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resection_cvx1.py
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resection_cvx1.py
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# Author: Jeffrey T. Walton, Paul Smith's College, New York
#
# Single-photo resection - calculates the camera orientation and location
# given camera calibration parameters, control point photo and world
# coordinates and initial guesses for camera exterior orientation.
#
# based on MATLAB code from:
# Introduction to Modern Photogrammetry by Mikhail, Bethel, McGlone
# John Wiley & Sons, Inc. 2001
import sys
import numpy as np
#from scipy.optimize import leastsq
from cvxopt import matrix, log, div, spdiag, solvers
def collinearity_eqn_residual(iop,eop,x,y,X,Y,Z):
"""
Usage:
collinearity_eqn_residual(iop,eop,x,y,X,Y,Z)
Inputs:
iop = dict of interior orientation parameters: x0, y0, f
eop = dict of exterior orientation parameters: omega, phi, kappa, XL, YL, ZL
x = array of x photo coordinates of control points
y = array of y photo coordinates of control points
X = array of X world coordinates of control points
Y = array of Y world coordinates of control points
Z = array of Z world coordinates of control points
Returns:
residuals in x and y collinearity equations for a single point as a tuple
"""
from math import sin, cos
x0 = iop['x0']
y0 = iop['y0']
focallength = iop['f']
om = eop['omega']
ph = eop['phi']
kp = eop['kappa']
XL = eop['XL']
YL = eop['YL']
ZL = eop['ZL']
Mom = np.matrix([[1, 0, 0], [0, cos(om), sin(om)], [0, -sin(om), cos(om)]])
Mph = np.matrix([[cos(ph), 0, -sin(ph)], [0, 1, 0], [sin(ph), 0, cos(ph)]])
Mkp = np.matrix([[cos(kp), sin(kp), 0], [-sin(kp), cos(kp), 0], [0, 0, 1]])
M = Mkp * Mph * Mom
uvw = M * np.matrix([[X-XL], [Y-YL], [Z-ZL]])
resx = x - x0 + focallength * uvw[0,0] / uvw[2,0]
resy = y - y0 + focallength * uvw[1,0] / uvw[2,0]
return resx, resy
def collinearity_eqn_residual_Jacobian(iop,eop,x,y,X,Y,Z):
"""
Usage:
collinearity_eqn_residual_Jacobian(iop,eop,x,y,X,Y,Z)
Inputs:
iop = dict of interior orientation parameters: x0, y0, f
eop = dict of exterior orientation parameters: omega, phi, kappa, XL, YL, ZL
x = array of x photo coordinates of control points
y = array of y photo coordinates of control points
X = array of X world coordinates of control points
Y = array of Y world coordinates of control points
Z = array of Z world coordinates of control points
Returns:
the Jacobian of the collinearity equations
a (2, 6) matrix of partial derivatives of x and y wrt om, ph, kp
"""
from math import sin, cos
#x0 = iop['x0']
#y0 = iop['y0']
focallength = iop['f']
om = eop['omega']
ph = eop['phi']
kp = eop['kappa']
XL = eop['XL']
YL = eop['YL']
ZL = eop['ZL']
# Appendix C, Mikhail et al.
Mom = np.matrix([[1, 0, 0], [0, cos(om), sin(om)], [0, -sin(om), cos(om)]])
Mph = np.matrix([[cos(ph), 0, -sin(ph)], [0, 1, 0], [sin(ph), 0, cos(ph)]])
Mkp = np.matrix([[cos(kp), sin(kp), 0], [-sin(kp), cos(kp), 0], [0, 0, 1]])
M = Mkp * Mph * Mom
UVW = M * np.matrix([[X-XL], [Y-YL], [Z-ZL]])
U = UVW[0,0]
V = UVW[1,0]
W = UVW[2,0]
jacobian = np.zeros((2,6))
dUVW_dom = M * np.matrix([[0.0], [Z-ZL], [YL-Y]])
dUVW_dph = np.matrix([[0, 0, -cos(kp)], [0, 0, sin(kp)], [cos(kp), -sin(kp), 0]]) * UVW
dUVW_dkp = np.matrix([[V], [-U], [0.0]])
dUVW_dXL = M * np.matrix([[-1.0], [0.0], [0.0]])
dUVW_dYL = M * np.matrix([[ 0.0], [-1.0], [0.0]])
dUVW_dZL = M * np.matrix([[ 0.0], [ 0.0], [-1.0]])
f_W = focallength / W
jacobian[0,0] = f_W *(dUVW_dom[0,0]-U/W*dUVW_dom[2,0])
jacobian[0,1] = f_W *(dUVW_dph[0,0]-U/W*dUVW_dph[2,0])
jacobian[0,2] = f_W *(dUVW_dkp[0,0]-U/W*dUVW_dkp[2,0])
jacobian[0,3] = f_W *(dUVW_dXL[0,0]-U/W*dUVW_dXL[2,0])
jacobian[0,4] = f_W *(dUVW_dYL[0,0]-U/W*dUVW_dYL[2,0])
jacobian[0,5] = f_W *(dUVW_dZL[0,0]-U/W*dUVW_dZL[2,0])
jacobian[1,0] = f_W *(dUVW_dom[1,0]-V/W*dUVW_dom[2,0])
jacobian[1,1] = f_W *(dUVW_dph[1,0]-V/W*dUVW_dph[2,0])
jacobian[1,2] = f_W *(dUVW_dkp[1,0]-V/W*dUVW_dkp[2,0])
jacobian[1,3] = f_W *(dUVW_dXL[1,0]-V/W*dUVW_dXL[2,0])
jacobian[1,4] = f_W *(dUVW_dYL[1,0]-V/W*dUVW_dYL[2,0])
jacobian[1,5] = f_W *(dUVW_dZL[1,0]-V/W*dUVW_dZL[2,0])
return jacobian
class CollinearityData:
"""
class to store data for the collinearity equations
"""
def __init__(self, camera_file, point_file):
"""
initilizes data for collinearity equations
reads camera parameters from camera_file
reads control point data from point_file
"""
f = open(camera_file,'r')
dat = np.loadtxt(f,float)
f.close
self.eop = {}
# data from lines 1-3 of the camera_file
self.eop['omega'] = dat[0]
self.eop['phi'] = dat[1]
self.eop['kappa'] = dat[2]
# data from lines 4-6 of the camera_file
self.eop['XL'] = dat[3]
self.eop['YL'] = dat[4]
self.eop['ZL'] = dat[5]
self.iop = {}
# data from lines 7-9 of the camera_file
self.iop['x0'] = dat[6]
self.iop['y0'] = dat[7]
self.iop['f'] = dat[8]
self.label = []
x = []
y = []
X = []
Y = []
Z = []
f = open(point_file,'r')
for line in f:
l = line.split()
# each line has 6 values: label, x, y, X, Y, Z (whitespace delimited)
self.label.append(l[0])
x.append(float(l[1]))
y.append(float(l[2]))
X.append(float(l[3]))
Y.append(float(l[4]))
Z.append(float(l[5]))
f.close
self.x = np.array(x)
self.y = np.array(y)
self.X = np.array(X)
self.Y = np.array(Y)
self.Z = np.array(Z)
def coll_func(indep_vars):
"""
collinearity function calculates a sum of the squared residuals of the
collinearity equations for all of the control points
This function is passed to scipy.optimize.minimize()
Inputs:
indep_vars (passed) are the exterior orientation parameters of the camera
data (global) camera interior calibration data, photo points, control points
Returns:
sum of squared residuals of collinearity eqns
"""
global data
iop = data.iop
#eop = data.eop
label = data.label
x = data.x
y = data.y
X = data.X
Y = data.Y
Z = data.Z
eop = {}
eop['omega'] = indep_vars[0]
eop['phi'] = indep_vars[1]
eop['kappa'] = indep_vars[2]
eop['XL'] = indep_vars[3]
eop['YL'] = indep_vars[4]
eop['ZL'] = indep_vars[5]
i = 0
F = np.zeros(2*len(label))
for l in label:
F[2*i], F[2*i+1] = collinearity_eqn_residual(iop,eop,x[i],y[i],X[i],Y[i],Z[i])
i += 1
return F
def coll_Dfunc(indep_vars):
"""
The Jacobian of the collinearity function calculates rate of change of the
residuals of the collinearity equations wrt the indep_vars (eop)
This function is passed to scipy.optimize.minimize()
Inputs:
indep_vars (passed) are the exterior orientation parameters of the camera
data (global) camera interior calibration data, photo points, control points
Returns:
Jacobian (first derivative) matrix
"""
global data
iop = data.iop
#eop = data.eop
label = data.label
x = data.x
y = data.y
X = data.X
Y = data.Y
Z = data.Z
eop = {}
eop['omega'] = indep_vars[0]
eop['phi'] = indep_vars[1]
eop['kappa'] = indep_vars[2]
eop['XL'] = indep_vars[3]
eop['YL'] = indep_vars[4]
eop['ZL'] = indep_vars[5]
i = 0
dF = np.zeros((2*len(label), len(indep_vars)))
for l in label:
dF[2*i:2*i+2,0:] = collinearity_eqn_residual_Jacobian(iop,eop,x[i],y[i],X[i],Y[i],Z[i])
i += 1
return dF
def F(x = None, z = None):
if x is None: return 0, matrix(0.0, (6,1))
if max(abs(x)) >= 1.0: return None
u = 1 - x**2
val = -sum(log(u))
Df = div(2*x, u).T
if z is None: return val, Df
H = spdiag(2 * z[0] * div(1 + u**2, u**2))
return val, Df, H
if len(sys.argv) > 1:
camera_file = sys.argv[1]
else:
camera_file = 'cam.inp'
if len(sys.argv) > 2:
point_file = sys.argv[2]
else:
point_file = 'resect.inp'
data = CollinearityData(camera_file, point_file)
x0 = np.zeros(6)
# initilaize guesses for eop as read from file
eop = data.eop
x0[0] = eop['omega']
x0[1] = eop['phi']
x0[2] = eop['kappa']
x0[3] = eop['XL']
x0[4] = eop['YL']
x0[5] = eop['ZL']
#x, cov_x, info, msg, ier = leastsq(coll_func, x0, full_output=True)
#x, cov_x, info, msg, ier = leastsq(coll_func, x0, Dfun=coll_Dfunc, full_output=True)
print 'Solution:'
print 'omega, ', x[0]
print 'phi, ', x[1]
print 'kappa, ', x[2]
print 'XL, ', x[3]
print 'YL, ', x[4]
print 'ZL, ', x[5]
print 'number of function evaluations: ', info['nfev']
print 'sum squared residuals: ', np.sum(info['fvec']**2)