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levenberg_marquardt.py
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levenberg_marquardt.py
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import numpy as np
from numpy.ma.core import cos, sin
import utilities as util
def derivatives_with_penalty(p_1, p_2, theta_1, theta_2, lambd):
x_1, y_1 = p_1.copy()
x_2, y_2 = p_2.copy()
alpha_1, sx_1, sy_1, skx_1, sky_1, x0_1, y0_1 = theta_1.copy()
alpha_2, sx_2, sy_2, skx_2, sky_2, x0_2, y0_2 = theta_2.copy()
ksi_1 = sx_1 * x_1 + sky_1 * y_1
eps_1 = skx_1 * x_1 + sy_1 * y_1
ksi_2 = sx_2 * x_2 + sky_2 * y_2
eps_2 = skx_2 * x_2 + sy_2 * y_2
XX = ksi_1 * cos(alpha_1) - eps_1 * sin(alpha_1) - x0_1 - ksi_2 * cos(alpha_2) + eps_2 * sin(alpha_2) + x0_2
YY = ksi_1 * sin(alpha_1) + eps_1 * cos(alpha_1) - y0_1 - ksi_2 * sin(alpha_2) - eps_2 * cos(alpha_2) + y0_2
#Resulting derivatives for 1 parameters
deriv_1 = np.zeros(theta_1.size).reshape(theta_1.shape)
#Resulting derivatives for 2 parameters
deriv_2 = np.zeros(theta_2.size).reshape(theta_2.shape)
#alpha
deriv_1[0] = XX * (-ksi_1 * sin(alpha_1) - eps_1 * cos(alpha_1)) + \
YY * (ksi_1 * cos(alpha_1) - eps_1 * sin(alpha_1))
#sx
deriv_1[1] = XX * (x_1 * cos(alpha_1)) + YY * (x_1 * sin(alpha_1))
#sy
deriv_1[2] = XX * (-y_1 * sin(alpha_1)) + YY * (y_1 * cos(alpha_1))
#skx
deriv_1[3] = XX * (-x_1 * sin(alpha_1)) + YY * (x_1 * cos(alpha_1))
#sky
deriv_1[4] = XX * (y_1 * cos(alpha_1)) + YY * (y_1 * sin(alpha_1))
#x0
deriv_1[5] = XX * (-1)
#y0
deriv_1[6] = YY * (-1)
#alpha
deriv_2[0] = XX * (ksi_2 * sin(alpha_2) + eps_2 * cos(alpha_2)) + YY * (-ksi_2 * cos(alpha_2) + eps_2 * sin(alpha_2))
#sx
deriv_2[1] = XX * (-x_2 * cos(alpha_2)) + YY * (-x_2 * sin(alpha_2))
#sy
deriv_2[2] = XX * (y_2 * sin(alpha_2)) + YY * (-y_2 * cos(alpha_2))
#skx
deriv_2[3] = XX * (x_2 * sin(alpha_2)) + YY * (-x_2 * cos(alpha_2))
#sky
deriv_2[4] = XX * (-y_2 * cos(alpha_2)) + YY * (-y_2 * sin(alpha_2))
#x0
deriv_2[5] = XX
#y0
deriv_2[6] = YY
#Penalize
deriv_1[0] = deriv_1[0] + lambd * theta_1[0]
deriv_2[0] = deriv_2[0] + lambd * theta_2[0]
deriv_1[3:5] = deriv_1[3:5] + lambd * theta_1[3:5]
deriv_2[3:5] = deriv_2[3:5] + lambd * theta_2[3:5]
#dummy_1 = lambd * np.abs(np.array([1., 1]) - theta_1[1:3])
#dummy_2 = lambd * np.abs(np.array([1., 1]) - theta_2[1:3])
#deriv_1[1:3] = deriv_1[1:3] + dummy_1#lambd * np.abs([1., 1] - der_1[1:3]) #sx, sy = 1
#deriv_2[1:3] = deriv_2[1:3] + dummy_2#lambd * np.abs([1., 1] - der_2[1:3]) #sx, sy = 1
#deriv_1[1:3] = np.array([0, 0])
#deriv_2[1:3] = np.array([0, 0])
return np.concatenate((deriv_1, deriv_2))
def getJacobian(points_1, points_2, params, penalty):
#Number of points
m = points_1.shape[0]
Jacobian = np.zeros([m, params.size])
#print "params 1 ", params[0:params.size/2]
for i in range(m):
Jacobian[i] = derivatives_with_penalty(points_1[i],
points_2[i],
params[0:params.size/2],
params[params.size/2:],
penalty / m)
return Jacobian
def getGradient(Jacobian, points_1, points_2, theta_1, theta_2, penalty):
n = theta_1.size + theta_2.size
m = points_1.shape[0]
#print "test ", points_1[3]
values = np.zeros((m, 1))
#print values
for i in range(m):
#print "Evaluate gradient, stage ", i
#print points_1[i], points_2[i]
values[i] = util.costFunctionOnePair(points_1[i], points_2[i], theta_1, theta_2, penalty / m)
return np.dot(np.transpose(Jacobian), values)
def levenberg_marquardt(points_1, points_2, theta_1, theta_2,
lambd, penalty, threshold, img1, img2):
#Number of points
m = points_1.shape[0]
#Vector of parameters
x = np.concatenate((theta_1, theta_2))
len_x = x.size
#Init
x_old = x + threshold * 2
delta_x = np.zeros(x.shape)
print "Initial X", x
#Needful Matrices
#Jacobian = np.zeros([m, x.size])
I = np.identity(len_x, np.float32)
iteration = -1
print "start"
print np.sum(np.abs(x_old - x) / len_x)
flag = True
#for i in range(5):
print"x_old", x_old
print "x", x
print "(np.sum(np.abs(x_old - x))", np.sum(np.abs(x_old - x))
#for i in range(200):
while ( (np.sum(np.abs(x_old - x) / 12) or (flag) ) > threshold):
iteration += 1
print "Iteration # ", iteration
print "Lambda", lambd
print "Cost function= ", util.costFunction(points_1,
points_2,
x[0:x.size/2],
x[x.size/2:],
penalty)
#For every point
Jacobian = getJacobian(points_1, points_2, x, penalty)
#print "Jacobian shape", Jacobian
Hessian = np.matrix(np.dot(np.transpose(Jacobian), Jacobian))
#print 'Hessian shape', Hessian.shape
#print "H det = ", np.linalg.det(Hessian)
#print "Sum of derivatives for 1st parameter = ", np.sum(Jacobian[:][0])
gradient = getGradient(Jacobian, points_1, points_2, x[0:x.size/2], x[x.size/2:], penalty)
#print "Jacobian", Jacobian
#tmp = np.matrix(Hessian + lambd * I)
#print "TMP", tmp
#delta_x = np.dot(tmp.I, -gradient)
delta_x = np.linalg.lstsq(Hessian + lambd * I * Hessian, -gradient)
#print "x", x
#print"delta_x", delta_x[0]
x_old = x.copy()
#print "delta_x", delta_x[0].ravel()
#Delta x
d_x = delta_x[0].ravel()
#x = x + d_x
x[0] = x[0] + d_x[0]
x[3:7] = x[3:7] + d_x[3:7]
x[7] = x[7] + d_x[7]
x[10:14] = x[10:14] + d_x[10:14]
# if (i % 300 == 0):
# c_y, c_x = (np.asarray(img1.shape[:2]) / 2.).tolist()
# size = (img1.shape[1] * 2, img1.shape[0] * 2)
# res = mos.stitch_for_visualization(img1, img2, x[0:x.size/2], x[x.size/2:14], c_x, c_y, size)
# matrix_1 = util.composeAffineMatrix(x[0:x.size/2])
# matrix_2 = util.composeAffineMatrix(x[x.size/2:14])
# mos.draw_distance_lines(res, points_1, points_2, x[0:x.size/2], x[x.size/2:14], c_x, c_y)
# winname = ""
# cv2.imshow(winname, res)
# 0xFF & cv2.waitKey()
# cv2.destroyAllWindows()
e = 0.2
if (np.abs(x[3]) > e or np.abs(x[4]) > e or np.abs(x[10]) > e or np.abs(x[11]) > e ):
x[3:5] = x_old[3:5]
x[10:12] = x_old[10:12]
#print "Current x= ", x
if (util.costFunction(points_1, points_2, x[0:7], x[7:14], penalty) >
util.costFunction(points_1, points_2, x_old[0:7], x_old[7:14], penalty)):
lambd *= 2
flag = True
x = x_old
else:
lambd /= 2
flag = False
#print"x_old", x_old
#print "x", x
#print "(np.sum(np.abs(x_old - x))", np.sum(np.abs(x_old - x))
return x