def bessel_cost_func(vol1_org, vol2_org, thetas, axis, mask=False, smooth = False, mode = 1):
'''
vol1: original image
vol2: volume to be rotated
thetas: list of degress to try
cf: cost function
arg: string for plot titles
'''
vol1 = vol1_org.copy()
vol2 = vol2_org.copy()
cost_func = np.zeros([len(thetas),])
if(mask):
for i in xrange(len(vol1)):
if(axis == 0):
vol1[i,:,:] = circle_mask(vol1[i,:,:], smooth, mode)
elif(axis == 1):
vol1[:,i,:] = circle_mask(vol1[:,i,:], smooth, mode)
else:
vol1[:,:,i] = circle_mask(vol1[:,:,i], smooth, mode)
for idx, t in enumerate(thetas):
print t,
new_vol2 = np.zeros(vol2.shape)
for i in xrange(len(vol2)):
if(axis == 0):
new_vol2[i,:,:] = bessel_rotate(vol2[i,:,:], t, mask, smooth, mode)
elif(axis == 1):
new_vol2[:,i,:] = bessel_rotate(vol2[:,i,:], t, mask, smooth, mode)
else:
new_vol2[:,:,i] = bessel_rotate(vol2[:,:,i], t, mask, smooth, mode)
cost_func[idx] = cf_ssd(new_vol2, vol1)
return cost_func
def imrotate(image_org, theta, interpolation = 'bilinear', mask=False, smooth = False, mode = 1,x=None, y=None):
image = image_org.copy()
if(mask):
image = circle_mask(image,smooth,mode)
theta = to_radian(theta)
ox = image.shape[1]/2.-0.5
oy = image.shape[0]/2.-0.5
if((x == None) and (y == None)): #i.e. x and y not specified
x = np.linspace(0, image.shape[1]-1, image.shape[1]).astype(int)
y = np.linspace(0, image.shape[0]-1, image.shape[0]).astype(int)
xx, yy = np.meshgrid(x,y)
dest_x, dest_y = rotate_coords(xx, yy, theta, ox, oy)
else:
dest_x, dest_y = rotate_coords(x, y, theta, ox, oy)
if(interpolation == 'bicubic'):
dest = bicubic_interp(image, dest_x, dest_y)
if(interpolation == 'bilinear'):
dest = bilinear_interp(image, dest_x, dest_y)
if(interpolation == 'bessel'):
dest = bessel_rotate(image, theta)
if(interpolation == 'spline'):
spline = scipy.interpolate.RectBivariateSpline(x, y, image)
dest = spline.ev(dest_y,dest_x)
return dest
def bessel_rotate(image_org, theta, mask = False, smooth = False, mode = 1):
image = image_org.copy()
if(mask):
image = circle_mask(image, smooth, mode)
Ib = np.zeros(image.shape)
theta = to_radian(theta)
s = (image.shape[0]-1)/2.
x = np.linspace(-s, s, image.shape[1])
y = np.linspace(-s, s, image.shape[0])
xx, yy = np.meshgrid(x,y)
rM = np.array([[np.cos(theta), -np.sin(theta)],[np.sin(theta), np.cos(theta)]])
for i in np.arange(-s,s+1):
for j in np.arange(-s,s+1):
new_x = np.dot(rM, np.array([i,j]))
if(np.sum(abs(np.round(new_x,5))>s)):
Ib[i+s,j+s] = 0
else:
R = np.sqrt((xx-new_x[1])**2 + (yy-new_x[0])**2)
mask_R = (R == 0)
Bess = np.zeros(R.shape)
Bess[~mask_R] = scipy.special.j1(np.pi*R[~mask_R])*hann(R[~mask_R],image.shape[0]*mode)/(np.pi*R[~mask_R])
Bess[mask_R] = 0.5
Bess = Bess/np.sum(Bess)
tmp = image*Bess
Ib[i+s,j+s] = np.sum(tmp) #np.round(np.sum(tmp),10)
return Ib
def rot_cost_func(vol1_org, vol2_org, thetas, axis, interpolation='bilinear', mask=False, smooth=False, mode=1, x=None, y=None):
'''
vol1: original image
vol2: volume to be rotated
thetas: list of degress to try
arg: string for plot titles
'''
vol1 = vol1_org.copy()
vol2 = vol2_org.copy()
if(mask):
for i in xrange(len(vol1)):
if(axis == 0):
vol1[i,:,:] = circle_mask(vol1[i,:,:], smooth, mode)
elif(axis == 1):
vol1[:,i,:] = circle_mask(vol1[:,i,:], smooth, mode)
else:
vol1[:,:,i] = circle_mask(vol1[:,:,i], smooth, mode)
cost_func = np.zeros([len(thetas),])
for idx, t in enumerate(thetas):
new_vol2 = np.ones(vol2.shape)
for i in xrange(len(vol2)):
if(axis == 0):
sub = vol2[i,:,:]
elif(axis == 1):
sub = vol2[:,i,:]
else:
sub = vol2[:,:,i]
rot = imrotate(sub, t, interpolation, mask, smooth, mode, x, y)
if(axis == 0):
new_vol2[i,:,:] = rot
elif(axis == 1):
new_vol2[:,i,:] = rot
else:
new_vol2[:,:,i] = rot
cost_func[idx] = cf_ssd(new_vol2,vol1)
return cost_func
def rot_halton_cost_func(vol1_org, vol2_org, N, thetas, axis, interpolation='bilinear', smooth = True, mode = 1):
'''
vol1: original image
vol2: volume to be rotated
thetas: list of degress to try
cf: cost function
arg: string for plot titles
'''
vol1 = vol1_org.copy()
vol2 = vol2_org.copy()
cost_func = np.zeros([len(thetas),])
# generate Halton sample points
s = (len(vol1)-1)/2.
sequencer = ghalton.GeneralizedHalton(ghalton.EA_PERMS[:3])
sequencer.reset()
points = sequencer.get(N)
pts = np.array(points)
xx1 = (len(vol1)-1) * pts[:,0] - s
yy1 = (len(vol1)-1) * pts[:,1] - s
mask = np.sqrt(xx1**2+yy1**2) < s*0.7
x1 = xx1[mask]
y1 = yy1[mask]
new_vol1 = np.zeros([len(vol1),len(x1)])
print len(x1),
for i in xrange(len(vol1)):
if(axis == 0):
sub1 = circle_mask(vol1[i,:,:], smooth = True, mode = 1)
elif(axis == 1):
sub1 = circle_mask(vol1[:,i,:], smooth = True, mode = 1)
else:
sub1 = circle_mask(vol1[:,:,i], smooth = True, mode = 1)
rot = imrotate(sub1, 0, interpolation, True, smooth, mode, x1, y1)
new_vol1[i] = rot
for idx, t in enumerate(thetas):
new_vol2 = np.empty([len(vol2),len(x1)])
for i in xrange(len(vol2)):
if(axis==0):
sub2 = circle_mask(vol2[i,:,:], smooth = True, mode = 1)
elif(axis==1):
sub2 = circle_mask(vol2[:,i,:], smooth = True, mode = 1)
else:
sub2 = circle_mask(vol2[:,:,i], smooth = True, mode = 1)
rot = imrotate(sub2, t, interpolation, True, smooth, mode, x1, y1)
new_vol2[i] = rot
cost_func[idx] = cf_ssd(new_vol2,new_vol1)
return cost_func
def bessel_halton_cost_func(vol1_org, vol2, N, thetas, axis):
'''
vol1: original image
vol2: volume to be rotated
thetas: list of degress to try
cf: cost function
arg: string for plot titles
'''
vol1 = vol1_org.copy()
# initialize vector to store cost
cost_func = np.zeros([len(thetas),])
# generate Halton sample points
s = (len(vol1)-1)/2.
sequencer = ghalton.GeneralizedHalton(ghalton.EA_PERMS[:3])
sequencer.reset()
points = sequencer.get(N)
pts = np.array(points)
x1 = (len(vol1)-1) * pts[:,0] - s
y1 = (len(vol1)-1) * pts[:,1] - s
new_vol1 = np.empty([len(vol1),N])
for i in xrange(len(vol1)):
if(axis == 0):
sub1 = circle_mask(vol1[i,:,:])
elif(axis == 1):
sub1 = circle_mask(vol1[:,i,:])
else:
sub1 = circle_mask(vol1[:,:,i])
rot = bessel_rotate_halton(sub1, 0, x1, y1)
new_vol1[i] = rot
for idx, t in enumerate(thetas):
print t,
new_vol2 = np.empty([len(vol2),N])
for i in xrange(len(vol2)):
if(axis==0):
sub2 = circle_mask(vol2[i,:,:])
elif(axis==1):
sub2 = circle_mask(vol2[:,i,:])
else:
sub2 = circle_mask(vol2[:,:,i])
new_vol2[i] = bessel_rotate_halton(sub2, t, x1, y1)
cost_func[idx] = cf_ssd(new_vol2,new_vol1)
return cost_func
