def ext_partial(spl, nth):
if knots[nth] < 0:
ust1 = 0.0
ued1 = knots[nth + deg + 1]
ust2 = knots[nth + nbr_lib]
ued2 = 1.0
n_dct1 = (ued1 - ust1) * n_total
n_dct2 = (ued2 - ust2) * n_total
n_dct1 = int(np.ceil(n_dct1))
n_dct2 = int(np.ceil(n_dct2))
return compute_energy_external_partial(spline=spl,
img=img,
ust=ust1, ued=ued1,
nbr_dct=n_dct1,
normalized=False) + \
compute_energy_external_partial(spline=spl,
img=img,
ust=ust2, ued=ued2,
nbr_dct=n_dct2,
normalized=False)
else:
ust = knots[nth]
ued = knots[nth + deg + 1]
n_dct = (ued - ust) * n_total
n_dct = int(np.ceil(n_dct))
return compute_energy_external_partial(spline=spl,
img=img,
ust=ust,
ued=ued,
nbr_dct=n_dct,
normalized=False)
def cost(ctrl_pts, nth):
nth = nth // 2
knots = spline.t
deg = spline.k
nbr_lib = len(ctrl_pts) / 2
n_total = 1000
if knots[nth] < 0:
ust1 = 0
ued1 = knots[nth + deg + 1]
ust2 = knots[nth + nbr_lib]
ued2 = 1.0
n_dct1 = (ued1 - ust1) * n_total
n_dct2 = (ued2 - ust2) * n_total
n_dct1 = int(np.ceil(n_dct1))
n_dct2 = int(np.ceil(n_dct2))
ctrl_pts = np.array(ctrl_pts)
ctrl_pts = np.reshape(ctrl_pts, ((len(ctrl_pts) / 2), 2))
spline.set_ctrl_pts(ctrl_pts, only_free=True)
if img is None:
ret1 = compute_energy_internal_partial(spline=spline,
ust=ust1, ued=ued1,
nbr_dct=n_dct1) + \
compute_energy_internal_partial(spline=spline,
ust=ust2, ued=ued2,
nbr_dct=n_dct2)
else:
ret1 = compute_energy_internal_partial(spline=spline,
ust=ust1, ued=ued1,
nbr_dct=n_dct1) + \
compute_energy_internal_partial(spline=spline,
ust=ust2, ued=ued2,
nbr_dct=n_dct2) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust1, ued=ued1,
nbr_dct=n_dct1) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust2, ued=ued2,
nbr_dct=n_dct2)
return ret1
else:
ust = knots[nth]
ued = knots[nth + deg + 1]
n_dct = (ued - ust) * n_total
n_dct = int(np.ceil(n_dct))
ctrl_pts = np.array(ctrl_pts)
ctrl_pts = np.reshape(ctrl_pts, ((len(ctrl_pts) / 2), 2))
spline.set_ctrl_pts(ctrl_pts, only_free=True)
if img is None:
ret2 = compute_energy_internal_partial(spline, ust, ued, n_dct)
else:
ret2 = compute_energy_internal_partial(spline=spline,
ust=ust, ued=ued,
nbr_dct=n_dct) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust, ued=ued,
nbr_dct=n_dct)
return ret2
def ext_partial(spline, nth):
'''
The function is used to compute the partial external energy given the
control point and the order of the varialbe. Firstly, we choose the
internal interval and compute the partial energy. It helps to compute
the simplified jacobian.
Parameters
----------
ctrl_pts : numpy.narray
The flattened vector of control points
nth: integer
The order of the control point of which we want to compute the
partial energy
Returns
-------
ret1(ret2) : float
Partial external energy corresponding the specified control point
'''
if knots[nth] < 0:
ust1 = 0
ued1 = knots[nth + deg + 1]
ust2 = knots[nth + nbr_lib]
ued2 = 1.0
n_dct1 = (ued1 - ust1) * n_total
n_dct2 = (ued2 - ust2) * n_total
n_dct1 = int(np.ceil(n_dct1))
n_dct2 = int(np.ceil(n_dct2))
ret1 = gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust1, ued=ued1,
nbr_dct=n_dct1,
normalized=False) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust2, ued=ued2,
nbr_dct=n_dct2,
normalized=False)
return ret1
else:
ust = knots[nth]
ued = knots[nth + deg + 1]
n_dct = (ued - ust) * n_total
n_dct = int(np.ceil(n_dct))
ret2 = gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust, ued=ued,
nbr_dct=n_dct,
normalized=False)
return ret2
def changement_discretisation():
# How the external energy changes with respect to the level of discretization
n_dct = np.linspace(start=10, stop=2000, num=100, dtype=np.int16)
energy = np.zeros(100)
plt.rcParams["font.family"] = "serif"
spl = spline_initialize(100)
img, imsh = create_image(30)
for i, data in enumerate(n_dct):
energy[i] = compute_energy_external_partial(spline=spl, img=img,
ust=0, ued=1.0,
nbr_dct=data)
fig = plt.figure()
fig.canvas.set_window_title("Dicretisation")
plt.plot(n_dct, energy)
plt.xlabel('Nombre de point de discretisation')
plt.ylabel('Energie')
plt.legend()
plt.show()
def cost_partial(ctrl_pts, nth):
'''
The function is used to compute the jacobian given the control point
and the order of the varialbe. Firstly, we choose the internal interval
and compute the partial energy. It helps to compute the simplified
jacobian
Parameters
----------
ctrl_pts : numpy.narray
The flattened vector of control points
nth: integer
The order of the control point of which we want to compute the
partial energy
Returns
-------
partial_energy : float
The partial energy corresponding to variables nth. If img=None, it
returns the partial internal energy. If not, it returns the partial
total (internal + external) energy.
References
----------
Les Piegl, Wayne Tiller, The NURBS book p.84
'''
ctrl_pts = np.array(ctrl_pts)
ctrl_pts = np.reshape(ctrl_pts, ((len(ctrl_pts) / 2), 2))
spline.set_ctrl_pts(ctrl_pts, only_free=True)
if knots[nth] < 0:
ust1 = 0
ued1 = knots[nth + deg + 1]
ust2 = knots[nth + nbr_lib]
ued2 = 1.0
n_dct1 = (ued1 - ust1) * n_total
n_dct2 = (ued2 - ust2) * n_total
n_dct1 = int(np.ceil(n_dct1))
n_dct2 = int(np.ceil(n_dct2))
if img is None:
ret1 = compute_energy_internal_partial(spline=spline,
ust=ust1, ued=ued1,
nbr_dct=n_dct1) + \
compute_energy_internal_partial(spline=spline,
ust=ust2, ued=ued2,
nbr_dct=n_dct2)
else:
ret1 = compute_energy_internal_partial(spline=spline,
ust=ust1, ued=ued1,
nbr_dct=n_dct1) + \
compute_energy_internal_partial(spline=spline,
ust=ust2, ued=ued2,
nbr_dct=n_dct2) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust1, ued=ued1,
nbr_dct=n_dct1) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust2, ued=ued2,
nbr_dct=n_dct2)
return ret1
else:
ust = knots[nth]
ued = knots[nth + deg + 1]
n_dct = (ued - ust) * n_total
n_dct = int(np.ceil(n_dct))
if img is None:
ret2 = compute_energy_internal_partial(spline, ust, ued, n_dct)
else:
ret2 = compute_energy_internal_partial(spline=spline,
ust=ust, ued=ued,
nbr_dct=n_dct) + gamma * \
compute_energy_external_partial(spline=spline, img=img,
ust=ust, ued=ued,
nbr_dct=n_dct)
return ret2