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) # x-coord of intersection of the line (src, det) with the horizontal line at y def intersect_line_horizontal(src, det, y): EPS = 1e-5 if np.abs(src[1] - det[1]) < EPS: return np.nan t = (y - src[1]) / (det[1] - src[1]) return src[0] + t * (det[0] - src[0]) # y-coord of intersection of the line (src, det) with the vertical line at x def intersect_line_vertical(src, det, x): src = ( src[1], src[0] ) det = ( det[1], det[0] ) return intersect_line_horizontal(src, det, x) # length of the intersection of the strip with boundaries edge1, edge2 with the horizontal # segment at y, with horizontal extent x_seg def intersect_ray_horizontal_segment(edge1, edge2, y, x_seg): e1 = intersect_line_horizontal(edge1[0], edge1[1], y) e2 = intersect_line_horizontal(edge2[0], edge2[1], y) if not (np.isfinite(e1) and np.isfinite(e2)): return np.nan (e1, e2) = np.sort([e1, e2]) (x1, x2) = np.sort(x_seg) l = np.max([e1, x1]) r = np.min([e2, x2]) #print(edge1, edge2, y, x_seg, r-l) return np.max([r-l, 0.0]) def intersect_ray_vertical_segment(edge1, edge2, x, y_seg): # mirror edge1 and edge2 edge1 = [ (a[1], a[0]) for a in edge1 ] edge2 = [ (a[1], a[0]) for a in edge2 ] return intersect_ray_horizontal_segment(edge1, edge2, x, y_seg) def area_signed(a, b): return a[0] * b[1] - a[1] * b[0] # is c to the left of ab def is_left_of(a, b, c): return area_signed( (b[0] - a[0], b[1] - a[1]), (c[0] - a[0], c[1] - a[1]) ) > 0 # compute area of rect on left side of line def halfarea_rect_line(src, det, xmin, xmax, ymin, ymax): pts = ( (xmin,ymin), (xmin,ymax), (xmax,ymin), (xmax,ymax) ) pts_left = list(filter( lambda p: is_left_of(src, det, p), pts )) npts_left = len(pts_left) if npts_left == 0: return 0.0 elif npts_left == 1: # triangle p = pts_left[0] xd = intersect_line_horizontal(src, det, p[1]) - p[0] yd = intersect_line_vertical(src, det, p[0]) - p[1] ret = 0.5 * abs(xd) * abs(yd) return ret elif npts_left == 2: p = pts_left[0] q = pts_left[1] if p[0] == q[0]: # vertical intersection x1 = intersect_line_horizontal(src, det, p[1]) - p[0] x2 = intersect_line_horizontal(src, det, q[1]) - q[0] ret = 0.5 * (ymax - ymin) * (abs(x1) + abs(x2)) return ret else: assert(p[1] == q[1]) # horizontal intersection y1 = intersect_line_vertical(src, det, p[0]) - p[1] y2 = intersect_line_vertical(src, det, q[0]) - q[1] ret = 0.5 * (xmax - xmin) * (abs(y1) + abs(y2)) return ret else: # mirror and invert ret = ((xmax - xmin) * (ymax - ymin)) - halfarea_rect_line(det, src, xmin, xmax, ymin, ymax) return ret # area of intersection of the strip with boundaries edge1, edge2 with rectangle def intersect_ray_rect(edge1, edge2, xmin, xmax, ymin, ymax): s1 = halfarea_rect_line(edge1[0], edge1[1], xmin, xmax, ymin, ymax) s2 = halfarea_rect_line(edge2[0], edge2[1], xmin, xmax, ymin, ymax) return abs(s1 - s2) # LINE GENERATORS # --------------- # # Per ray these yield three lines, at respectively the center and two edges of the detector pixel. # Each line is given by two points on the line. # ( ( (p0x, p0y), (q0x, q0y) ), ( (p1x, p1y), (q1x, q1y) ), ( (p2x, p2y), (q2x, q2y) ) ) 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), (src, detb + (i - 0.5) * detu), (src, detb + (i + 0.5) * 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), (src, detb + (i - 0.5) * detu), (src, detb + (i + 0.5) * 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), (detb + (i - 0.5) * detu - ray, detb + (i - 0.5) * detu), (detb + (i + 0.5) * detu - ray, detb + (i + 0.5) * 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), (detb + (i - 0.5) * detu - ray, detb + (i - 0.5) * detu), (detb + (i + 0.5) * detu - ray, detb + (i + 0.5) * 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 Test2DKernel(unittest.TestCase): def single_test(self, type, proj_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(proj_type, pg, vg) elif type == 'parallel_vec': pg = gen_random_geometry_parallel_vec() projector_id = astra.create_projector(proj_type, pg, vg) elif type == 'fanflat': pg = gen_random_geometry_fanflat() projector_id = astra.create_projector(proj_type + '_fanflat', pg, vg) elif type == 'fanflat_vec': pg = gen_random_geometry_fanflat_vec() projector_id = astra.create_projector(proj_type + '_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) if proj_type == 'line': 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 center, edge1, edge2 in gen_lines(pg): (src, det) = center #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() elif proj_type == 'distance_driven': a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32) i = 0 for center, edge1, edge2 in gen_lines(pg): (xd, yd) = center[1] - center[0] l = 0.0 if np.abs(xd) > np.abs(yd): # horizontal ray y_seg = (origin[1] + (+0.5 * shape[1] - rect_max[1]) * pixsize[1], origin[1] + (+0.5 * shape[1] - rect_min[1]) * pixsize[1]) for j in range(rect_min[0], rect_max[0]): x = origin[0] + (-0.5 * shape[0] + j + 0.5) * pixsize[0] l += intersect_ray_vertical_segment(edge1, edge2, x, y_seg) * pixsize[0] else: x_seg = (origin[0] + (-0.5 * shape[0] + rect_max[0]) * pixsize[0], origin[0] + (-0.5 * shape[0] + rect_min[0]) * pixsize[0]) for j in range(rect_min[1], rect_max[1]): y = origin[1] + (+0.5 * shape[1] - j - 0.5) * pixsize[1] l += intersect_ray_horizontal_segment(edge1, edge2, y, x_seg) * pixsize[1] a[i] = l i += 1 a = a.reshape(astra.functions.geom_size(pg)) x = np.max(np.abs(sinogram-a)) if x > 2e-3: pylab.gray() pylab.imshow(data) pylab.figure() pylab.imshow(sinogram) pylab.figure() pylab.imshow(a) pylab.figure() pylab.imshow(sinogram-a) pylab.show() self.assertFalse(x > 2e-3) elif proj_type == 'strip': xmin = origin[0] + (-0.5 * shape[0] + rect_min[0]) * pixsize[0] xmax = origin[0] + (-0.5 * shape[0] + rect_max[0]) * pixsize[0] ymin = origin[1] + (+0.5 * shape[1] - rect_max[1]) * pixsize[1] ymax = origin[1] + (+0.5 * shape[1] - rect_min[1]) * pixsize[1] a = np.zeros(np.prod(astra.functions.geom_size(pg)), dtype=np.float32) i = 0 for center, edge1, edge2 in gen_lines(pg): a[i] = intersect_ray_rect(edge1, edge2, xmin, xmax, ymin, ymax) i += 1 a = a.reshape(astra.functions.geom_size(pg)) x = np.max(np.abs(sinogram-a)) if x > 2e-3: print(x) if False and x > 2e-3: pylab.gray() pylab.imshow(data) pylab.figure() pylab.imshow(sinogram) pylab.figure() pylab.imshow(a) pylab.figure() pylab.imshow(sinogram-a) pylab.show() self.assertFalse(x > 2e-3) def test_par(self): np.random.seed(seed) for _ in range(nloops): self.single_test('parallel', 'line') def test_par_dd(self): np.random.seed(seed) for _ in range(nloops): self.single_test('parallel', 'distance_driven') def test_par_strip(self): np.random.seed(seed) for _ in range(nloops): self.single_test('parallel', 'strip') def test_fan(self): np.random.seed(seed) for _ in range(nloops): self.single_test('fanflat', 'line') def test_fan_strip(self): np.random.seed(seed) for _ in range(nloops): self.single_test('fanflat', 'strip') def test_parvec(self): np.random.seed(seed) for _ in range(nloops): self.single_test('parallel_vec', 'line') def test_parvec_dd(self): np.random.seed(seed) for _ in range(nloops): self.single_test('parallel_vec', 'distance_driven') def test_parvec_strip(self): np.random.seed(seed) for _ in range(nloops): self.single_test('parallel_vec', 'strip') def test_fanvec(self): np.random.seed(seed) for _ in range(nloops): self.single_test('fanflat_vec', 'line') if __name__ == '__main__': unittest.main() #print(intersect_line_rectangle((0.,-256.),(-27.,0.),11.6368454385 20.173128227 3.18989047649 5.62882841606)