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)
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);
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
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)
# 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)
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
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()
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
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