imcui/third_party/rdd/benchmarks/utils.py

import numpy as np
import torch
from kornia.geometry.epipolar import numeric
from kornia.geometry.conversions import convert_points_to_homogeneous
import cv2

def pose_auc(errors, thresholds):
    sort_idx = np.argsort(errors)
    errors = np.array(errors.copy())[sort_idx]
    recall = (np.arange(len(errors)) + 1) / len(errors)
    errors = np.r_[0.0, errors]
    recall = np.r_[0.0, recall]
    aucs = []
    for t in thresholds:
        last_index = np.searchsorted(errors, t)
        r = np.r_[recall[:last_index], recall[last_index - 1]]
        e = np.r_[errors[:last_index], t]
        aucs.append(np.trapz(r, x=e) / t)
    return aucs

def angle_error_vec(v1, v2):
    n = np.linalg.norm(v1) * np.linalg.norm(v2)
    return np.rad2deg(np.arccos(np.clip(np.dot(v1, v2) / n, -1.0, 1.0)))

def angle_error_mat(R1, R2):
    cos = (np.trace(np.dot(R1.T, R2)) - 1) / 2
    cos = np.clip(cos, -1.0, 1.0)  # numercial errors can make it out of bounds
    return np.rad2deg(np.abs(np.arccos(cos)))

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]
        E (torch.Tensor): [3, 3]
    """
    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

def compute_symmetrical_epipolar_errors(T_0to1, pts0, pts1, K0, K1, device='cuda'):
    """ 
    Update:
        data (dict):{"epi_errs": [M]}
    """
    pts0 = torch.tensor(pts0, device=device)
    pts1 = torch.tensor(pts1, device=device)
    K0 = torch.tensor(K0, device=device)
    K1 = torch.tensor(K1, device=device)
    T_0to1 = torch.tensor(T_0to1, device=device)
    Tx = numeric.cross_product_matrix(T_0to1[:3, 3])
    E_mat = Tx @ T_0to1[:3, :3]
    
    epi_err = symmetric_epipolar_distance(pts0, pts1, E_mat, K0, K1)
    return epi_err

def compute_pose_error(T_0to1, R, t):
    R_gt = T_0to1[:3, :3]
    t_gt = T_0to1[:3, 3]
    error_t = angle_error_vec(t.squeeze(), t_gt)
    error_t = np.minimum(error_t, 180 - error_t)  # ambiguity of E estimation
    error_R = angle_error_mat(R, R_gt)
    return error_t, error_R

def compute_relative_pose(R1, t1, R2, t2):
    rots = R2 @ (R1.T)
    trans = -rots @ t1 + t2
    return rots, trans

def estimate_pose(kpts0, kpts1, K0, K1, norm_thresh, conf=0.99999):
    if len(kpts0) < 5:
        return None
    K0inv = np.linalg.inv(K0[:2,:2])
    K1inv = np.linalg.inv(K1[:2,:2])

    kpts0 = (K0inv @ (kpts0-K0[None,:2,2]).T).T 
    kpts1 = (K1inv @ (kpts1-K1[None,:2,2]).T).T
    E, mask = cv2.findEssentialMat(
        kpts0, kpts1, np.eye(3), threshold=norm_thresh, prob=conf
    )

    ret = None
    if E is not None:
        best_num_inliers = 0

        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:
                best_num_inliers = n
                ret = (R, t, mask.ravel() > 0)
    return ret

def dynamic_alpha(n_matches,
                  milestones=[0, 300, 1000, 2000],
                  alphas=[1.0, 0.8, 0.4, 0.2]):
    if n_matches == 0:
        return 1.0
    ranges = list(zip(alphas, alphas[1:] + [None]))
    loc = bisect.bisect_right(milestones, n_matches) - 1
    _range = ranges[loc]
    if _range[1] is None:
        return _range[0]
    return _range[1] + (milestones[loc + 1] - n_matches) / (
        milestones[loc + 1] - milestones[loc]) * (_range[0] - _range[1])