def __runOptimization(self, problem, deltaJ, deltaX, maxIt):
"""Run the given optimization problem problem"""
print("run new optimisation with initial values:")
self.__printResults()
# verbose and choldmod solving with schur complement trick
options = aopt.Optimizer2Options()
options.verbose = True
options.nThreads = max(1, multiprocessing.cpu_count() - 1)
options.doSchurComplement = True
options.linearSolver = aopt.BlockCholeskyLinearSystemSolver(
) #does not have multi-threading support
# stopping criteria
options.maxIterations = maxIt
options.convergenceDeltaJ = deltaJ
options.convergenceDeltaX = deltaX
# use the dogleg trustregion policy
options.trustRegionPolicy = aopt.DogLegTrustRegionPolicy()
# create the optimizer
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(problem)
# go for it:
return optimizer.optimize()
def optimize(self, options=None, maxIterations=30, recoverCov=False):
if options is None:
options = aopt.Optimizer2Options()
options.verbose = True
options.doLevenbergMarquardt = True
options.levenbergMarquardtLambdaInit = 100.0
options.nThreads = max(1,multiprocessing.cpu_count()-1)
options.convergenceDeltaX = 1e-4
options.convergenceDeltaJ = 1
options.maxIterations = maxIterations
options.trustRegionPolicy = aopt.LevenbergMarquardtTrustRegionPolicy(options.levenbergMarquardtLambdaInit)
#run the optimization
self.optimizer = aopt.Optimizer2(options)
self.optimizer.setProblem(self.problem)
optimizationFailed=False
try:
retval = self.optimizer.optimize()
if retval.linearSolverFailure:
optimizationFailed = True
except:
optimizationFailed = True
if optimizationFailed:
sm.logError("Optimization failed!")
raise RuntimeError("Optimization failed!")
#free some memory
del self.optimizer
gc.collect()
if recoverCov:
self.recoverCovariance()
def optimize(problem, options=None, maxIterations=30):
if options is None:
options = aopt.Optimizer2Options()
options.verbose = True
options.doLevenbergMarquardt = True
options.levenbergMarquardtLambdaInit = 10.0
options.nThreads = max(1, multiprocessing.cpu_count() - 1)
options.convergenceDeltaX = 1e-5
options.convergenceJDescentRatioThreshold = 1e-6
options.maxIterations = maxIterations
options.trustRegionPolicy = aopt.LevenbergMarquardtTrustRegionPolicy(
options.levenbergMarquardtLambdaInit)
options.linearSolver = aopt.BlockCholeskyLinearSystemSolver()
# run the optimization
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(problem)
optimizationFailed = False
try:
retval = optimizer.optimize()
if retval.linearSolverFailure:
optimizationFailed = True
except:
optimizationFailed = True
if optimizationFailed:
sm.logError("Optimization failed!")
raise RuntimeError("Optimization failed!")
# free some memory
del optimizer
gc.collect()
def maximization_step(self, t_source, target, estep_res, w=0.0,
objective_type='pt2pt'):
m, ndim = t_source.shape
n = target.shape[0]
assert ndim == 3, "ndim must be 3."
m0, m1, nx = estep_res
c = w / (1.0 - w) * n / m
m0[m0==0] = np.finfo(np.float32).eps
m1m0 = np.divide(m1.T, m0).T
m0m0 = m0 / (m0 + c)
drxdx = m0m0
errs = []
self.problem.clearAllErrorTerms()
if objective_type == 'pt2pt':
for i in xrange(m):
T_l_l = self.T_b_l_Dv.toExpression().inverse() * \
aopt.TransformationExpression(self._sensor_tfs[i]) * \
self.T_b_l_Dv.toExpression()
predicted = T_l_l.toRotationExpression() * t_source[i] + T_l_l.toEuclideanExpression()
err = ket.EuclideanError(m1m0[i], drxdx[i]*np.eye(3, dtype=np.float64), predicted)
errs.append(err)
self.problem.addErrorTerm(err)
else:
raise ValueError('Unknown objective_type: %s.' % objective_type)
# define the optimization
options = aopt.Optimizer2Options()
options.verbose = False
options.linearSolver = aopt.BlockCholeskyLinearSystemSolver()
options.nThreads = 2
options.convergenceDeltaX = 1e-4
options.convergenceJDescentRatioThreshold = 1e-6
options.maxIterations = 50
# run the optimization
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(self.problem)
# get the prior
try:
optimizer.optimize()
except:
sm.logFatal("Failed to obtain orientation prior!")
sys.exit(-1)
q = np.array([np.linalg.norm(e.error()) for e in errs]).sum()
return MstepResult(self.T_b_l_Dv.toExpression().toTransformationMatrix(), q)
def findOrientationPriorCameraToImu(self, imu):
print
print "Estimating imu-camera rotation prior"
# build the problem
problem = aopt.OptimizationProblem()
# Add the rotation as design variable
q_i_c_Dv = aopt.RotationQuaternionDv(self.T_extrinsic.q())
q_i_c_Dv.setActive(True)
problem.addDesignVariable(q_i_c_Dv)
# Add the gyro bias as design variable
gyroBiasDv = aopt.EuclideanPointDv(np.zeros(3))
gyroBiasDv.setActive(True)
problem.addDesignVariable(gyroBiasDv)
#initialize a pose spline using the camera poses
poseSpline = self.initPoseSplineFromCamera(timeOffsetPadding=0.0)
for im in imu.imuData:
tk = im.stamp.toSec()
if tk > poseSpline.t_min() and tk < poseSpline.t_max():
#DV expressions
R_i_c = q_i_c_Dv.toExpression()
bias = gyroBiasDv.toExpression()
#get the vision predicted omega and measured omega (IMU)
omega_predicted = R_i_c * aopt.EuclideanExpression(
np.matrix(
poseSpline.angularVelocityBodyFrame(tk)).transpose())
omega_measured = im.omega
#error term
gerr = ket.GyroscopeError(omega_measured, im.omegaInvR,
omega_predicted, bias)
problem.addErrorTerm(gerr)
#define the optimization
options = aopt.Optimizer2Options()
options.verbose = False
options.linearSolver = aopt.BlockCholeskyLinearSystemSolver()
options.nThreads = 2
options.convergenceDeltaX = 1e-4
options.convergenceDeltaJ = 1
options.maxIterations = 50
#run the optimization
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(problem)
#get the prior
try:
optimizer.optimize()
except:
sm.logFatal("Failed to obtain orientation prior!")
sys.exit(-1)
#overwrite the external rotation prior (keep the external translation prior)
R_i_c = q_i_c_Dv.toRotationMatrix().transpose()
self.T_extrinsic = sm.Transformation(
sm.rt2Transform(R_i_c, self.T_extrinsic.t()))
#set the gyro bias prior (if we have more than 1 cameras use recursive average)
b_gyro = bias.toEuclidean()
imu.GyroBiasPriorCount += 1
imu.GyroBiasPrior = (
imu.GyroBiasPriorCount - 1.0
) / imu.GyroBiasPriorCount * imu.GyroBiasPrior + 1.0 / imu.GyroBiasPriorCount * b_gyro
#print result
print " Orientation prior camera-imu found as: (T_i_c)"
print R_i_c
print " Gyro bias prior found as: (b_gyro)"
print b_gyro
def solveFullBatch(cameras, baseline_guesses, graph):
############################################
## solve the bundle adjustment
############################################
problem = aopt.OptimizationProblem()
#add camera dvs
for cam in cameras:
cam.setDvActiveStatus(True, True, False)
problem.addDesignVariable(cam.dv.distortionDesignVariable())
problem.addDesignVariable(cam.dv.projectionDesignVariable())
problem.addDesignVariable(cam.dv.shutterDesignVariable())
baseline_dvs = list()
for baseline_idx in range(0, len(cameras) - 1):
baseline_dv = aopt.TransformationDv(baseline_guesses[baseline_idx])
for i in range(0, baseline_dv.numDesignVariables()):
problem.addDesignVariable(baseline_dv.getDesignVariable(i))
baseline_dvs.append(baseline_dv)
#corner uncertainty
cornerUncertainty = 1.0
R = np.eye(2) * cornerUncertainty * cornerUncertainty
invR = np.linalg.inv(R)
#get the target
target = cameras[0].ctarget.detector.target()
#Add calibration target reprojection error terms for all camera in chain
target_pose_dvs = list()
#shuffle the views
reprojectionErrors = []
timestamps = graph.obs_db.getAllViewTimestamps()
for view_id, timestamp in enumerate(timestamps):
#get all observations for all cams at this time
obs_tuple = graph.obs_db.getAllObsAtTimestamp(timestamp)
#create a target pose dv for all target views (= T_cam0_w)
T0 = graph.getTargetPoseGuess(timestamp, cameras, baseline_guesses)
target_pose_dv = addPoseDesignVariable(problem, T0)
target_pose_dvs.append(target_pose_dv)
for cidx, obs in obs_tuple:
cam = cameras[cidx]
#calibration target coords to camera X coords
T_cam0_calib = target_pose_dv.toExpression().inverse()
#build pose chain (target->cam0->baselines->camN)
T_camN_calib = T_cam0_calib
for idx in range(0, cidx):
T_camN_calib = baseline_dvs[idx].toExpression() * T_camN_calib
## add error terms
for i in range(0, target.size()):
p_target = aopt.HomogeneousExpression(
sm.toHomogeneous(target.point(i)))
valid, y = obs.imagePoint(i)
if valid:
rerr = cameras[cidx].model.reprojectionError(
y, invR, T_camN_calib * p_target, cameras[cidx].dv)
problem.addErrorTerm(rerr)
reprojectionErrors.append(rerr)
sm.logDebug("solveFullBatch: added {0} camera error terms".format(
len(reprojectionErrors)))
############################################
## solve
############################################
options = aopt.Optimizer2Options()
options.verbose = True if sm.getLoggingLevel(
) == sm.LoggingLevel.Debug else False
options.nThreads = 4
options.convergenceDeltaX = 1e-3
options.convergenceDeltaJ = 1
options.maxIterations = 250
options.trustRegionPolicy = aopt.LevenbergMarquardtTrustRegionPolicy(10)
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(problem)
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
sm.logDebug("Before optimization:")
e2 = np.array([e.evaluateError() for e in reprojectionErrors])
sm.logDebug(
" Reprojection error squarred (camL): mean {0}, median {1}, std: {2}"
.format(np.mean(e2), np.median(e2), np.std(e2)))
#run intrinsic calibration
try:
retval = optimizer.optimize()
if retval.linearSolverFailure:
sm.logError("calibrateIntrinsics: Optimization failed!")
success = not retval.linearSolverFailure
except:
sm.logError("calibrateIntrinsics: Optimization failed!")
success = False
baselines = list()
for baseline_dv in baseline_dvs:
baselines.append(sm.Transformation(baseline_dv.T()))
return success, baselines
def calibrateIntrinsics(cam_geometry,
obslist,
distortionActive=True,
intrinsicsActive=True):
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
d = cam_geometry.geometry.projection().distortion().getParameters(
).flatten()
p = cam_geometry.geometry.projection().getParameters().flatten()
sm.logDebug("calibrateIntrinsics: intrinsics guess: {0}".format(p))
sm.logDebug("calibrateIntrinsics: distortion guess: {0}".format(d))
############################################
## solve the bundle adjustment
############################################
problem = aopt.OptimizationProblem()
#add camera dvs
cam_geometry.setDvActiveStatus(intrinsicsActive, distortionActive, False)
problem.addDesignVariable(cam_geometry.dv.distortionDesignVariable())
problem.addDesignVariable(cam_geometry.dv.projectionDesignVariable())
problem.addDesignVariable(cam_geometry.dv.shutterDesignVariable())
#corner uncertainty
cornerUncertainty = 1.0
R = np.eye(2) * cornerUncertainty * cornerUncertainty
invR = np.linalg.inv(R)
#get the image and target points corresponding to the frame
target = cam_geometry.ctarget.detector.target()
#target pose dv for all target views (=T_camL_w)
reprojectionErrors = []
sm.logDebug(
"calibrateIntrinsics: adding camera error terms for {0} calibration targets"
.format(len(obslist)))
target_pose_dvs = list()
for obs in obslist:
success, T_t_c = cam_geometry.geometry.estimateTransformation(obs)
target_pose_dv = addPoseDesignVariable(problem, T_t_c)
target_pose_dvs.append(target_pose_dv)
T_cam_w = target_pose_dv.toExpression().inverse()
## add error terms
for i in range(0, target.size()):
p_target = aopt.HomogeneousExpression(
sm.toHomogeneous(target.point(i)))
valid, y = obs.imagePoint(i)
if valid:
rerr = cam_geometry.model.reprojectionError(
y, invR, T_cam_w * p_target, cam_geometry.dv)
problem.addErrorTerm(rerr)
reprojectionErrors.append(rerr)
sm.logDebug("calibrateIntrinsics: added {0} camera error terms".format(
len(reprojectionErrors)))
############################################
## solve
############################################
options = aopt.Optimizer2Options()
options.verbose = True if sm.getLoggingLevel(
) == sm.LoggingLevel.Debug else False
options.nThreads = 4
options.convergenceDeltaX = 1e-3
options.convergenceDeltaJ = 1
options.maxIterations = 200
options.trustRegionPolicy = aopt.LevenbergMarquardtTrustRegionPolicy(10)
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(problem)
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
sm.logDebug("Before optimization:")
e2 = np.array([e.evaluateError() for e in reprojectionErrors])
sm.logDebug(
" Reprojection error squarred (camL): mean {0}, median {1}, std: {2}"
.format(np.mean(e2), np.median(e2), np.std(e2)))
#run intrinsic calibration
try:
retval = optimizer.optimize()
if retval.linearSolverFailure:
sm.logError("calibrateIntrinsics: Optimization failed!")
success = not retval.linearSolverFailure
except:
sm.logError("calibrateIntrinsics: Optimization failed!")
success = False
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
d = cam_geometry.geometry.projection().distortion().getParameters(
).flatten()
p = cam_geometry.geometry.projection().getParameters().flatten()
sm.logDebug(
"calibrateIntrinsics: guess for intrinsics cam: {0}".format(p))
sm.logDebug(
"calibrateIntrinsics: guess for distortion cam: {0}".format(d))
return success
def stereoCalibrate(camL_geometry,
camH_geometry,
obslist,
distortionActive=False,
baseline=None):
#####################################################
## find initial guess as median of all pnp solutions
#####################################################
if baseline is None:
r = []
t = []
for obsL, obsH in obslist:
#if we have observations for both camss
if obsL is not None and obsH is not None:
success, T_L = camL_geometry.geometry.estimateTransformation(
obsL)
success, T_H = camH_geometry.geometry.estimateTransformation(
obsH)
baseline = T_H.inverse() * T_L
t.append(baseline.t())
rv = sm.RotationVector()
r.append(rv.rotationMatrixToParameters(baseline.C()))
r_median = np.median(np.asmatrix(r), axis=0).flatten().T
R_median = rv.parametersToRotationMatrix(r_median)
t_median = np.median(np.asmatrix(t), axis=0).flatten().T
baseline_HL = sm.Transformation(sm.rt2Transform(R_median, t_median))
else:
baseline_HL = baseline
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
dL = camL_geometry.geometry.projection().distortion().getParameters(
).flatten()
pL = camL_geometry.geometry.projection().getParameters().flatten()
dH = camH_geometry.geometry.projection().distortion().getParameters(
).flatten()
pH = camH_geometry.geometry.projection().getParameters().flatten()
sm.logDebug("initial guess for stereo calib: {0}".format(
baseline_HL.T()))
sm.logDebug("initial guess for intrinsics camL: {0}".format(pL))
sm.logDebug("initial guess for intrinsics camH: {0}".format(pH))
sm.logDebug("initial guess for distortion camL: {0}".format(dL))
sm.logDebug("initial guess for distortion camH: {0}".format(dH))
############################################
## solve the bundle adjustment
############################################
problem = aopt.OptimizationProblem()
#baseline design variable
baseline_dv = addPoseDesignVariable(problem, baseline_HL)
#target pose dv for all target views (=T_camL_w)
target_pose_dvs = list()
for obsL, obsH in obslist:
if obsL is not None: #use camL if we have an obs for this one
success, T_t_cL = camL_geometry.geometry.estimateTransformation(
obsL)
else:
success, T_t_cH = camH_geometry.geometry.estimateTransformation(
obsH)
T_t_cL = T_t_cH * baseline_HL #apply baseline for the second camera
target_pose_dv = addPoseDesignVariable(problem, T_t_cL)
target_pose_dvs.append(target_pose_dv)
#add camera dvs
camL_geometry.setDvActiveStatus(True, distortionActive, False)
camH_geometry.setDvActiveStatus(True, distortionActive, False)
problem.addDesignVariable(camL_geometry.dv.distortionDesignVariable())
problem.addDesignVariable(camL_geometry.dv.projectionDesignVariable())
problem.addDesignVariable(camL_geometry.dv.shutterDesignVariable())
problem.addDesignVariable(camH_geometry.dv.distortionDesignVariable())
problem.addDesignVariable(camH_geometry.dv.projectionDesignVariable())
problem.addDesignVariable(camH_geometry.dv.shutterDesignVariable())
############################################
## add error terms
############################################
#corner uncertainty
# \todo pass in the detector uncertainty somehow.
cornerUncertainty = 1.0
R = np.eye(2) * cornerUncertainty * cornerUncertainty
invR = np.linalg.inv(R)
#Add reprojection error terms for both cameras
reprojectionErrors0 = []
reprojectionErrors1 = []
for cidx, cam in enumerate([camL_geometry, camH_geometry]):
sm.logDebug(
"stereoCalibration: adding camera error terms for {0} calibration targets"
.format(len(obslist)))
#get the image and target points corresponding to the frame
target = cam.ctarget.detector.target()
#add error terms for all observations
for view_id, obstuple in enumerate(obslist):
#add error terms if we have an observation for this cam
obs = obstuple[cidx]
if obs is not None:
T_cam_w = target_pose_dvs[view_id].toExpression().inverse()
#add the baseline for the second camera
if cidx != 0:
T_cam_w = baseline_dv.toExpression() * T_cam_w
for i in range(0, target.size()):
p_target = aopt.HomogeneousExpression(
sm.toHomogeneous(target.point(i)))
valid, y = obs.imagePoint(i)
if valid:
# Create an error term.
rerr = cam.model.reprojectionError(
y, invR, T_cam_w * p_target, cam.dv)
rerr.idx = i
problem.addErrorTerm(rerr)
if cidx == 0:
reprojectionErrors0.append(rerr)
else:
reprojectionErrors1.append(rerr)
sm.logDebug("stereoCalibrate: added {0} camera error terms".format(
len(reprojectionErrors0) + len(reprojectionErrors1)))
############################################
## solve
############################################
options = aopt.Optimizer2Options()
options.verbose = True if sm.getLoggingLevel(
) == sm.LoggingLevel.Debug else False
options.nThreads = 4
options.convergenceDeltaX = 1e-3
options.convergenceDeltaJ = 1
options.maxIterations = 200
options.trustRegionPolicy = aopt.LevenbergMarquardtTrustRegionPolicy(10)
optimizer = aopt.Optimizer2(options)
optimizer.setProblem(problem)
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
sm.logDebug("Before optimization:")
e2 = np.array([e.evaluateError() for e in reprojectionErrors0])
sm.logDebug(
" Reprojection error squarred (camL): mean {0}, median {1}, std: {2}"
.format(np.mean(e2), np.median(e2), np.std(e2)))
e2 = np.array([e.evaluateError() for e in reprojectionErrors1])
sm.logDebug(
" Reprojection error squarred (camH): mean {0}, median {1}, std: {2}"
.format(np.mean(e2), np.median(e2), np.std(e2)))
sm.logDebug("baseline={0}".format(
baseline_dv.toTransformationMatrix()))
try:
retval = optimizer.optimize()
if retval.linearSolverFailure:
sm.logError("stereoCalibrate: Optimization failed!")
success = not retval.linearSolverFailure
except:
sm.logError("stereoCalibrate: Optimization failed!")
success = False
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
sm.logDebug("After optimization:")
e2 = np.array([e.evaluateError() for e in reprojectionErrors0])
sm.logDebug(
" Reprojection error squarred (camL): mean {0}, median {1}, std: {2}"
.format(np.mean(e2), np.median(e2), np.std(e2)))
e2 = np.array([e.evaluateError() for e in reprojectionErrors1])
sm.logDebug(
" Reprojection error squarred (camH): mean {0}, median {1}, std: {2}"
.format(np.mean(e2), np.median(e2), np.std(e2)))
#verbose output
if sm.getLoggingLevel() == sm.LoggingLevel.Debug:
dL = camL_geometry.geometry.projection().distortion().getParameters(
).flatten()
pL = camL_geometry.geometry.projection().getParameters().flatten()
dH = camH_geometry.geometry.projection().distortion().getParameters(
).flatten()
pH = camH_geometry.geometry.projection().getParameters().flatten()
sm.logDebug("guess for intrinsics camL: {0}".format(pL))
sm.logDebug("guess for intrinsics camH: {0}".format(pH))
sm.logDebug("guess for distortion camL: {0}".format(dL))
sm.logDebug("guess for distortion camH: {0}".format(dH))
if success:
baseline_HL = sm.Transformation(baseline_dv.toTransformationMatrix())
return success, baseline_HL
else:
#return the initial guess if we fail
return success, baseline_HL
