From f64c471e882c925417336354e15ca46d586bdc70 Mon Sep 17 00:00:00 2001
From: Willem Jan Palenstijn <Willem.Jan.Palenstijn@cwi.nl>
Date: Fri, 6 Oct 2017 13:30:25 +0200
Subject: Add tests for 2D line kernels
---
tests/python/test_line2d.py | 310 ++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 310 insertions(+)
create mode 100644 tests/python/test_line2d.py
(limited to 'tests/python')
diff --git a/tests/python/test_line2d.py b/tests/python/test_line2d.py
new file mode 100644
index 0000000..de68033
--- /dev/null
+++ b/tests/python/test_line2d.py
@@ -0,0 +1,310 @@
+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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