def run(self):
G = np.gradient(self.X)
A = np.zeros((6,6)+self.dim, dtype = np.float32)
b = np.zeros((6,)+self.dim, dtype = np.float32)
A[0,0,:,:,:] = self.convol(G[0]*G[0])
A[1,0,:,:,:] = self.convol(G[0]*G[1])
A[1,1,:,:,:] = self.convol(G[1]*G[1])
A[2,0,:,:,:] = self.convol(G[0]) + self.convol(G[0]*G[0], (1,0,0))
A[2,1,:,:,:] = self.convol(G[1]) + self.convol(G[0]*G[1], (1,0,0))
A[2,2,:,:,:] = self.convol(self.X) + 2*self.convol(G[0], (1,0,0)) + self.convol(G[0]*G[0], (2,0,0))
A[3,0,:,:,:] = self.convol(G[0]) + self.convol(G[0]*G[1], (0,1,0))
A[3,1,:,:,:] = self.convol(G[1]) + self.convol(G[1]*G[1], (0,1,0))
A[3,2,:,:,:] = (self.convol(self.X) + self.convol(G[0], (1,0,0))
+ self.convol(G[1], (0,1,0)) + self.convol(G[0]*G[1], (1,1,0)))
A[3,3,:,:,:] = self.convol(self.X) + 2*self.convol(G[1], (0,1,0)) + self.convol(G[1]*G[1], (0,2,0))
A[4,0,:,:,:] = self.convol(G[0]*G[0], (0,1,0))
A[4,1,:,:,:] = self.convol(G[0]*G[1], (0,1,0))
A[4,2,:,:,:] = self.convol(G[0], (0,1,0)) + self.convol(G[0]*G[0], (1,1,0))
A[4,3,:,:,:] = self.convol(G[0], (0,1,0)) + self.convol(G[0]*G[1], (0,2,0))
A[4,4,:,:,:] = self.convol(G[0]*G[0], (0,2,0))
A[5,0,:,:,:] = self.convol(G[0]*G[1], (1,0,0))
A[5,1,:,:,:] = self.convol(G[1]*G[1], (1,0,0))
A[5,2,:,:,:] = self.convol(G[1], (1,0,0)) + self.convol(G[0]*G[1], (2,0,0))
A[5,3,:,:,:] = self.convol(G[1], (1,0,0)) + self.convol(G[1]*G[1], (1,1,0))
A[5,4,:,:,:] = self.convol(G[0]*G[1], (1,1,0))
A[5,5,:,:,:] = self.convol(G[1]*G[1], (2,0,0))
b[0,:,:,:] = self.convol(G[0]*G[2])
b[1,:,:,:] = self.convol(G[1]*G[2])
b[2,:,:,:] = self.convol(G[2]) + self.convol(G[0]*G[2], (1,0,0))
b[3,:,:,:] = self.convol(G[2]) + self.convol(G[1]*G[2], (0,1,0))
b[4,:,:,:] = self.convol(G[0]*G[2], (0,1,0))
b[5,:,:,:] = self.convol(G[1]*G[2], (1,0,0))
for i in range(1,6):
for j in range(0,i):
A[j,i,:,:,:] = A[i,j,:,:,:]
self.cle = Solver(np.array(A, dtype = np.float32),np.array(b, dtype = np.float32), self.method, self.threshold).run()
return self
class DAVE():
def __init__(self, X, sigma = (3,3,3), method = "lusol", threshold = 1.):
self.sigma = sigma
self.X = X.astype(np.float32)
self.dim = self.X.shape
self.method = method
self.threshold = threshold
h = np.floor(sigma).astype(np.int32)
self.x = [np.arange(-4*h[i],4*h[i]+1, dtype = np.float32) for i in range(0,3)]
self.exp = [np.exp(-self.x[i]**2./2/sigma[i]**2.)/sigma[i] for i in range(0,3)]
def convol(self, X, mul = (0,0,0)):
out = np.array(X).astype(np.float32)
for i in range(0,3):
if (mul[i] == 0):
correlate1d(out, self.exp[i], axis=i, output = out)
if (mul[i] == 1):
correlate1d(out, self.exp[i]*self.x[i], axis=i, output = out)
if (mul[i] == 2):
correlate1d(out, self.exp[i]*self.x[i]**2, axis=i, output = out)
return out
def run(self):
G = np.gradient(self.X)
A = np.zeros((6,6)+self.dim, dtype = np.float32)
b = np.zeros((6,)+self.dim, dtype = np.float32)
A[0,0,:,:,:] = self.convol(G[0]*G[0])
A[1,0,:,:,:] = self.convol(G[0]*G[1])
A[1,1,:,:,:] = self.convol(G[1]*G[1])
A[2,0,:,:,:] = self.convol(G[0]) + self.convol(G[0]*G[0], (1,0,0))
A[2,1,:,:,:] = self.convol(G[1]) + self.convol(G[0]*G[1], (1,0,0))
A[2,2,:,:,:] = self.convol(self.X) + 2*self.convol(G[0], (1,0,0)) + self.convol(G[0]*G[0], (2,0,0))
A[3,0,:,:,:] = self.convol(G[0]) + self.convol(G[0]*G[1], (0,1,0))
A[3,1,:,:,:] = self.convol(G[1]) + self.convol(G[1]*G[1], (0,1,0))
A[3,2,:,:,:] = (self.convol(self.X) + self.convol(G[0], (1,0,0))
+ self.convol(G[1], (0,1,0)) + self.convol(G[0]*G[1], (1,1,0)))
A[3,3,:,:,:] = self.convol(self.X) + 2*self.convol(G[1], (0,1,0)) + self.convol(G[1]*G[1], (0,2,0))
A[4,0,:,:,:] = self.convol(G[0]*G[0], (0,1,0))
A[4,1,:,:,:] = self.convol(G[0]*G[1], (0,1,0))
A[4,2,:,:,:] = self.convol(G[0], (0,1,0)) + self.convol(G[0]*G[0], (1,1,0))
A[4,3,:,:,:] = self.convol(G[0], (0,1,0)) + self.convol(G[0]*G[1], (0,2,0))
A[4,4,:,:,:] = self.convol(G[0]*G[0], (0,2,0))
A[5,0,:,:,:] = self.convol(G[0]*G[1], (1,0,0))
A[5,1,:,:,:] = self.convol(G[1]*G[1], (1,0,0))
A[5,2,:,:,:] = self.convol(G[1], (1,0,0)) + self.convol(G[0]*G[1], (2,0,0))
A[5,3,:,:,:] = self.convol(G[1], (1,0,0)) + self.convol(G[1]*G[1], (1,1,0))
A[5,4,:,:,:] = self.convol(G[0]*G[1], (1,1,0))
A[5,5,:,:,:] = self.convol(G[1]*G[1], (2,0,0))
b[0,:,:,:] = self.convol(G[0]*G[2])
b[1,:,:,:] = self.convol(G[1]*G[2])
b[2,:,:,:] = self.convol(G[2]) + self.convol(G[0]*G[2], (1,0,0))
b[3,:,:,:] = self.convol(G[2]) + self.convol(G[1]*G[2], (0,1,0))
b[4,:,:,:] = self.convol(G[0]*G[2], (0,1,0))
b[5,:,:,:] = self.convol(G[1]*G[2], (1,0,0))
for i in range(1,6):
for j in range(0,i):
A[j,i,:,:,:] = A[i,j,:,:,:]
self.cle = Solver(np.array(A, dtype = np.float32),np.array(b, dtype = np.float32), self.method, self.threshold).run()
return self
def get(self):
return self.cle.get()