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import cv2
import torch
import numpy as np
from collections import OrderedDict
from kornia.geometry.epipolar import numeric
from kornia.geometry.conversions import convert_points_to_homogeneous
# --- METRICS ---
def relative_pose_error(T_0to1, R, t, ignore_gt_t_thr=0.0):
# angle error between 2 vectors
t_gt = T_0to1[:3, 3]
n = np.linalg.norm(t) * np.linalg.norm(t_gt)
t_err = np.rad2deg(np.arccos(np.clip(np.dot(t, t_gt) / n, -1.0, 1.0)))
t_err = np.minimum(t_err, 180 - t_err) # handle E ambiguity
if np.linalg.norm(t_gt) < ignore_gt_t_thr: # pure rotation is challenging
t_err = 0
r = np.linalg.norm(t_gt) / np.linalg.norm(t)
t_err2 = np.linalg.norm((t*r - t_gt))
# angle error between 2 rotation matrices
R_gt = T_0to1[:3, :3]
cos = (np.trace(np.dot(R.T, R_gt)) - 1) / 2
cos = np.clip(cos, -1., 1.) # handle numercial errors
R_err = np.rad2deg(np.abs(np.arccos(cos)))
return t_err, R_err, t_err2
def symmetric_epipolar_distance(pts0, pts1, E, K0, K1):
"""Squared symmetric epipolar distance.
This can be seen as a biased estimation of the reprojection error.
Args:
pts0 (torch.Tensor): [N, 2]
pts1 (torch.Tensor): [N, 2]
E (torch.Tensor): [3, 3]
K0:
K1:
"""
pts0 = (pts0 - K0[[0, 1], [2, 2]][None]) / K0[[0, 1], [0, 1]][None]
pts1 = (pts1 - K1[[0, 1], [2, 2]][None]) / K1[[0, 1], [0, 1]][None]
pts0 = convert_points_to_homogeneous(pts0)
pts1 = convert_points_to_homogeneous(pts1)
Ep0 = pts0 @ E.T # [N, 3]
p1Ep0 = torch.sum(pts1 * Ep0, -1) # [N,]
Etp1 = pts1 @ E # [N, 3]
d = p1Ep0**2 * (1.0 / (Ep0[:, 0]**2 + Ep0[:, 1]**2) + 1.0 / (Etp1[:, 0]**2 + Etp1[:, 1]**2)) # N
return d
@torch.no_grad()
def compute_symmetrical_epipolar_errors(data):
"""
Update:
data (dict):{"epi_errs": [M]}
"""
Tx = numeric.cross_product_matrix(data['T_0to1'][:, :3, 3])
E_mat = Tx @ data['T_0to1'][:, :3, :3]
m_bids = data['m_bids']
pts0 = data['mkpts0_f']
pts1 = data['mkpts1_f']
epi_errs = []
for bs in range(Tx.size(0)):
mask = m_bids == bs
epi_errs.append(symmetric_epipolar_distance(pts0[mask], pts1[mask], E_mat[bs], data['K0'][bs], data['K1'][bs]))
epi_errs = torch.cat(epi_errs, dim=0)
data.update({'epi_errs': epi_errs})
def estimate_pose(kpts0, kpts1, K0, K1, thresh, conf=0.99999):
if len(kpts0) < 5:
return None
# normalize keypoints
kpts0 = (kpts0 - K0[[0, 1], [2, 2]][None]) / K0[[0, 1], [0, 1]][None]
kpts1 = (kpts1 - K1[[0, 1], [2, 2]][None]) / K1[[0, 1], [0, 1]][None]
# normalize ransac threshold
ransac_thr = thresh / np.mean([K0[0, 0], K1[1, 1], K0[0, 0], K1[1, 1]])
# compute pose with cv2
E, mask = cv2.findEssentialMat(
kpts0, kpts1, np.eye(3), threshold=ransac_thr, prob=conf, method=cv2.RANSAC)
if E is None:
# print("\nE is None while trying to recover pose.\n")
return None
# recover pose from E
best_num_inliers = 0
ret = None
for _E in np.split(E, len(E) / 3):
n, R, t, _ = cv2.recoverPose(_E, kpts0, kpts1, np.eye(3), 1e9, mask=mask)
if n > best_num_inliers:
ret = (R, t[:, 0], mask.ravel() > 0)
best_num_inliers = n
return ret
@torch.no_grad()
def compute_pose_errors(data, config):
"""
Update:
data (dict):{
"R_errs" List[float]: [N]
"t_errs" List[float]: [N]
"inliers" List[np.ndarray]: [N]
}
"""
pixel_thr = config.TRAINER.RANSAC_PIXEL_THR # 0.25/0.5/0.75
conf = config.TRAINER.RANSAC_CONF # 0.999999
iters = config.TRAINER.RANSAC_MAX_ITERS # 100000
method = config.TRAINER.POSE_ESTIMATION_METHOD
data.update({'R_errs': [], 't_errs': [], 'inliers': []})
data.update({'Rot': [], 'Tns': []})
data.update({'Rot1': [], 'Tns1': []})
data.update({'t_errs2': []})
m_bids = data['m_bids'].cpu().numpy()
pts0 = data['mkpts0_f'].cpu().numpy()
pts1 = data['mkpts1_f'].cpu().numpy()
K0 = data['K0'].cpu().numpy()
K1 = data['K1'].cpu().numpy()
T_0to1 = data['T_0to1'].cpu().numpy()
# depth0 = data['depth0'].cpu()
# depth1 = data['depth1'].cpu()
# weights = data['weights']
for bs in range(K0.shape[0]):
mask = m_bids == bs
ret1 = None
ret = estimate_pose(pts0[mask], pts1[mask], K0[bs], K1[bs], 0.5, conf=0.99999)
# ret = estimate_pose(pts0[mask], pts1[mask], K0[bs], K1[bs], method=method, thresh=pixel_thr, conf=conf, maxIters=iters)
# weight = weights[bs][-1].cpu().numpy()
# ret = estimate_pose_w_weight(pts0[mask], pts1[mask], weight, K0[bs], K1[bs], pixel_thr, conf=conf)
if ret is None:
data['R_errs'].append(np.inf)
data['t_errs'].append(np.inf)
data['t_errs2'].append(np.inf)
data['inliers'].append(np.array([]).astype(bool))
data['Rot'].append(np.eye(3))
data['Tns'].append(np.zeros(3))
else:
R, t, inliers = ret
t_err, R_err, t_err2 = relative_pose_error(T_0to1[bs], R, t, ignore_gt_t_thr=0.0)
data['R_errs'].append(R_err)
data['t_errs'].append(t_err)
data['t_errs2'].append(t_err2)
data['inliers'].append(inliers)
data['Rot'].append(R)
data['Tns'].append(t)
if ret1 is None:
data['Rot1'].append(np.eye(3))
data['Tns1'].append(np.zeros(3))
else:
# noinspection PyTupleAssignmentBalance
R1, t1, inliers = ret1
data['Rot1'].append(R1)
data['Tns1'].append(t1)
def error_auc(errs, thres):
if isinstance(errs, list): errs = np.array(errs)
pass_ratio = [np.sum(errs < th) / len(errs) for th in thres]
# mAP = {f'AUC@{t}':np.mean(pass_ratio[:i+1]) for i, t in enumerate(thres)}
mAP = {f'AUC@{t}':pass_ratio[i] for i, t in enumerate(thres)}
return mAP
def epidist_prec(errors, thresholds, ret_dict=False):
precs = []
for thr in thresholds:
prec_ = []
for errs in errors:
correct_mask = errs < thr
prec_.append(np.mean(correct_mask) if len(correct_mask) > 0 else 0)
precs.append(np.mean(prec_) if len(prec_) > 0 else 0)
if ret_dict:
return {f'Prec@{t:.0e}': prec for t, prec in zip(thresholds, precs)}
else:
return precs
def aggregate_metrics(metrics, epi_err_thr=5e-4, test=False):
""" Aggregate metrics for the whole dataset:
(This method should be called once per dataset)
1. AUC of the pose error (angular) at the threshold [5, 10, 20]
2. Mean matching precision at the threshold 5e-4(ScanNet), 1e-4(MegaDepth)
"""
# filter duplicates
unq_ids = OrderedDict((iden, i) for i, iden in enumerate(metrics['identifiers']))
unq_ids = list(unq_ids.values())
# pose auc
angular_thresholds = [5, 10, 20]
pose_errors = np.max(np.stack([metrics['R_errs'], metrics['t_errs']]), axis=0)[unq_ids]
aucs = error_auc(pose_errors, angular_thresholds) # (auc@5, auc@10, auc@20)
# matching precision
dist_thresholds = [epi_err_thr]
precs = epidist_prec(np.array(metrics['epi_errs'], dtype=object)[unq_ids], dist_thresholds, True) # (prec@err_thr)
metric = {**aucs, **precs}
metric = {**metric, **{'Num': len(unq_ids)}} if test else metric
return metric
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