [ -np.Inf ]
post = [ np.Inf ]
for p, q in check:
r = p / (1.0 * q)
if q > 0:
post.append(r) # exiting half-plane
else:
pre.append(r) # entering half-plane
end_r = np.min(post)
start_r = np.max(pre)
if end_r > start_r:
return end_r - start_r
else:
return 0.0
def intersect_line_rectangle_feather(src, det, xmin, xmax, ymin, ymax, feather):
return intersect_line_rectangle(src, det,
xmin-feather, xmax+feather,
ymin-feather, ymax+feather)
def intersect_line_rectangle_interval(src, det, xmin, xmax, ymin, ymax, f):
a = intersect_line_rectangle_feather(src, det, xmin, xmax, ymin, ymax, -f)
b = intersect_line_rectangle(src, det, xmin, xmax, ymin, ymax)
c = intersect_line_rectangle_feather(src, det, xmin, xmax, ymin, ymax, f)
return (a,b,c)
def gen_lines_fanflat(proj_geom):
angles = proj_geom['ProjectionAngles']
for theta in angles:
#theta = -theta
src = ( math.sin(theta) * proj_geom['DistanceOriginSource'],
-math.cos(theta) * proj_geom['DistanceOriginSource'] )
detc= (-math.sin(theta) * proj_geom['DistanceOriginDetector'],
math.cos(theta) * proj_geom['DistanceOriginDetector'] )
detu= ( math.cos(theta) * proj_geom['DetectorWidth'],
math.sin(theta) * proj_geom['DetectorWidth'] )
src = np.array(src, dtype=np.float64)
detc= np.array(detc, dtype=np.float64)
detu= np.array(detu, dtype=np.float64)
detb= detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu
for i in range(proj_geom['DetectorCount']):
yield (src, detb + i * detu)
def gen_lines_fanflat_vec(proj_geom):
v = proj_geom['Vectors']
for i in range(v.shape[0]):
src = v[i,0:2]
detc = v[i,2:4]
detu = v[i,4:6]
detb = detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu
for i in range(proj_geom['DetectorCount']):
yield (src, detb + i * detu)
def gen_lines_parallel(proj_geom):
angles = proj_geom['ProjectionAngles']
for theta in angles:
ray = ( math.sin(theta),
-math.cos(theta) )
detc= (0, 0 )
detu= ( math.cos(theta) * proj_geom['DetectorWidth'],
math.sin(theta) * proj_geom['DetectorWidth'] )
ray = np.array(ray, dtype=np.float64)
detc= np.array(detc, dtype=np.float64)
detu= np.array(detu, dtype=np.float64)
detb= detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu
for i in range(proj_geom['DetectorCount']):
yield (detb + i * detu - ray, detb + i * detu)
def gen_lines_parallel_vec(proj_geom):
v = proj_geom['Vectors']
for i in range(v.shape[0]):
ray = v[i,0:2]
detc = v[i,2:4]
detu = v[i,4:6]
detb = detc + (0.5 - 0.5*proj_geom['DetectorCount']) * detu
for i in range(proj_geom['DetectorCount']):
yield (detb + i * detu - ray, detb + i * detu)
def gen_lines(proj_geom):
g = { 'fanflat': gen_lines_fanflat,
'fanflat_vec': gen_lines_fanflat_vec,
'parallel': gen_lines_parallel,
'parallel_vec': gen_lines_parallel_vec }
for l in g[proj_geom['type']](proj_geom):
yield l
range2d = ( 8, 64 )
def gen_random_geometry_fanflat():
pg = astra.create_proj_geom('fanflat', 0.6 + 0.8 * np.random.random(), np.random.randint(*range2d), np.linspace(0, 2*np.pi, np.random.randint(*range2d), endpoint=False), 256 * (0.5 + np.random.random()), 256 * np.random.random())
return pg
def gen_random_geometry_parallel():
pg = astra.create_proj_geom('parallel', 0.8 + 0.4 * np.random.random(), np.random.randint(*range2d), np.linspace(0, 2*np.pi, np.random.randint(*range2d), endpoint=False))
return pg
def gen_random_geometry_fanflat_vec():
Vectors = np.zeros([16,6])
# We assume constant detector width in these tests
w = 0.6 + 0.8 * np.random.random()
for i in range(Vectors.shape[0]):
angle1 = 2*np.pi*np.random.random()
angle2 = angle1 + 0.5 * np.random.random()
dist1 = 256 * (0.5 + np.random.random())
detc = 10 * np.random.random(size=2)
detu = [ math.cos(angle1) * w, math.sin(angle1) * w ]
src = [ math.sin(angle2) * dist1, -math.cos(angle2) * dist1 ]
Vectors[i, :] = [ src[0], src[1], detc[0], detc[1], detu[0], detu[1] ]
pg = astra.create_proj_geom('fanflat_vec', np.random.randint(*range2d), Vectors)
# TODO: Randomize more
pg = astra.create_proj_geom('fanflat_vec', np.random.randint(*range2d), Vectors)
return pg
def gen_random_geometry_parallel_vec():
Vectors = np.zeros([16,6])
# We assume constant detector width in these tests
w = 0.6 + 0.8 * np.random.random()
for i in range(Vectors.shape[0]):
l = 0.6 + 0.8 * np.random.random()
angle1 = 2*np.pi*np.random.random()
angle2 = angle1 + 0.5 * np.random.random()
detc = 10 * np.random.random(size=2)
detu = [ math.cos(angle1) * w, math.sin(angle1) * w ]
ray = [ math.sin(angle2) * l, -math.cos(angle2) * l ]
Vectors[i, :] = [ ray[0], ray[1], detc[0], detc[1], detu[0], detu[1] ]
pg = astra.create_proj_geom('parallel_vec', np.random.randint(*range2d), Vectors)
return pg
nloops = 50
seed = 123
class TestLineKernel(unittest.TestCase):
def single_test(self, type):
shape = np.random.randint(*range2d, size=2)
# these rectangles are biased, but that shouldn't matter
rect_min = [ np.random.randint(0, a) for a in shape ]
rect_max = [ np.random.randint(rect_min[i]+1, shape[i]+1) for i in range(len(shape))]
if True:
#pixsize = 0.5 + np.random.random(size=2)
pixsize = np.array([0.5, 0.5]) + np.random.random()
origin = 10 * np.random.random(size=2)
else:
pixsize = (1.,1.)
origin = (0.,0.)
vg = astra.create_vol_geom(shape[1], shape[0],
origin[0] - 0.5 * shape[0] * pixsize[0],
origin[0] + 0.5 * shape[0] * pixsize[0],
origin[1] - 0.5 * shape[1] * pixsize[1],
origin[1] + 0.5 * shape[1] * pixsize[1])
#print(vg)
if type == 'parallel':
pg = gen_random_geometry_parallel()
projector_id = astra.create_projector('line', pg, vg)
elif type == 'parallel_vec':
pg = gen_random_geometry_parallel_vec()
projector_id = astra.create_projector('line', pg, vg)
elif type == 'fanflat':
pg = gen_random_geometry_fanflat()
projector_id = astra.create_projector('line_fanflat', pg, vg)
elif type == 'fanflat_vec':
pg = gen_random_geometry_fanflat_vec()
projector_id = astra.create_projector('line_fanflat', pg, vg)
data = np.zeros((shape[1], shape[0]), dtype=np.float32)
data[rect_min[1]:rect_max[1],rect_min[0]:rect_max[0]] = 1
sinogram_id, sinogram = astra.create_sino(data, projector_id)
#print(pg)
#print(vg)
astra.data2d.delete(sinogram_id)
astra.projector.delete(projector_id)
a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
b = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
c = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32)
i = 0
#print( origin[0] + (-0.5 * shape[0] + rect_min[0]) * pixsize[0], origin[0] + (-0.5 * shape[0] + rect_max[0]) * pixsize[0], origin[1] + (-0.5 * shape[1] + rect_min[1]) * pixsize[1], origin[1] + (-0.5 * shape[1] + rect_max[1]) * pixsize[1])
for src, det in gen_lines(pg):
#print(src,det)
# NB: Flipped y-axis here, since that is how astra interprets 2D volumes
# We compute line intersections with slightly bigger (cw) and
# smaller (aw) rectangles, and see if the kernel falls
# between these two values.
(aw,bw,cw) = intersect_line_rectangle_interval(src, det,
origin[0] + (-0.5 * shape[0] + rect_min[0]) * pixsize[0],
origin[0] + (-0.5 * shape[0] + rect_max[0]) * pixsize[0],
origin[1] + (+0.5 * shape[1] - rect_max[1]) * pixsize[1],
origin[1] + (+0.5 * shape[1] - rect_min[1]) * pixsize[1],
1e-3)
a[i] = aw
b[i] = bw
c[i] = cw
i += 1
# Add weight for pixel / voxel size
try:
detweight = pg['DetectorWidth']
except KeyError:
detweight = np.sqrt(pg['Vectors'][0,4]*pg['Vectors'][0,4] + pg['Vectors'][0,5]*pg['Vectors'][0,5] )
a *= detweight
b *= detweight
c *= detweight
a = a.reshape(astra.functions.geom_size(pg))
b = b.reshape(astra.functions.geom_size(pg))
c = c.reshape(astra.functions.geom_size(pg))
# Check if sinogram lies between a and c
y = np.min(sinogram-a)
z = np.min(c-sinogram)
x = np.max(np.abs(sinogram-b)) # ideally this is small, but can be large
# due to discontinuities in line kernel
self.assertFalse(z < 0 or y < 0)
if z < 0 or y < 0:
print(y,z,x)
pylab.gray()
pylab.imshow(data)
pylab.figure()
pylab.imshow(sinogram)
pylab.figure()
pylab.imshow(b)
pylab.figure()
pylab.imshow(a)
pylab.figure()
pylab.imshow(c)
pylab.figure()
pylab.imshow(sinogram-a)
pylab.figure()
pylab.imshow(c-sinogram)
pylab.show()
def test_par(self):
np.random.seed(seed)
for _ in range(nloops):
self.single_test('parallel')
def test_fan(self):
np.random.seed(seed)
for _ in range(nloops):
self.single_test('fanflat')
def test_parvec(self):
np.random.seed(seed)
for _ in range(nloops):
self.single_test('parallel_vec')
def test_fanvec(self):
np.random.seed(seed)
for _ in range(nloops):
self.single_test('fanflat_vec')
if __name__ == '__main__':
unittest.main()
#print(intersect_line_rectangle((0.,-256.),(-27.,0.),11.6368454385 20.173128227 3.18989047649 5.62882841606)
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