def add_vertex_pose(self, id, pose, fixed=False): v_se3 = g2o.VertexSE3Expmap() v_se3.set_id(id) v_se3.set_estimate(pose) v_se3.set_fixed(fixed) super().add_vertex(v_se3) return v_se3
def bundle_adjustment(ps_1, ps_2, r_mat, t_vec): optimizer = g2o.SparseOptimizer() solver = g2o.BlockSolverSim3(g2o.LinearSolverCSparseSim3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) optimizer.set_algorithm(solver) pose = g2o.VertexSE3Expmap() pose.set_estimate(g2o.SE3Quat(np.identity(3), np.zeros((3,)))) pose.set_id(0) optimizer.add_vertex(pose) index = 1 for p1, p2 in zip(ps_1, ps_2): edge = g2o.EdgeStereoSE3ProjectXYZOnlyPose() edge.cam_project(p2) edge.set_id(index) edge.set_vertex(0, pose) edge.set_measurement(p1) edge.set_information(np.identity(3)) optimizer.add_edge(edge) index += 1 optimizer.initialize_optimization() optimizer.set_verbose(True) optimizer.optimize(100) print('T = \n', pose.estimate().matrix())
def add_pose(self, pose_id, pose, fixed=False): v_se3 = g2o.VertexSE3Expmap() v_se3.set_id(pose_id) v_se3.set_fixed(fixed) ## ## v_se3.set_estimate(pose.inverse()) super().add_vertex(v_se3) return v_se3
def add_pose(self, pose_id, pose, fixed=False): if isinstance(pose, sp.sophuspy.SE3): pose = g2o.SE3Quat(pose.rotationMatrix(), pose.translation()) elif isinstance(pose, np.ndarray): pose = g2o.SE3Quat(pose[:3, :3], pose[:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_id(pose_id * 2) # camera poses use even number v_se3.set_estimate(pose) v_se3.set_fixed(fixed) super().add_vertex(v_se3)
def add_frames(self, frames, local_frames): # add frames to graph for f in (local_frames if self.fix_points else frames): pose = f.pose se3 = g2o.SE3Quat(pose[0:3, 0:3], pose[0:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(f.id * 2) v_se3.set_fixed(f.id <= 1 or f not in local_frames) #v_se3.set_fixed(f.id != 0) self.opt.add_vertex(v_se3) # confirm pose correctness est = v_se3.estimate() assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) assert np.allclose(pose[0:3, 3], est.translation()) self.graph_frames[f] = v_se3
def bundle_adjustment(points_3d, points_2d, r_mat, t_vec): optimizer = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) optimizer.set_algorithm(solver) pose = g2o.VertexSE3Expmap() pose.set_estimate(g2o.SE3Quat(r_mat, t_vec.reshape((3, )))) pose.set_id(0) optimizer.add_vertex(pose) index = 1 for p_3d in points_3d: point = g2o.VertexSBAPointXYZ() point.set_id(index) point.set_estimate(p_3d) point.set_marginalized(True) optimizer.add_vertex(point) index += 1 camera = g2o.CameraParameters(K[0, 0], np.array([K[0, 2], K[1, 2]]), 0) camera.set_id(0) optimizer.add_parameter(camera) index = 1 for p_2d in points_2d: edge = g2o.EdgeProjectXYZ2UV() edge.set_id(index) edge.set_vertex(0, optimizer.vertex(index)) edge.set_vertex(1, pose) edge.set_measurement(p_2d) edge.set_parameter_id(0, 0) edge.set_information(np.identity(2)) optimizer.add_edge(edge) index += 1 optimizer.initialize_optimization() optimizer.set_verbose(True) optimizer.optimize(100) print('T = \n', pose.estimate().matrix())
def main(): optimizer = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) optimizer.set_algorithm(solver) true_points = np.hstack([ np.random.random((500, 1)) * 3 - 1.5, np.random.random((500, 1)) - 0.5, np.random.random((500, 1)) + 3 ]) focal_length = [500, 500] principal_point = [320, 240] baseline = 0.075 camera = g2o.CameraParameters(500, [320, 240], 0.075) camera.set_id(10000) optimizer.add_parameter(camera) true_poses = [] num_pose = 5 for i in range(num_pose): # pose here transform points from world coordinates to camera coordinates pose = g2o.SE3Quat(np.identity(3), [i * 0.04 - 1, 0, 0]) true_poses.append(pose) v_se3 = g2o.VertexSE3Expmap() v_se3.set_id(i) v_se3.set_estimate(pose) if i < 2: v_se3.set_fixed(True) optimizer.add_vertex(v_se3) point_id = num_pose inliers = dict() sse = defaultdict(float) for i, point in enumerate(true_points): visible = [] for j, pose in enumerate(true_poses): z = camera.cam_map(pose * point) if 0 <= z[0] < 640 and 0 <= z[1] < 480: visible.append((j, z)) if len(visible) < 2: continue vp = g2o.VertexSBAPointXYZ() vp.set_id(point_id) vp.set_marginalized(True) vp.set_estimate(point + np.random.randn(3)) optimizer.add_vertex(vp) inlier = True for j, z in visible: if np.random.random() < args.outlier_ratio: inlier = False z = np.array([ np.random.uniform(64, 640), np.random.uniform(0, 480), np.random.uniform(0, 64) ]) # disparity z[2] = z[0] - z[2] z += np.random.randn(2) * args.pixel_noise edge = g2o.Edge_XYZ_VSC() edge.set_vertex(0, vp) edge.set_vertex(1, optimizer.vertex(j)) edge.set_measurement(z) edge.set_information(np.identity(2)) if args.robust_kernel: edge.set_robust_kernel(g2o.RobustKernelHuber()) edge.set_parameter_id(0, 0) optimizer.add_edge(edge) if inlier: inliers[point_id] = i error = vp.estimate() - true_points[i] sse[0] += np.sum(error**2) point_id += 1 print('Performing full BA:') optimizer.initialize_optimization() optimizer.set_verbose(True) optimizer.optimize(10) for i in inliers: vp = optimizer.vertex(i) error = vp.estimate() - true_points[inliers[i]] sse[1] += np.sum(error**2) print('\nCamera focal: \n{}\n'.format(camera.focal_length)) print('\nCamera principal point: \n{}\n'.format(camera.principal_point)) print('\nRMSE (inliers only):') print('before optimization:', np.sqrt(sse[0] / len(inliers))) print('after optimization:', np.sqrt(sse[1] / len(inliers)))
def add_pose(self, pose_id, pose, fixed=False): vertex_se3 = g2o.VertexSE3Expmap() vertex_se3.set_id(pose_id) vertex_se3.set_estimate(pose) vertex_se3.set_fixed(fixed) self._optimizer.add_vertex(vertex_se3)
def bundle_adjustment(keyframes, points, local_window, fixed_points=False, verbose=False, rounds=10, use_robust_kernel=False, abort_flag=g2o.Flag()): if local_window is None: local_frames = keyframes else: local_frames = keyframes[-local_window:] # create g2o optimizer opt = g2o.SparseOptimizer() block_solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) #block_solver = g2o.BlockSolverSE3(g2o.LinearSolverCholmodSE3()) solver = g2o.OptimizationAlgorithmLevenberg(block_solver) opt.set_algorithm(solver) opt.set_force_stop_flag(abort_flag) thHuberMono = math.sqrt(5.991); # chi-square 2 DOFS graph_keyframes, graph_points = {}, {} # add frame vertices to graph for kf in (local_frames if fixed_points else keyframes): # if points are fixed then consider just the local frames, otherwise we need all frames or at least two frames for each point if kf.is_bad: continue #print('adding vertex frame ', f.id, ' to graph') se3 = g2o.SE3Quat(kf.Rcw, kf.tcw) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(kf.kid * 2) # even ids (use f.kid here!) v_se3.set_fixed(kf.kid==0 or kf not in local_frames) #(use f.kid here!) opt.add_vertex(v_se3) # confirm pose correctness #est = v_se3.estimate() #assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) #assert np.allclose(pose[0:3, 3], est.translation()) graph_keyframes[kf] = v_se3 num_edges = 0 # add point vertices to graph for p in points: assert(p is not None) if p.is_bad: # do not consider bad points continue if __debug__: if not any([f in keyframes for f in p.keyframes()]): Printer.red('point without a viewing frame!!') continue #print('adding vertex point ', p.id,' to graph') v_p = g2o.VertexSBAPointXYZ() v_p.set_id(p.id * 2 + 1) # odd ids v_p.set_estimate(p.pt[0:3]) v_p.set_marginalized(True) v_p.set_fixed(fixed_points) opt.add_vertex(v_p) graph_points[p] = v_p # add edges for kf, idx in p.observations(): if kf.is_bad: continue if kf not in graph_keyframes: continue #print('adding edge between point ', p.id,' and frame ', f.id) edge = g2o.EdgeSE3ProjectXYZ() edge.set_vertex(0, v_p) edge.set_vertex(1, graph_keyframes[kf]) edge.set_measurement(kf.kpsu[idx]) invSigma2 = Frame.feature_manager.inv_level_sigmas2[kf.octaves[idx]] edge.set_information(np.eye(2)*invSigma2) if use_robust_kernel: edge.set_robust_kernel(g2o.RobustKernelHuber(thHuberMono)) edge.fx = kf.camera.fx edge.fy = kf.camera.fy edge.cx = kf.camera.cx edge.cy = kf.camera.cy opt.add_edge(edge) num_edges += 1 if verbose: opt.set_verbose(True) opt.initialize_optimization() opt.optimize(rounds) # put frames back for kf in graph_keyframes: est = graph_keyframes[kf].estimate() #R = est.rotation().matrix() #t = est.translation() #f.update_pose(poseRt(R, t)) kf.update_pose(g2o.Isometry3d(est.orientation(), est.position())) # put points back if not fixed_points: for p in graph_points: p.update_position(np.array(graph_points[p].estimate())) p.update_normal_and_depth(force=True) mean_squared_error = opt.active_chi2()/max(num_edges,1) return mean_squared_error
def local_bundle_adjustment(keyframes, points, keyframes_ref=[], fixed_points=False, verbose=False, rounds=10, abort_flag=g2o.Flag(), map_lock=None): # create g2o optimizer opt = g2o.SparseOptimizer() block_solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) #block_solver = g2o.BlockSolverSE3(g2o.LinearSolverEigenSE3()) #block_solver = g2o.BlockSolverSE3(g2o.LinearSolverCholmodSE3()) solver = g2o.OptimizationAlgorithmLevenberg(block_solver) opt.set_algorithm(solver) opt.set_force_stop_flag(abort_flag) #robust_kernel = g2o.RobustKernelHuber(np.sqrt(5.991)) # chi-square 2 DOFs thHuberMono = math.sqrt(5.991); # chi-square 2 DOFS graph_keyframes, graph_points = {}, {} # add frame vertices to graph for kf in keyframes: if kf.is_bad: continue #print('adding vertex frame ', f.id, ' to graph') se3 = g2o.SE3Quat(kf.Rcw, kf.tcw) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(kf.kid * 2) # even ids (use f.kid here!) v_se3.set_fixed(kf.kid==0) # (use f.kid here!) opt.add_vertex(v_se3) graph_keyframes[kf] = v_se3 # confirm pose correctness #est = v_se3.estimate() #assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) #assert np.allclose(pose[0:3, 3], est.translation()) # add reference frame vertices to graph for kf in keyframes_ref: if kf.is_bad: continue #print('adding vertex frame ', f.id, ' to graph') se3 = g2o.SE3Quat(kf.Rcw, kf.tcw) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(kf.kid * 2) # even ids (use f.kid here!) v_se3.set_fixed(True) opt.add_vertex(v_se3) graph_keyframes[kf] = v_se3 graph_edges = {} num_edges = 0 num_bad_edges = 0 # add point vertices to graph for p in points: assert(p is not None) if p.is_bad: # do not consider bad points continue if not any([f in keyframes for f in p.keyframes()]): Printer.orange('point %d without a viewing keyframe in input keyframes!!' %(p.id)) #Printer.orange(' keyframes: ',p.observations_string()) continue #print('adding vertex point ', p.id,' to graph') v_p = g2o.VertexSBAPointXYZ() v_p.set_id(p.id * 2 + 1) # odd ids v_p.set_estimate(p.pt[0:3]) v_p.set_marginalized(True) v_p.set_fixed(fixed_points) opt.add_vertex(v_p) graph_points[p] = v_p # add edges for kf, p_idx in p.observations(): if kf.is_bad: continue if kf not in graph_keyframes: continue if __debug__: p_f = kf.get_point_match(p_idx) if p_f != p: print('frame: ', kf.id, ' missing point ', p.id, ' at index p_idx: ', p_idx) if p_f is not None: print('p_f:', p_f) print('p:',p) assert(kf.get_point_match(p_idx) is p) #print('adding edge between point ', p.id,' and frame ', f.id) edge = g2o.EdgeSE3ProjectXYZ() edge.set_vertex(0, v_p) edge.set_vertex(1, graph_keyframes[kf]) edge.set_measurement(kf.kpsu[p_idx]) invSigma2 = Frame.feature_manager.inv_level_sigmas2[kf.octaves[p_idx]] edge.set_information(np.eye(2)*invSigma2) edge.set_robust_kernel(g2o.RobustKernelHuber(thHuberMono)) edge.fx = kf.camera.fx edge.fy = kf.camera.fy edge.cx = kf.camera.cx edge.cy = kf.camera.cy opt.add_edge(edge) graph_edges[edge] = (p,kf,p_idx) # one has kf.points[p_idx] == p num_edges += 1 if verbose: opt.set_verbose(True) if abort_flag.value: return -1,0 # initial optimization opt.initialize_optimization() opt.optimize(5) if not abort_flag.value: chi2Mono = 5.991 # chi-square 2 DOFs # check inliers observation for edge, edge_data in graph_edges.items(): p = edge_data[0] if p.is_bad: continue if edge.chi2() > chi2Mono or not edge.is_depth_positive(): edge.set_level(1) num_bad_edges += 1 edge.set_robust_kernel(None) # optimize again without outliers opt.initialize_optimization() opt.optimize(rounds) # search for final outlier observations and clean map num_bad_observations = 0 # final bad observations outliers_data = [] for edge, edge_data in graph_edges.items(): p, kf, p_idx = edge_data if p.is_bad: continue assert(kf.get_point_match(p_idx) is p) if edge.chi2() > chi2Mono or not edge.is_depth_positive(): num_bad_observations += 1 outliers_data.append(edge_data) if map_lock is None: map_lock = RLock() # put a fake lock with map_lock: # remove outlier observations for d in outliers_data: p, kf, p_idx = d p_f = kf.get_point_match(p_idx) if p_f is not None: assert(p_f is p) p.remove_observation(kf,p_idx) # the following instruction is now included in p.remove_observation() #f.remove_point(p) # it removes multiple point instances (if these are present) #f.remove_point_match(p_idx) # this does not remove multiple point instances, but now there cannot be multiple instances any more # put frames back for kf in graph_keyframes: est = graph_keyframes[kf].estimate() #R = est.rotation().matrix() #t = est.translation() #f.update_pose(poseRt(R, t)) kf.update_pose(g2o.Isometry3d(est.orientation(), est.position())) # put points back if not fixed_points: for p in graph_points: p.update_position(np.array(graph_points[p].estimate())) p.update_normal_and_depth(force=True) active_edges = num_edges-num_bad_edges mean_squared_error = opt.active_chi2()/active_edges return mean_squared_error, num_bad_observations/max(num_edges,1)
def pose_optimization(frame, verbose=False, rounds=10): is_ok = True # create g2o optimizer opt = g2o.SparseOptimizer() #block_solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) #block_solver = g2o.BlockSolverSE3(g2o.LinearSolverDenseSE3()) block_solver = g2o.BlockSolverSE3(g2o.LinearSolverEigenSE3()) solver = g2o.OptimizationAlgorithmLevenberg(block_solver) opt.set_algorithm(solver) #robust_kernel = g2o.RobustKernelHuber(np.sqrt(5.991)) # chi-square 2 DOFs thHuberMono = math.sqrt(5.991); # chi-square 2 DOFS point_edge_pairs = {} num_point_edges = 0 v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(g2o.SE3Quat(frame.Rcw, frame.tcw)) v_se3.set_id(0) v_se3.set_fixed(False) opt.add_vertex(v_se3) with MapPoint.global_lock: # add point vertices to graph for idx, p in enumerate(frame.points): if p is None: continue # reset outlier flag frame.outliers[idx] = False # add edge #print('adding edge between point ', p.id,' and frame ', frame.id) edge = g2o.EdgeSE3ProjectXYZOnlyPose() edge.set_vertex(0, opt.vertex(0)) edge.set_measurement(frame.kpsu[idx]) invSigma2 = Frame.feature_manager.inv_level_sigmas2[frame.octaves[idx]] edge.set_information(np.eye(2)*invSigma2) edge.set_robust_kernel(g2o.RobustKernelHuber(thHuberMono)) edge.fx = frame.camera.fx edge.fy = frame.camera.fy edge.cx = frame.camera.cx edge.cy = frame.camera.cy edge.Xw = p.pt[0:3] opt.add_edge(edge) point_edge_pairs[p] = (edge, idx) # one edge per point num_point_edges += 1 if num_point_edges < 3: Printer.red('pose_optimization: not enough correspondences!') is_ok = False return 0, is_ok, 0 if verbose: opt.set_verbose(True) # perform 4 optimizations: # after each optimization we classify observation as inlier/outlier; # at the next optimization, outliers are not included, but at the end they can be classified as inliers again chi2Mono = 5.991 # chi-square 2 DOFs num_bad_point_edges = 0 for it in range(4): v_se3.set_estimate(g2o.SE3Quat(frame.Rcw, frame.tcw)) opt.initialize_optimization() opt.optimize(rounds) num_bad_point_edges = 0 for p, edge_pair in point_edge_pairs.items(): edge, idx = edge_pair if frame.outliers[idx]: edge.compute_error() chi2 = edge.chi2() if chi2 > chi2Mono: frame.outliers[idx] = True edge.set_level(1) num_bad_point_edges +=1 else: frame.outliers[idx] = False edge.set_level(0) if it == 2: edge.set_robust_kernel(None) if len(opt.edges()) < 10: Printer.red('pose_optimization: stopped - not enough edges!') is_ok = False break print('pose optimization: available ', num_point_edges, ' points, found ', num_bad_point_edges, ' bad points') if num_point_edges == num_bad_point_edges: Printer.red('pose_optimization: all the available correspondences are bad!') is_ok = False # update pose estimation if is_ok: est = v_se3.estimate() # R = est.rotation().matrix() # t = est.translation() # frame.update_pose(poseRt(R, t)) frame.update_pose(g2o.Isometry3d(est.orientation(), est.position())) # since we have only one frame here, each edge corresponds to a single distinct point num_valid_points = num_point_edges - num_bad_point_edges mean_squared_error = opt.active_chi2()/max(num_valid_points,1) return mean_squared_error, is_ok, num_valid_points
def poseOptimization(frame, verbose=False, rounds=10): is_ok = True # create g2o optimizer opt = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) opt.set_algorithm(solver) #robust_kernel = g2o.RobustKernelHuber(np.sqrt(5.991)) # chi-square 2 DOFs thHuberMono = math.sqrt(5.991) # chi-square 2 DOFS point_edge_pairs = {} num_point_edges = 0 se3 = g2o.SE3Quat(frame.pose[0:3, 0:3], frame.pose[0:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(0) v_se3.set_fixed(False) opt.add_vertex(v_se3) # add point vertices to graph for idx, p in enumerate(frame.points): if p is None: # do not use p.is_bad here since a single point observation is ok for pose optimization continue frame.outliers[idx] = False # add edge #print('adding edge between point ', p.id,' and frame ', frame.id) edge = g2o.EdgeSE3ProjectXYZOnlyPose() edge.set_vertex(0, opt.vertex(0)) edge.set_measurement(frame.kpsu[idx]) invSigma2 = Frame.detector.inv_level_sigmas2[frame.octaves[idx]] edge.set_information(np.eye(2) * invSigma2) edge.set_robust_kernel(g2o.RobustKernelHuber(thHuberMono)) edge.fx = frame.fx edge.fy = frame.fy edge.cx = frame.cx edge.cy = frame.cy edge.Xw = p.pt[0:3] opt.add_edge(edge) point_edge_pairs[p] = (edge, idx) # one edge per point num_point_edges += 1 if num_point_edges < 3: Printer.red('poseOptimization: not enough correspondences!') is_ok = False return 0, is_ok, 0 if verbose: opt.set_verbose(True) # We perform 4 optimizations, after each optimization we classify observation as inlier/outlier # At the next optimization, outliers are not included, but at the end they can be classified as inliers again. chi2Mono = 5.991 # chi-square 2 DOFs num_bad_points = 0 for it in range(4): opt.initialize_optimization() opt.optimize(rounds) num_bad_points = 0 for p, edge_pair in point_edge_pairs.items(): if frame.outliers[edge_pair[1]] is True: edge_pair[0].compute_error() chi2 = edge_pair[0].chi2() if chi2 > chi2Mono: frame.outliers[edge_pair[1]] = True edge_pair[0].set_level(1) num_bad_points += 1 else: frame.outliers[edge_pair[1]] = False edge_pair[0].set_level(0) if it == 2: edge_pair[0].set_robust_kernel(None) if len(opt.edges()) < 10: Printer.red('poseOptimization: stopped - not enough edges!') is_ok = False break print('pose optimization: initial ', num_point_edges, ' points, found ', num_bad_points, ' bad points') if num_point_edges == num_bad_points: Printer.red( 'poseOptimization: all the initial correspondences are bad!') is_ok = False # update pose estimation if is_ok is True: est = v_se3.estimate() R = est.rotation().matrix() t = est.translation() frame.pose = poseRt(R, t) num_valid_points = num_point_edges - num_bad_points return opt.active_chi2(), is_ok, num_valid_points
def main(): optimizer = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCholmodSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) optimizer.set_algorithm(solver) focal_length = 1000 principal_point = (320, 240) cam = g2o.CameraParameters(focal_length, principal_point, 0) cam.set_id(0) optimizer.add_parameter(cam) true_points = np.hstack([ np.random.random((500, 1)) * 3 - 1.5, np.random.random((500, 1)) - 0.5, np.random.random((500, 1)) + 3 ]) true_poses = [] num_pose = 15 for i in range(num_pose): # pose here means transform points from world coordinates to camera coordinates pose = g2o.SE3Quat(np.identity(3), [i * 0.04 - 1, 0, 0]) true_poses.append(pose) v_se3 = g2o.VertexSE3Expmap() v_se3.set_id(i) v_se3.set_estimate(pose) if i < 2: v_se3.set_fixed(True) optimizer.add_vertex(v_se3) point_id = num_pose inliers = dict() sse = defaultdict(float) for i, point in enumerate(true_points): visible = [] for j, pose in enumerate(true_poses): z = cam.cam_map(pose * point) if 0 <= z[0] < 640 and 0 <= z[1] < 480: visible.append((j, z)) if len(visible) < 2: continue vp = g2o.VertexSBAPointXYZ() vp.set_id(point_id) vp.set_marginalized(True) vp.set_estimate(point + np.random.randn(3)) optimizer.add_vertex(vp) inlier = True for j, z in visible: if np.random.random() < args.outlier_ratio: inlier = False z = np.random.random(2) * [640, 480] z += np.random.randn(2) * args.pixel_noise edge = g2o.EdgeProjectXYZ2UV() edge.set_vertex(0, vp) edge.set_vertex(1, optimizer.vertex(j)) edge.set_measurement(z) edge.set_information(np.identity(2)) if args.robust_kernel: edge.set_robust_kernel(g2o.RobustKernelHuber()) edge.set_parameter_id(0, 0) optimizer.add_edge(edge) if inlier: inliers[point_id] = i error = vp.estimate() - true_points[i] sse[0] += np.sum(error**2) point_id += 1 print('num vertices:', len(optimizer.vertices())) print('num edges:', len(optimizer.edges())) print('Performing full BA:') optimizer.initialize_optimization() optimizer.set_verbose(True) optimizer.optimize(10) for i in inliers: print(i) vp = optimizer.vertex(i) error = vp.estimate() - true_points[inliers[i]] sse[1] += np.sum(error**2) print('\nRMSE (inliers only):') print('before optimization:', np.sqrt(sse[0] / len(inliers))) print('after optimization:', np.sqrt(sse[1] / len(inliers)))
def graph_to_optimizer(self): """Convert a :class: graph to a :class: g2o.SparseOptimizer. Only the edges and vertices fields need to be filled out. Returns: A :class: g2o.SparseOptimizer that can be optimized via its optimize class method. """ optimizer = g2o.SparseOptimizer() optimizer.set_algorithm(g2o.OptimizationAlgorithmLevenberg( g2o.BlockSolverSE3(g2o.LinearSolverCholmodSE3()))) if self.is_sparse_bundle_adjustment: for i in self.vertices: if self.vertices[i].mode == VertexType.TAGPOINT: vertex = g2o.VertexSBAPointXYZ() vertex.set_estimate(self.vertices[i].estimate[:3]) else: vertex = g2o.VertexSE3Expmap() vertex.set_estimate(pose_to_se3quat(self.vertices[i].estimate)) vertex.set_id(i) vertex.set_fixed(self.vertices[i].fixed) optimizer.add_vertex(vertex) cam_idx = 0 for i in self.edges: if self.edges[i].corner_ids is None: edge = g2o.EdgeSE3Expmap() for j, k in enumerate([self.edges[i].startuid, self.edges[i].enduid]): edge.set_vertex(j, optimizer.vertex(k)) edge.set_measurement(pose_to_se3quat(self.edges[i].measurement)) edge.set_information(self.edges[i].information) optimizer.add_edge(edge) else: # Note: we only use the focal length in the x direction since: (a) that's all that g2o supports and # (b) it is always the same in ARKit (at least currently) cam = g2o.CameraParameters(self.edges[i].camera_intrinsics[0], self.edges[i].camera_intrinsics[2:], 0) cam.set_id(cam_idx) optimizer.add_parameter(cam) for corner_idx, corner_id in enumerate(self.edges[i].corner_ids): edge = g2o.EdgeProjectPSI2UV() edge.resize(3) edge.set_vertex(0, optimizer.vertex(corner_id)) edge.set_vertex(1, optimizer.vertex(self.edges[i].startuid)) edge.set_vertex(2, optimizer.vertex(self.edges[i].enduid)) edge.set_information(self.edges[i].information) edge.set_measurement(self.edges[i].measurement[corner_idx * 2:corner_idx * 2 + 2]) edge.set_parameter_id(0, cam_idx) if self.use_huber: edge.set_robust_kernel(g2o.RobustKernelHuber(self.huber_delta)) optimizer.add_edge(edge) cam_idx += 1 else: for i in self.vertices: vertex = g2o.VertexSE3() vertex.set_id(i) vertex.set_estimate(pose_to_isometry(self.vertices[i].estimate)) vertex.set_fixed(self.vertices[i].fixed) optimizer.add_vertex(vertex) for i in self.edges: edge = g2o.EdgeSE3() for j, k in enumerate([self.edges[i].startuid, self.edges[i].enduid]): edge.set_vertex(j, optimizer.vertex(k)) edge.set_measurement(pose_to_isometry(self.edges[i].measurement)) edge.set_information(self.edges[i].information) edge.set_id(i) optimizer.add_edge(edge) return optimizer
def optimize(self, local_window=20, fix_points=False, verbose=False): # create g2o optimizer opt = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) opt.set_algorithm(solver) if self.alt: principal_point = (self.frames[0].K[0][2], self.frames[0].K[1][2]) cam = g2o.CameraParameters(self.frames[0].K[0][0], principal_point, 0) cam.set_id(0) opt.add_parameter(cam) robust_kernel = g2o.RobustKernelHuber(np.sqrt(5.991)) if local_window is None: local_frames = self.frames else: local_frames = self.frames[-local_window:] graph_frames, graph_points = {}, {} # add frames to graph for f in (local_frames if fix_points else self.frames): if not self.alt: pose = np.linalg.inv(f.pose) se3 = g2o.SE3Quat(pose[0:3, 0:3], pose[0:3, 3]) sbacam = g2o.SBACam(se3) sbacam.set_cam(f.K[0][0], f.K[1][1], f.K[0][2], f.K[1][2], 0.0) v_se3 = g2o.VertexCam() v_se3.set_estimate(sbacam) else: pose = f.pose se3 = g2o.SE3Quat(pose[0:3, 0:3], pose[0:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(f.id * 2) v_se3.set_fixed(f.id <= 1 or f not in local_frames) # v_se3.set_fixed(f.id != 0) opt.add_vertex(v_se3) # confirm pose correctness est = v_se3.estimate() assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) assert np.allclose(pose[0:3, 3], est.translation()) graph_frames[f] = v_se3 # add points to frames for p in self.points: if not any([f in local_frames for f in p.frames]): continue pt = g2o.VertexSBAPointXYZ() pt.set_id(p.id * 2 + 1) pt.set_estimate(p.loc[0:3]) pt.set_marginalized(True) pt.set_fixed(fix_points) opt.add_vertex(pt) graph_points[p] = pt # add edges for f, idx in zip(p.frames, p.idxs): if f not in graph_frames: continue if not self.alt: edge = g2o.EdgeProjectP2MC() else: edge = g2o.EdgeProjectXYZ2UV() edge.set_parameter_id(0, 0) edge.set_vertex(0, pt) edge.set_vertex(1, graph_frames[f]) uv = f.raw_pts[idx] edge.set_measurement(uv) edge.set_information(np.eye(2)) edge.set_robust_kernel(robust_kernel) opt.add_edge(edge) if verbose: opt.set_verbose(True) opt.initialize_optimization() opt.optimize(50) # put frames back for f in graph_frames: est = graph_frames[f].estimate() R = est.rotation().matrix() t = est.translation() if not self.alt: f.pose = np.linalg.inv(pose_homogeneous(R, t)) else: f.pose = pose_homogeneous(R, t) # put points back (and cull) if not fix_points: culled_pt_count = 0 for p in graph_points: est = graph_points[p].estimate() p.pt = np.array(est) # remove points if the number of observations <= (n-1) old_point = len( p.frames) <= 9 and p.frames[-1].id + 17 < self.max_frame # compute reprojection error errs = [] for f, idx in zip(p.frames, p.idxs): uv = f.raw_pts[idx] proj = np.dot(np.dot(f.K, f.pose[:3]), np.array([est[0], est[1], est[2], 1.0])) proj = proj[0:2] / proj[2] errs.append(np.linalg.norm(proj - uv)) # cull if old_point or np.mean(errs) > 2: culled_pt_count += 1 self.points.remove(p) p.delete() print("Culled: %d points" % culled_pt_count) return opt.active_chi2()
def optimization(frames, points, local_window, fixed_points=False, verbose=False, rounds=40, use_robust_kernel=False): if local_window is None: local_frames = frames else: local_frames = frames[-local_window:] # create g2o optimizer opt = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) opt.set_algorithm(solver) thHuberMono = math.sqrt(5.991) # chi-square 2 DOFS graph_frames, graph_points = {}, {} # add frame vertices to graph for f in ( local_frames if fixed_points else frames ): # if points are fixed then consider just the local frames, otherwise we need all frames or at least two frames for each point #print('adding vertex frame ', f.id, ' to graph') pose = f.pose se3 = g2o.SE3Quat(pose[0:3, 0:3], pose[0:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(f.id * 2) # even ids v_se3.set_fixed(f.id < 1 or f not in local_frames) opt.add_vertex(v_se3) # confirm pose correctness #est = v_se3.estimate() #assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) #assert np.allclose(pose[0:3, 3], est.translation()) graph_frames[f] = v_se3 # add point vertices to graph for p in points: if p.is_bad and not fixed_points: continue if not any([f in local_frames for f in p.frames]): continue #print('adding vertex point ', p.id,' to graph') v_p = g2o.VertexSBAPointXYZ() v_p.set_id(p.id * 2 + 1) # odd ids v_p.set_estimate(p.pt[0:3]) v_p.set_marginalized(True) v_p.set_fixed(fixed_points) opt.add_vertex(v_p) graph_points[p] = v_p # add edges for f, idx in zip(p.frames, p.idxs): if f not in graph_frames: continue #print('adding edge between point ', p.id,' and frame ', f.id) edge = g2o.EdgeSE3ProjectXYZ() edge.set_vertex(0, v_p) edge.set_vertex(1, graph_frames[f]) edge.set_measurement(f.kpsu[idx]) invSigma2 = Frame.detector.inv_level_sigmas2[f.octaves[idx]] edge.set_information(np.eye(2) * invSigma2) if use_robust_kernel: edge.set_robust_kernel(g2o.RobustKernelHuber(thHuberMono)) edge.fx = f.fx edge.fy = f.fy edge.cx = f.cx edge.cy = f.cy opt.add_edge(edge) if verbose: opt.set_verbose(True) opt.initialize_optimization() opt.optimize(rounds) # put frames back for f in graph_frames: est = graph_frames[f].estimate() R = est.rotation().matrix() t = est.translation() f.pose = poseRt(R, t) # put points back if not fixed_points: for p in graph_points: p.pt = np.array(graph_points[p].estimate()) return opt.active_chi2()
def localOptimization(frames, points, frames_ref=[], fixed_points=False, verbose=False, rounds=10): # create g2o optimizer opt = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) opt.set_algorithm(solver) #robust_kernel = g2o.RobustKernelHuber(np.sqrt(5.991)) # chi-square 2 DOFs thHuberMono = math.sqrt(5.991) # chi-square 2 DOFS graph_frames, graph_points = {}, {} all_frames = frames + frames_ref # add frame vertices to graph for f in all_frames: #print('adding vertex frame ', f.id, ' to graph') pose = f.pose se3 = g2o.SE3Quat(pose[0:3, 0:3], pose[0:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(f.id * 2) # even ids v_se3.set_fixed(f.id < 1 or f in frames_ref) opt.add_vertex(v_se3) graph_frames[f] = v_se3 # confirm pose correctness #est = v_se3.estimate() #assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) #assert np.allclose(pose[0:3, 3], est.translation()) graph_edges = {} num_point_edges = 0 # add point vertices to graph for p in points: assert (p is not None) if p.is_bad and not fixed_points: # do not consider bad points unless they are fixed continue if not any([f in frames for f in p.frames]): # this is redundant now continue #print('adding vertex point ', p.id,' to graph') v_p = g2o.VertexSBAPointXYZ() v_p.set_id(p.id * 2 + 1) # odd ids v_p.set_estimate(p.pt[0:3]) v_p.set_marginalized(True) v_p.set_fixed(fixed_points) opt.add_vertex(v_p) graph_points[p] = v_p # add edges for f, p_idx in zip(p.frames, p.idxs): assert (f.points[p_idx] == p) if f not in graph_frames: continue #print('adding edge between point ', p.id,' and frame ', f.id) edge = g2o.EdgeSE3ProjectXYZ() edge.set_vertex(0, v_p) edge.set_vertex(1, graph_frames[f]) edge.set_measurement(f.kpsu[p_idx]) invSigma2 = Frame.detector.inv_level_sigmas2[f.octaves[p_idx]] edge.set_information(np.eye(2) * invSigma2) edge.set_robust_kernel(g2o.RobustKernelHuber(thHuberMono)) edge.fx = f.fx edge.fy = f.fy edge.cx = f.cx edge.cy = f.cy opt.add_edge(edge) graph_edges[edge] = (p, f, p_idx) # f.points[p_idx] == p num_point_edges += 1 if verbose: opt.set_verbose(True) # initial optimization opt.initialize_optimization() opt.optimize(5) chi2Mono = 5.991 # chi-square 2 DOFs # check inliers observation for edge, edge_data in graph_edges.items(): p = edge_data[0] if p.is_bad is True: continue if edge.chi2() > chi2Mono or not edge.is_depth_positive(): edge.set_level(1) edge.set_robust_kernel(None) # optimize again without outliers opt.initialize_optimization() opt.optimize(rounds) # clean map observations num_bad_observations = 0 outliers_data = [] for edge, edge_data in graph_edges.items(): p, f, p_idx = edge_data if p.is_bad is True: continue assert (f.points[p_idx] == p) if edge.chi2() > chi2Mono or not edge.is_depth_positive(): num_bad_observations += 1 outliers_data.append((p, f, p_idx)) for d in outliers_data: (p, f, p_idx) = d assert (f.points[p_idx] == p) p.remove_observation(f, p_idx) f.remove_point(p) # put frames back for f in graph_frames: est = graph_frames[f].estimate() R = est.rotation().matrix() t = est.translation() f.pose = poseRt(R, t) # put points back if not fixed_points: for p in graph_points: p.pt = np.array(graph_points[p].estimate()) return opt.active_chi2(), num_bad_observations / num_point_edges
def main(): optimizer = g2o.SparseOptimizer() # solver = g2o.BlockSolverSE3(g2o.LinearSolverEigenSE3()) solver = g2o.BlockSolverSE3(g2o.LinearSolverCholmodSE3()) # solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) optimizer.set_algorithm(solver) # Convergence Criterion terminate = g2o.SparseOptimizerTerminateAction() terminate.set_gain_threshold(1e-6) optimizer.add_post_iteration_action(terminate) # Robust cost Function (Huber function) delta delta = np.sqrt(5.991) true_points = np.hstack([ np.random.random((25, 1)) * 3 - 1.5, np.random.random((25, 1)) - 0.5, np.random.random((25, 1)) + 3]) fx = 600. fy = 600. cx = 320. cy = 240. principal_point = (cx, cy) cam = g2o.CameraParameters(fx, principal_point, 0) true_poses = [] num_pose = 10 for i in range(num_pose): # pose here means transform points from world coordinates to camera coordinates pose = g2o.SE3Quat(np.identity(3), [i*0.04-1, 0, 0]) true_poses.append(pose) v_se3 = g2o.VertexSE3Expmap() v_se3.set_id(i) v_se3.set_estimate(pose) if i < 2: v_se3.set_fixed(True) optimizer.add_vertex(v_se3) print(optimizer.vertices()) point_id = num_pose inliers = dict() sse = defaultdict(float) vp_edge = [] for i, point in enumerate(true_points): visible = [] for j, pose in enumerate(true_poses): z = cam.cam_map(pose * point) if 0 <= z[0] < 640 and 0 <= z[1] < 480: visible.append((j, z)) if len(visible) < 2: continue vp = g2o.VertexSBAPointXYZ() vp.set_estimate(point + np.random.randn(3)) vp.set_id(point_id) vp.set_marginalized(True) optimizer.add_vertex(vp) inlier = True for j, z in visible: if np.random.random() < args.outlier_ratio: inlier = False z = np.random.random(2) * [640, 480] z += np.random.randn(2) * args.pixel_noise e = g2o.EdgeSE3ProjectXYZ() e.set_vertex(0,vp) e.set_vertex(1,optimizer.vertex(j)) e.set_measurement(z) e.set_information(np.identity(2)) rk = g2o.RobustKernelHuber() e.set_robust_kernel(rk) rk.set_delta(delta) e.fx = fx e.fy = fy e.cx = cx e.cy = cy optimizer.add_edge(e) vp_edge.append(e) if inlier: inliers[point_id] = i error = vp.estimate() - true_points[i] sse[0] += np.sum(error**2) point_id += 1 print('num vertices:', len(optimizer.vertices())) print('num edges:', len(optimizer.edges())) print(optimizer.vertices()) print() print('Performing full BA:') optimizer.initialize_optimization() optimizer.set_verbose(True) optimizer.optimize(5) for i in inliers: vp = optimizer.vertex(i) error = vp.estimate() - true_points[inliers[i]] sse[1] += np.sum(error**2) print('\nRMSE (inliers only):') print('before optimization:', np.sqrt(sse[0] / len(inliers))) print('after optimization:', np.sqrt(sse[1] / len(inliers))) # print(optimizer.vertices()) print() for i in xrange(num_pose): print(optimizer.vertex(i).estimate().inverse().matrix()) j = num_pose for i in xrange(len(inliers)): print(optimizer.vertex(j).estimate().shape) j += 1 i = 0 """
def optimize(frames, points, local_window, fix_points, verbose=False, rounds=50): if local_window is None: local_frames = frames else: local_frames = frames[-local_window:] # create g2o optimizer opt = g2o.SparseOptimizer() solver = g2o.BlockSolverSE3(g2o.LinearSolverCSparseSE3()) solver = g2o.OptimizationAlgorithmLevenberg(solver) opt.set_algorithm(solver) # add normalized camera cam = g2o.CameraParameters(1.0, (0.0, 0.0), 0) cam.set_id(0) opt.add_parameter(cam) robust_kernel = g2o.RobustKernelHuber(np.sqrt(5.991)) graph_frames, graph_points = {}, {} # add frames to graph for f in (local_frames if fix_points else frames): pose = f.pose se3 = g2o.SE3Quat(pose[0:3, 0:3], pose[0:3, 3]) v_se3 = g2o.VertexSE3Expmap() v_se3.set_estimate(se3) v_se3.set_id(f.id * 2) v_se3.set_fixed(f.id <= 1 or f not in local_frames) #v_se3.set_fixed(f.id != 0) opt.add_vertex(v_se3) # confirm pose correctness est = v_se3.estimate() assert np.allclose(pose[0:3, 0:3], est.rotation().matrix()) assert np.allclose(pose[0:3, 3], est.translation()) graph_frames[f] = v_se3 # add points to frames for p in points: if not any([f in local_frames for f in p.frames]): continue pt = g2o.VertexSBAPointXYZ() pt.set_id(p.id * 2 + 1) pt.set_estimate(p.pt[0:3]) pt.set_marginalized(True) pt.set_fixed(fix_points) opt.add_vertex(pt) graph_points[p] = pt # add edges for f, idx in zip(p.frames, p.idxs): if f not in graph_frames: continue edge = g2o.EdgeProjectXYZ2UV() edge.set_parameter_id(0, 0) edge.set_vertex(0, pt) edge.set_vertex(1, graph_frames[f]) edge.set_measurement(f.kps[idx]) edge.set_information(np.eye(2)) edge.set_robust_kernel(robust_kernel) opt.add_edge(edge) if verbose: opt.set_verbose(True) opt.initialize_optimization() opt.optimize(rounds) # put frames back for f in graph_frames: est = graph_frames[f].estimate() R = est.rotation().matrix() t = est.translation() f.pose = poseRt(R, t) # put points back if not fix_points: for p in graph_points: p.pt = np.array(graph_points[p].estimate()) return opt.active_chi2()