def fit_cirlce(pp, warnIfIllDefined=True):
""" fit_cirlce(pp, warnIfIllDefined=True)
Calculate the circle (x - c.x)**2 + (y - x.y)**2 = c.r**2
From the set of points pp. Returns a point instance with an added
attribute "r" specifying the radius.
In case the three points are on a line, the algorithm will fail, and
return 0 for x,y and r. This waring can be suppressed.
The solution is a Least Squares fit. The method as describes in [1] is
called Modified Least Squares (MLS) and poses a closed form solution
which is very robust.
[1]
Dale Umbach and Kerry N. Jones
2000
A Few Methods for Fitting Circles to Data
IEEE Transactions on Instrumentation and Measurement
"""
# Init error point
ce = Point(0,0)
ce.r = 0.0
def cov(a, b):
n = len(a)
Ex = a.sum() / n
Ey = b.sum() / n
return ( (a-Ex)*(b-Ey) ).sum() / (n-1)
# Get x and y elements
X = pp[:,0]
Y = pp[:,1]
# In the paper there is a factor n*(n-1) in all equations below. However,
# this factor is removed by devision in the equations in the following cell
A = cov(X,X)
B = cov(X,Y)
C = cov(Y,Y)
D = 0.5 * ( cov(X,Y**2) + cov(X,X**2) )
E = 0.5 * ( cov(Y,X**2) + cov(Y,Y**2) )
# Calculate denumerator
denum = A*C - B*B
if denum==0:
if warnIfIllDefined:
print("Warning: can not fit a circle to the given points.")
return ce
# Calculate point
c = Point( (D*C-B*E)/denum, (A*E-B*D)/denum )
# Calculate radius
c.r = c.distance(pp).sum() / len(pp)
# Done
return c
def get_slice(vol, sampling, center_point, global_direction,
look_for_bifurcation, alpha):
"""
Given two center points and the direction of the stent, the algorithm will
first create a slice on the second center point. A new center point is
calculated on this slice, which is used to find a local direction. The
local direction is used to update the global direction with weigthing
factor alpha (where 0 is following the local direction and 1 the global
direction). Using this new direction a slice is created on the first center
point.
"""
vec1 = Point(1, 0, 0)
vec2 = Point(0, 1, 0)
#Set second center point as rotation point
rotation_point = Point(center_point[2], center_point[1],
center_point[0]) + global_direction
#Create the slice using the global direction
slice, vec1, vec2 = slice_from_volume(vol, sampling, global_direction,
rotation_point, vec1, vec2)
#Search for points in this slice and filter these with the clustering method
points_in_slice = stentPoints2d.detect_points(slice)
try:
points_in_slice_filtered = stentPoints2d.cluster_points(points_in_slice, \
Point(128,128))
except AssertionError:
points_in_slice_filtered = []
#if filtering did not succeed the unfiltered points are used
if not points_in_slice_filtered:
points_in_slice_filtered = points_in_slice
succeeded = False
else:
succeeded = True
#if looking for bifurcation than the radius has to be calculated
if succeeded and look_for_bifurcation:
center_point_with_radius = stentPoints2d.fit_cirlce( \
points_in_slice_filtered)
#convert 2d center point to 3d for the event that the bifurcation
#is found
center_point_3d_with_radius = convert_2d_point_to_3d_point( \
Point(rotation_point[2], rotation_point[1], rotation_point[0]), vec1, vec2, center_point_with_radius)
#Convert pointset into point
center_point_3d_with_radius = Point(center_point_3d_with_radius[0])
#Give the 3d center point the radius as attribute
center_point_3d_with_radius.r = center_point_with_radius.r
else:
center_point_3d_with_radius = Point(0, 0, 0)
center_point_3d_with_radius.r = []
#Now the local direction of the stent has to be found. Note that it is not
#done when the chopstick filtering did not succeed.
if succeeded:
better_center_point = stentPoints2d.converge_to_centre(points_in_slice_filtered, \
Point(128,128))
else:
better_center_point = Point(0, 0), []
#If no better center point has been found, there is no need to update global
#direction
if better_center_point[0] == Point(0, 0):
updated_direction = global_direction
else:
better_center_point_3d = convert_2d_point_to_3d_point(\
Point(rotation_point[2], rotation_point[1], rotation_point[0]), \
vec1, vec2, better_center_point[0])
#Change pointset into a point
better_center_point_3d = Point(better_center_point_3d[0])
#local direction (from starting center point to the better center point)
local_direction = Point(better_center_point_3d[2]-center_point[2], \
better_center_point_3d[1]-center_point[1], better_center_point_3d[0] \
-center_point[0]).Normalize()
#calculate updated direction
updated_direction = ((1 - alpha) * local_direction +
alpha * global_direction).Normalize()
#Now a new slice can be created using the first center point as rotation point.
rotation_point = Point(center_point[2], center_point[1], center_point[0])
slice, vec1, vec2 = slice_from_volume(vol, sampling, updated_direction,
rotation_point, vec1, vec2)
#Change order
rotation_point = Point(center_point[0], center_point[1], center_point[2])
#return new center point
new_center_point = center_point + Point(updated_direction[2], \
updated_direction[1], updated_direction[0])
return slice, new_center_point, updated_direction, rotation_point, vec1, vec2, \
center_point_3d_with_radius
def converge_to_centre(pp, c, nDirections=5, maxRadius=50, pauseTime=0):
""" converge_to_centre(pp, c)
Given a set of points and an initial center point c,
will find a better estimate of the center.
Returns (c, L), with L indices in pp that were uses to fit
the final circle.
"""
# Shorter names
N = nDirections
pi = np.pi
# Init point to return on error
ce = Point(0,0)
ce.r = 0
# Are there enough points?
if len(pp) < 3:
return ce, []
# Init a pointset of centers we've has so far
cc = Pointset(2)
# Init list with vis objects (to be able to delete them)
showObjects = []
if pauseTime:
fig = vv.gcf()
while c not in cc:
# Add previous center
cc.append(c)
# Calculate distances and angles
dists = c.distance(pp)
angs = c.angle2(pp)
# Get index of closest points
i, = np.where(dists==dists.min())
i = iClosest = int(i[0])
# Offset the angles with the angle relative to the closest point.
refAng = angs[i]
angs = subtract_angles(angs, refAng)
# Init L, the indices to the closest point in each direction
L = []
# Get closest point on N directions
for angle in [float(angnr)/N*2*pi for angnr in range(N)]:
# Get indices of points that are in this direction
dangs = subtract_angles(angs, angle)
I, = np.where(np.abs(dangs) < pi/N )
# Select closest
if len(I):
distSelection = dists[I]
minDist = distSelection.min()
J, = np.where(distSelection==minDist)
if len(J) and minDist < maxRadius:
L.append( int(I[J[0]]) )
# Check if ok
if len(L) < 3:
return ce, []
# Remove spurious points (points much furter away that the 3 closest)
distSelection = dists[L]
tmp = [d for d in distSelection]
d3 = sorted(tmp)[2] # Get distance of 3th closest point
I, = np.where(distSelection < d3*2)
L = [L[i] for i in I]
# Select points
ppSelect = Pointset(2)
for i in L:
ppSelect.append(pp[i])
# Refit circle
cnew = fit_cirlce(ppSelect,False)
if cnew.r==0:
return ce, []
# Show
if pauseTime>0:
# Delete
for ob in showObjects:
ob.Destroy()
# Plot center and new center
ob1 = vv.plot(c, ls='', ms='x', mc='r', mw=10, axesAdjust=0)
ob2 = vv.plot(cnew, ls='', ms='x', mc='r', mw=10, mew=0, axesAdjust=0)
# Plot selection points
ob3 = vv.plot(ppSelect, ls='', ms='.', mc='y', mw=10, axesAdjust=0)
# Plot lines dividing the directions
tmpSet1 = Pointset(2)
tmpSet2 = Pointset(2)
for angle in [float(angnr)/N*2*pi for angnr in range(N)]:
angle = -subtract_angles(angle, refAng)
dx, dy = np.cos(angle), np.sin(angle)
tmpSet1.append(c.x, c.y)
tmpSet1.append(c.x+dx*d3*2, c.y+dy*d3*2)
for angle in [float(angnr+0.5)/N*2*pi for angnr in range(N)]:
angle = -subtract_angles(angle, refAng)
dx, dy = np.cos(angle), np.sin(angle)
tmpSet2.append(c.x, c.y)
tmpSet2.append(c.x+dx*d3*2, c.y+dy*d3*2)
ob4 = vv.plot(tmpSet1, lc='y', ls='--', axesAdjust=0)
ob5 = vv.plot(tmpSet2, lc='y', lw=3, axesAdjust=0)
# Store objects and wait
showObjects = [ob1,ob2,ob3,ob4,ob5]
fig.DrawNow()
time.sleep(pauseTime)
# Use new
c = cnew
# Done
for ob in showObjects:
ob.Destroy()
return c, L
