Beispiel #1
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    def test_simple_sampling_problem(self):
        '''Sample from a twodimensional Gaussian distribution N(0, I)
        '''

        options = ab.SamplerMetropolisHastingsOptions()
        options.transitionKernelSigma = 0.1
        sampler = ab.SamplerMetropolisHastings(options)
        negLogDensity = ab.OptimizationProblem()

        # Add a scalar design variables.
        point = ab.Point2d(np.array([0, 0]))
        point.setBlockIndex(0)
        point.setActive(True)
        negLogDensity.addDesignVariable(point)

        # Add the error term.
        grad = np.array([-1., -1.])
        err = ab.TestNonSquaredError(point, grad)
        err._p = 0.0
        # set mean
        negLogDensity.addScalarNonSquaredErrorTerm(err)

        # Now let's sample.
        sampler.setNegativeLogDensity(negLogDensity)
        sampler.checkNegativeLogDensitySetup()
        sampler.run(10000)
Beispiel #2
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    def test_construction(self):
        splineOrder = 4;
        spline = createUniformKnotOldBSpline(splineOrder, 6, 3)
        sdv = aslam_splines.EuclideanBSplineDesignVariable(spline)

        tMin = spline.t_min();
        tMax = spline.t_max();
        sqrtW = numpy.matrix(numpy.random.random((3, 3)))
        W = sqrtW.T * sqrtW;
        for derivativeOrder in range(0, splineOrder - 1):
            p = aslam_backend.OptimizationProblem()
            for i in range(0, sdv.numDesignVariables()) : p.addDesignVariable(sdv.designVariable(i))
            aslam_splines.addQuadraticIntegralEuclideanExpressionErrorTermsToProblem(p, tMin, tMax, 100, lambda time : sdv.toEuclideanExpression(time, derivativeOrder), sqrtW)
            E = 0;
            for i in range(0, p.numErrorTerms()):
                E += p.errorTerm(i).evaluateError()
    
            evalQF = lambda t: (numpy.matrix(spline.evalD(t, derivativeOrder)) * W * numpy.matrix(spline.evalD(t, derivativeOrder)).T)[0, 0];
            Epy = integrate.quad(evalQF, tMin, tMax)[0]
            
            self.assertAlmostEqual(E, Epy, 3); 
Beispiel #3
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    def registration(self, target, w=0.0,
                     objective_type='pt2pt',
                     maxiter=50, tol=0.001,
                     feature_fn=lambda x: x):
        q = None
        ftarget = feature_fn(target)

        # build the problem
        self.problem = aopt.OptimizationProblem()
        T_init = np.array([[-0.99813747, -0.05730897, -0.02091093, 0.03399231],
                           [0.05726434, -0.99835533, 0.00272772, 0.31433327],
                           [-0.02103286, 0.00152519, 0.99977762, 0.22997991],
                           [0., 0., 0., 1.]])
        self.T_b_l_Dv = aopt.TransformationDv(sm.Transformation(), rotationActive=True, translationActive=True)
        for i in range(0, self.T_b_l_Dv.numDesignVariables()):
            self.problem.addDesignVariable(self.T_b_l_Dv.getDesignVariable(i))

        for _ in range(maxiter):
            T_b_l = self.T_b_l_Dv.toExpression().toTransformationMatrix()
            print("Inital laser to body transformation: T_b_l ")
            print(T_b_l)
            T_l_b = np.linalg.inv(T_b_l)

            numPoints = self._source.shape[0]
            source = np.hstack([self._source, np.ones((numPoints, 1), dtype=self._source.dtype)])
            t_source = np.array([np.dot(T_l_b, np.dot(self._sensor_tfs[i], np.dot(T_b_l, source[i]))) for i in xrange(numPoints)])
            t_source = t_source[:, :3]
            util.showPointCloud([t_source, target])
            fsource = feature_fn(t_source)
            estep_res = self.expectation_step(fsource, ftarget, target, objective_type)

            res = self.maximization_step(self._source, target, estep_res, w=w,
                                         objective_type=objective_type)

            if not q is None and abs(res.q - q) < tol:
                break
            q = res.q
        return res.transformation
Beispiel #4
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    def test_simple_optimization(self):
        options = ab.OptimizerOptionsRprop()
        options.maxIterations = 500
        options.numThreads = 1
        options.convergenceGradientNorm = 1e-6
        options.method = ab.RpropMethod.RPROP_PLUS
        optimizer = ab.OptimizerRprop(options)
        problem = ab.OptimizationProblem()

        D = 2
        E = 3

        # Add some design variables.
        p2ds = []
        for d in range(0, D):
            point = ab.Point2d(np.array([d, d]))
            p2ds.append(point)
            problem.addDesignVariable(point)
            point.setBlockIndex(d)
            point.setActive(True)

        # Add some error terms.
        errors = []
        for e in range(0, E):
            for d in range(0, D):
                grad = np.array([d + 1, e + 1])
                err = ab.TestNonSquaredError(p2ds[d], grad)
                err._p = 1.0
                errors.append(err)
                problem.addScalarNonSquaredErrorTerm(err)

        # Now let's optimize.
        optimizer.setProblem(problem)
        optimizer.checkProblemSetup()
        optimizer.optimize()

        self.assertLessEqual(optimizer.status.gradientNorm, 1e-3)
Beispiel #5
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# Create random odometry
true_u_k = np.random.random(K);
u_k = true_u_k + sigma_u * np.random.randn(K)      

# Integrate the odometry
x_k = np.cumsum(u_k)
true_x_k = np.cumsum(true_u_k)

# Create the noisy measurments
y_k = np.zeros(K)
for k in range(0,K):
    y_k[k] = 1.0 / (true_w - true_x_k[k]) + sigma_n * np.random.randn()


# Now we can build an optimization problem.
problem = aslam.OptimizationProblem()

#  Create a design variable for the wall position
dv_w = abt.ScalarDesignVariable(true_w + np.random.randn())
# Setting this active means we estimate it.
dv_w.setActive(True)
# Add it to the optimization problem.
problem.addDesignVariable(dv_w)

# Now we add the initial state.
dv_x_km1 = abt.ScalarDesignVariable(x_k[0])
# Setting this active means we estimate it.
dv_x_km1.setActive(True)
# Add it to the optimization problem.
problem.addDesignVariable(dv_x_km1)
Beispiel #6
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    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
Beispiel #7
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import fcl_python as fcl
import sm

# Setup
plotCircles = False

sm.setLoggingLevel(sm.LoggingLevel.Debug)
scene = putil.populateScene(2, 7.0)

fig = pl.figure()
ax = fig.add_subplot(111)
ax.grid('on')
putil.plotScene(scene, ax, plotCircles=plotCircles)

# Aslam optimizer optimization problem
problem = opt.OptimizationProblem()

for id, optAgent in scene.optAgents.iteritems():
    optAgent.trajectory.addDesignVariables(problem)
    print "Added {0} design varibales of agent {1}".format(len(optAgent.trajectory.getDesignVariables()), id)

featureContainer = planner.FeatureContainer()
featureContainer.push_back('singleton_integrated_acceleration', planner.OptAgentType.PEDESTRIAN, 1.0)
featureContainer.push_back('singleton_integrated_velocity', planner.OptAgentType.PEDESTRIAN, 1.0)
featureContainer.push_back('singleton_integrated_rotation_rate', planner.OptAgentType.PEDESTRIAN, 1.0)
featureContainer.push_back('pairwise_integrated_distance', planner.OptAgentType.PEDESTRIAN, 0.0)

featureContainer.addErrorTerms(scene, problem)

# Optimization options
options = opt.OptimizerRpropOptions()
Beispiel #8
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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
Beispiel #9
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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
Beispiel #10
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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
sm.seed(int(time.time()*1000000)) # required to add randomness to the sampling procedure

s = pputil.populateScene(2, spline_coeff_noise = 0.000)
scene = Sampling.ContinuousSceneWrapper(s)

usedFeatures = {
                'singleton_integrated_acceleration': (True, pp.OptAgentType.PEDESTRIAN, 2.0),
#                 'singleton_integrated_velocity': (True, pp.OptAgentType.PEDESTRIAN, 1.0),
                'singleton_integrated_rotation_rate': (True, pp.OptAgentType.PEDESTRIAN, 1.0),
                'pairwise_integrated_distance': (True, pp.OptAgentType.PEDESTRIAN, 10.0),
                }
features = pp.FeatureContainerModifiable()
for fname,info in usedFeatures.iteritems():
  features.push_back(fname, info[1], info[2])
  
negLogDensity = opt.OptimizationProblem()

for id,oa in scene.base.optAgents.iteritems():
  oa.trajectory.addDesignVariables(negLogDensity)

for f in features.getContainer():
  f.addErrorTerms(scene.base, negLogDensity)
  
# Bring the system to it's maximum likelihood state as an alternative to burn in
# nRpropIterations = 1000
# options = opt.OptimizerRpropOptions()
# options.convergenceGradientNorm
# options.verbose=False
# options.initialDelta=0.5
# options.maxIterations=1
# options.nThreads=2