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funs.py
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funs.py
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################################################
# Functions for Subsea pipe case. Phantom and CT acquisition geometry.
# By Silja L. Christensen
# April 2024
################################################
import numpy as np
#%%
#=======================================================================
# Phantom
#=========================================================================
def DeepSeaOilPipe8(N,defects):
radii = np.array([9,11,16,17.5,23])
domain = 55
c = np.round(np.array([N/2,N/2]))
axis1 = np.linspace(-c[0]-1,N-c[0],N, endpoint=True)
axis2 = np.linspace(-c[0]-1,N-c[0],N, endpoint=True)
x, y = np.meshgrid(axis1,axis2)
center = np.array([0,0])
phantom = 2e-2*7.9*drawPipe(N,domain,x,y,center,center,radii[0],radii[1]) # Steel (8.05g/cm^3)
phantom = phantom+5.1e-2*0.15*drawPipe(N,domain,x,y,center,center,radii[1],radii[2]) # PE-foam
phantom = phantom+5.1e-2*0.94*drawPipe(N,domain,x,y,center,center,radii[2],radii[3]) # PU rubber 0.93-0.97 g / cm^3 (Might be PVC, 1400 kg /m^3)
phantom = phantom+4.56e-2*2.3*drawPipe(N,domain,x,y,center,center,radii[3],radii[4]) # Concrete 2.3 g/cm^3
# radial cracks
if defects == True:
defectmask = []
vertices = []
# radial and angular cracks
no = 12
ang = np.array([-3*np.pi/9, -2*np.pi/9, -np.pi/9, 0, np.pi/2, np.pi/2, np.pi/2, np.pi/2, 2*np.pi/3, 5*np.pi/4-np.pi/9, 5*np.pi/4, 5*np.pi/4+np.pi/9])-60/180*np.pi
dist = np.array([20.25, 20.25, 20.25, 20.25, 20.25, 16.75, 13.5, 10, 20.25, 16.75+2, 16.75, 16.75-2])/domain*N
w = np.array([0.5, 0.4, 0.3, 0.2, 4, 4, 4, 4, 0.4, 0.4, 0.4, 0.4])/domain*N
l = np.array([4, 4, 4, 4, 0.4, 0.4, 0.4, 0.4, 4, 4, 4, 4])/domain*N
vals = np.zeros(no)
vals[8] = 2e-2*7.9
for i in range(no):
# coordinates in (x,y), -1 to 1 system
coordinates0 = np.array([
[c[0]+w[i]/2, c[1]+dist[i] + l[i]/2],
[c[0]-w[i]/2, c[1]+dist[i] + l[i]/2],
[c[0]-w[i]/2, c[1]+dist[i] - l[i]/2],
[c[0]+w[i]/2, c[1]+dist[i] - l[i]/2]
])
R = np.array([
[np.cos(ang[i]), -np.sin(ang[i])],
[np.sin(ang[i]), np.cos(ang[i])]
])
# Rotate around image center
coordinates = R @ (coordinates0.T - np.array([[c[0]],[c[1]]])) + np.array([[c[0]],[c[1]]])
coordinates = coordinates.T
# transform into (row, column) indicies
vertices.append(np.ceil(np.fliplr(coordinates)))
# create mask
tmpmask = create_polygon([N,N], vertices[i])
defectmask.append(np.array(tmpmask, dtype=bool))
phantom[defectmask[i]] = vals[i]
# Cross
c_cross_ang = -np.pi/2
c_cross_dist = 20.25/domain*N
c_cross = c_cross_dist*np.array([np.cos(c_cross_ang), np.sin(c_cross_ang)])+N/2
#np.array([c[1]-20.25/domain*N, c[0]])
a = (2/np.sqrt(2))/domain*N
b = (0.2/np.sqrt(2))/domain*N
coordinates_cross1 = np.array([
[c_cross[0]-a+b, c_cross[1]-a],
[c_cross[0]+a, c_cross[1]+a-b],
[c_cross[0]+a-b, c_cross[1]+a],
[c_cross[0]-a, c_cross[1]-a+b]])
coordinates_cross2 = np.array([
[c_cross[0]+a-b, c_cross[1]-a],
[c_cross[0]+a, c_cross[1]-a+b],
[c_cross[0]-a+b, c_cross[1]+a],
[c_cross[0]-a, c_cross[1]+a-b]])
# transform into (row, column) indicies
vertices.append(np.ceil(np.flipud(coordinates_cross1)))
# create mask
tmpmask = create_polygon([N,N], vertices[12])
defectmask.append(np.array(tmpmask, dtype=bool))
phantom[defectmask[12]] = 0
# transform into (row, column) indicies
vertices.append(np.ceil(np.flipud(coordinates_cross2)))
# create mask
tmpmask = create_polygon([N,N], vertices[13])
defectmask.append(np.array(tmpmask, dtype=bool))
phantom[defectmask[13]] = 0
# Circles
ang_circ = np.array([3*np.pi/4+np.pi/9, 3*np.pi/4+np.pi/9, 3*np.pi/4, 3*np.pi/4, 3*np.pi/4-np.pi/9])-60/180*np.pi
dist_circ = 20.25/domain*N
siz = np.array([1, 0.3, 1, 0.3, 0.3])/domain*N
val = np.array([0, 2e-2*7.9, 0, 4.56e-2*2.3, 2e-2*7.9])
for i in range(len(ang_circ)):
tmpmask = ((x-np.cos(ang_circ[i])*dist_circ)**2 + (y-np.sin(ang_circ[i])*dist_circ)**2 <= siz[i]**2)
defectmask.append(np.array(tmpmask, dtype=bool))
phantom[defectmask[14+i]] = val[i]
center_dists = np.hstack([dist, c_cross_dist, dist_circ*np.ones(3)])
center_x = center_dists*np.hstack([np.sin(-ang), np.sin(np.array([c_cross_ang])), np.cos(ang_circ[np.array([0,2,4])])])+N/2
center_y = center_dists*np.hstack([np.cos(-ang), np.cos(np.array([c_cross_ang])), np.sin(ang_circ[np.array([0,2,4])])])+N/2
centers = np.vstack([center_x, center_y])
return phantom, radii, defectmask, vertices, centers
else:
return phantom, radii
def drawPipe(N, domain, x,y ,c1,c2, r1, r2):
# N is number of pixels on one axis
# domain is true size of one axis
# x and y is a meshgrid of the domain
# r1 and r2 are the inner and outer radii of the pipe layer
R1 = r1/domain*N
R2 = r2/domain*N
M1 = (x-c1[0]/domain*N)**2+(y-c1[1]/domain*N)**2>=R1**2
M2 = (x-c2[0]/domain*N)**2+(y-c2[1]/domain*N)**2<=R2**2
return np.logical_and(M1, M2)
def check(p1, p2, base_array):
"""
Source: https://stackoverflow.com/questions/37117878/generating-a-filled-polygon-inside-a-numpy-array
Uses the line defined by p1 and p2 to check array of
input indices against interpolated value
Returns boolean array, with True inside and False outside of shape
"""
idxs = np.indices(base_array.shape) # Create 3D array of indices
p1 = p1.astype(float)
p2 = p2.astype(float)
# Calculate max column idx for each row idx based on interpolated line between two points
if p1[0] == p2[0]:
max_col_idx = (idxs[0] - p1[0]) * idxs.shape[1]
sign = np.sign(p2[1] - p1[1])
else:
max_col_idx = (idxs[0] - p1[0]) / (p2[0] - p1[0]) * (p2[1] - p1[1]) + p1[1]
sign = np.sign(p2[0] - p1[0])
return idxs[1] * sign <= max_col_idx * sign
def create_polygon(shape, vertices):
"""
Creates np.array with dimensions defined by shape
Fills polygon defined by vertices with ones, all other values zero"""
base_array = np.zeros(shape, dtype=float) # Initialize your array of zeros
fill = np.ones(base_array.shape) * True # Initialize boolean array defining shape fill
# Create check array for each edge segment, combine into fill array
for k in range(vertices.shape[0]):
fill = np.all([fill, check(vertices[k-1], vertices[k], base_array)], axis=0)
# Set all values inside polygon to one
base_array[fill] = 1
return base_array
#%%
#=======================================================================
# Acquisition geometry
#=========================================================================
def geom_Data20180911(size):
offset = 0 # angular offset
shift = -12.5 # source offset from center
stc = 60 # source to center distance
ctd = 50 # center to detector distance
det_full = 512
startAngle = 0
if size == "sparseangles":
p = 510 # p: number of detector pixels
q = 36 # q: number of projection angles
maxAngle = 360 # measurement max angle
if size == "sparseangles20percent":
p = 510 # p: number of detector pixels
q = 72 # q: number of projection angles
maxAngle = 360 # measurement max angle
if size == "sparseangles50percent":
p = 510 # p: number of detector pixels
q = 180 # q: number of projection angles
maxAngle = 360 # measurement max angle
elif size == "full":
p = 510 # p: number of detector pixels
q = 360 # q: number of projection angles
maxAngle = 360 # measurement max angle
elif size == "overfull":
p = 510 # p: number of detector pixels
q = 720 # q: number of projection angles
maxAngle = 364 # measurement max angle
elif size == "limited90":
p = 510 # p: number of detector pixels
q = 90 # q: number of projection angles
startAngle = 15
maxAngle = 105
elif size == "limited120":
p = 510 # p: number of detector pixels
q = 120 # q: number of projection angles
maxAngle = 120
elif size == "limited180":
p = 510 # p: number of detector pixels
q = 180 # q: number of projection angles
startAngle = 15
maxAngle = 195
elif size == "limited180_2":
p = 510 # p: number of detector pixels
q = 180 # q: number of projection angles
startAngle = 180
maxAngle = 360
dlA = 41.1*(p/det_full) # full detector length
dl = dlA/p # length of detector element
# view angles in rad
theta = np.linspace(startAngle, maxAngle, q, endpoint=False)
theta = theta/180*np.pi
s0 = np.array([shift, -stc])
d0 = np.array([shift, ctd])
u0 = np.array([dl, 0])
vectors = np.empty([q, 6])
for i, val in enumerate(theta):
R = np.array([[np.cos(val), -np.sin(val)], [np.sin(val), np.cos(val)]])
s = R @ s0
d = R @ d0
u = R @ u0
vectors[i, 0:2] = s
vectors[i, 2:4] = d
vectors[i, 4:6] = u
return p, theta, stc, ctd, shift, vectors, dl, dlA