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import warnings
import numpy as np
import cv2
import math
import torch
from torchvision import transforms
from torchvision.transforms.functional import InterpolationMode
import torch.nn.functional as F
from PIL import Image
import kornia
def recover_pose(E, kpts0, kpts1, K0, K1, mask):
best_num_inliers = 0
K0inv = np.linalg.inv(K0[:2, :2])
K1inv = np.linalg.inv(K1[:2, :2])
kpts0_n = (K0inv @ (kpts0 - K0[None, :2, 2]).T).T
kpts1_n = (K1inv @ (kpts1 - K1[None, :2, 2]).T).T
for _E in np.split(E, len(E) / 3):
n, R, t, _ = cv2.recoverPose(_E, kpts0_n, kpts1_n, np.eye(3), 1e9, mask=mask)
if n > best_num_inliers:
best_num_inliers = n
ret = (R, t, mask.ravel() > 0)
return ret
# Code taken from https://github.com/PruneTruong/DenseMatching/blob/40c29a6b5c35e86b9509e65ab0cd12553d998e5f/validation/utils_pose_estimation.py
# --- GEOMETRY ---
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 estimate_pose_uncalibrated(kpts0, kpts1, K0, K1, norm_thresh, conf=0.99999):
if len(kpts0) < 5:
return None
method = cv2.USAC_ACCURATE
F, mask = cv2.findFundamentalMat(
kpts0,
kpts1,
ransacReprojThreshold=norm_thresh,
confidence=conf,
method=method,
maxIters=10000,
)
E = K1.T @ F @ K0
ret = None
if E is not None:
best_num_inliers = 0
K0inv = np.linalg.inv(K0[:2, :2])
K1inv = np.linalg.inv(K1[:2, :2])
kpts0_n = (K0inv @ (kpts0 - K0[None, :2, 2]).T).T
kpts1_n = (K1inv @ (kpts1 - K1[None, :2, 2]).T).T
for _E in np.split(E, len(E) / 3):
n, R, t, _ = cv2.recoverPose(
_E, kpts0_n, kpts1_n, np.eye(3), 1e9, mask=mask
)
if n > best_num_inliers:
best_num_inliers = n
ret = (R, t, mask.ravel() > 0)
return ret
def unnormalize_coords(x_n, h, w):
x = torch.stack(
(w * (x_n[..., 0] + 1) / 2, h * (x_n[..., 1] + 1) / 2), dim=-1
) # [-1+1/h, 1-1/h] -> [0.5, h-0.5]
return x
def rotate_intrinsic(K, n):
base_rot = np.array([[0, 1, 0], [-1, 0, 0], [0, 0, 1]])
rot = np.linalg.matrix_power(base_rot, n)
return rot @ K
def rotate_pose_inplane(i_T_w, rot):
rotation_matrices = [
np.array(
[
[np.cos(r), -np.sin(r), 0.0, 0.0],
[np.sin(r), np.cos(r), 0.0, 0.0],
[0.0, 0.0, 1.0, 0.0],
[0.0, 0.0, 0.0, 1.0],
],
dtype=np.float32,
)
for r in [np.deg2rad(d) for d in (0, 270, 180, 90)]
]
return np.dot(rotation_matrices[rot], i_T_w)
def scale_intrinsics(K, scales):
scales = np.diag([1.0 / scales[0], 1.0 / scales[1], 1.0])
return np.dot(scales, K)
def to_homogeneous(points):
return np.concatenate([points, np.ones_like(points[:, :1])], axis=-1)
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 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 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 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
# From Patch2Pix https://github.com/GrumpyZhou/patch2pix
def get_depth_tuple_transform_ops_nearest_exact(resize=None):
ops = []
if resize:
ops.append(TupleResizeNearestExact(resize))
return TupleCompose(ops)
def get_depth_tuple_transform_ops(resize=None, normalize=True, unscale=False):
ops = []
if resize:
ops.append(TupleResize(resize, mode=InterpolationMode.BILINEAR))
return TupleCompose(ops)
def get_tuple_transform_ops(
resize=None, normalize=True, unscale=False, clahe=False, colorjiggle_params=None
):
ops = []
if resize:
ops.append(TupleResize(resize))
ops.append(TupleToTensorScaled())
if normalize:
ops.append(
TupleNormalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225])
) # Imagenet mean/std
return TupleCompose(ops)
class ToTensorScaled(object):
"""Convert a RGB PIL Image to a CHW ordered Tensor, scale the range to [0, 1]"""
def __call__(self, im):
if not isinstance(im, torch.Tensor):
im = np.array(im, dtype=np.float32).transpose((2, 0, 1))
im /= 255.0
return torch.from_numpy(im)
else:
return im
def __repr__(self):
return "ToTensorScaled(./255)"
class TupleToTensorScaled(object):
def __init__(self):
self.to_tensor = ToTensorScaled()
def __call__(self, im_tuple):
return [self.to_tensor(im) for im in im_tuple]
def __repr__(self):
return "TupleToTensorScaled(./255)"
class ToTensorUnscaled(object):
"""Convert a RGB PIL Image to a CHW ordered Tensor"""
def __call__(self, im):
return torch.from_numpy(np.array(im, dtype=np.float32).transpose((2, 0, 1)))
def __repr__(self):
return "ToTensorUnscaled()"
class TupleToTensorUnscaled(object):
"""Convert a RGB PIL Image to a CHW ordered Tensor"""
def __init__(self):
self.to_tensor = ToTensorUnscaled()
def __call__(self, im_tuple):
return [self.to_tensor(im) for im in im_tuple]
def __repr__(self):
return "TupleToTensorUnscaled()"
class TupleResizeNearestExact:
def __init__(self, size):
self.size = size
def __call__(self, im_tuple):
return [
F.interpolate(im, size=self.size, mode="nearest-exact") for im in im_tuple
]
def __repr__(self):
return "TupleResizeNearestExact(size={})".format(self.size)
class TupleResize(object):
def __init__(self, size, mode=InterpolationMode.BICUBIC):
self.size = size
self.resize = transforms.Resize(size, mode)
def __call__(self, im_tuple):
return [self.resize(im) for im in im_tuple]
def __repr__(self):
return "TupleResize(size={})".format(self.size)
class Normalize:
def __call__(self, im):
mean = im.mean(dim=(1, 2), keepdims=True)
std = im.std(dim=(1, 2), keepdims=True)
return (im - mean) / std
class TupleNormalize(object):
def __init__(self, mean, std):
self.mean = mean
self.std = std
self.normalize = transforms.Normalize(mean=mean, std=std)
def __call__(self, im_tuple):
c, h, w = im_tuple[0].shape
if c > 3:
warnings.warn(f"Number of channels c={c} > 3, assuming first 3 are rgb")
return [self.normalize(im[:3]) for im in im_tuple]
def __repr__(self):
return "TupleNormalize(mean={}, std={})".format(self.mean, self.std)
class TupleCompose(object):
def __init__(self, transforms):
self.transforms = transforms
def __call__(self, im_tuple):
for t in self.transforms:
im_tuple = t(im_tuple)
return im_tuple
def __repr__(self):
format_string = self.__class__.__name__ + "("
for t in self.transforms:
format_string += "\n"
format_string += " {0}".format(t)
format_string += "\n)"
return format_string
@torch.no_grad()
def cls_to_flow(cls, deterministic_sampling=True):
B, C, H, W = cls.shape
device = cls.device
res = round(math.sqrt(C))
G = torch.meshgrid(
*[
torch.linspace(-1 + 1 / res, 1 - 1 / res, steps=res, device=device)
for _ in range(2)
]
)
G = torch.stack([G[1], G[0]], dim=-1).reshape(C, 2)
if deterministic_sampling:
sampled_cls = cls.max(dim=1).indices
else:
sampled_cls = torch.multinomial(
cls.permute(0, 2, 3, 1).reshape(B * H * W, C).softmax(dim=-1), 1
).reshape(B, H, W)
flow = G[sampled_cls]
return flow
@torch.no_grad()
def cls_to_flow_refine(cls):
B, C, H, W = cls.shape
device = cls.device
res = round(math.sqrt(C))
G = torch.meshgrid(
*[
torch.linspace(-1 + 1 / res, 1 - 1 / res, steps=res, device=device)
for _ in range(2)
]
)
G = torch.stack([G[1], G[0]], dim=-1).reshape(C, 2)
cls = cls.softmax(dim=1)
mode = cls.max(dim=1).indices
index = (
torch.stack((mode - 1, mode, mode + 1, mode - res, mode + res), dim=1)
.clamp(0, C - 1)
.long()
)
neighbours = torch.gather(cls, dim=1, index=index)[..., None]
flow = (
neighbours[:, 0] * G[index[:, 0]]
+ neighbours[:, 1] * G[index[:, 1]]
+ neighbours[:, 2] * G[index[:, 2]]
+ neighbours[:, 3] * G[index[:, 3]]
+ neighbours[:, 4] * G[index[:, 4]]
)
tot_prob = neighbours.sum(dim=1)
flow = flow / tot_prob
return flow
def get_gt_warp(
depth1,
depth2,
T_1to2,
K1,
K2,
depth_interpolation_mode="bilinear",
relative_depth_error_threshold=0.05,
H=None,
W=None,
):
if H is None:
B, H, W = depth1.shape
else:
B = depth1.shape[0]
with torch.no_grad():
x1_n = torch.meshgrid(
*[
torch.linspace(-1 + 1 / n, 1 - 1 / n, n, device=depth1.device)
for n in (B, H, W)
]
)
x1_n = torch.stack((x1_n[2], x1_n[1]), dim=-1).reshape(B, H * W, 2)
mask, x2 = warp_kpts(
x1_n.double(),
depth1.double(),
depth2.double(),
T_1to2.double(),
K1.double(),
K2.double(),
depth_interpolation_mode=depth_interpolation_mode,
relative_depth_error_threshold=relative_depth_error_threshold,
)
prob = mask.float().reshape(B, H, W)
x2 = x2.reshape(B, H, W, 2)
return x2, prob
@torch.no_grad()
def warp_kpts(
kpts0,
depth0,
depth1,
T_0to1,
K0,
K1,
smooth_mask=False,
return_relative_depth_error=False,
depth_interpolation_mode="bilinear",
relative_depth_error_threshold=0.05,
):
"""Warp kpts0 from I0 to I1 with depth, K and Rt
Also check covisibility and depth consistency.
Depth is consistent if relative error < 0.2 (hard-coded).
# https://github.com/zju3dv/LoFTR/blob/94e98b695be18acb43d5d3250f52226a8e36f839/src/loftr/utils/geometry.py adapted from here
Args:
kpts0 (torch.Tensor): [N, L, 2] - <x, y>, should be normalized in (-1,1)
depth0 (torch.Tensor): [N, H, W],
depth1 (torch.Tensor): [N, H, W],
T_0to1 (torch.Tensor): [N, 3, 4],
K0 (torch.Tensor): [N, 3, 3],
K1 (torch.Tensor): [N, 3, 3],
Returns:
calculable_mask (torch.Tensor): [N, L]
warped_keypoints0 (torch.Tensor): [N, L, 2] <x0_hat, y1_hat>
"""
(
n,
h,
w,
) = depth0.shape
if depth_interpolation_mode == "combined":
# Inspired by approach in inloc, try to fill holes from bilinear interpolation by nearest neighbour interpolation
if smooth_mask:
raise NotImplementedError("Combined bilinear and NN warp not implemented")
valid_bilinear, warp_bilinear = warp_kpts(
kpts0,
depth0,
depth1,
T_0to1,
K0,
K1,
smooth_mask=smooth_mask,
return_relative_depth_error=return_relative_depth_error,
depth_interpolation_mode="bilinear",
relative_depth_error_threshold=relative_depth_error_threshold,
)
valid_nearest, warp_nearest = warp_kpts(
kpts0,
depth0,
depth1,
T_0to1,
K0,
K1,
smooth_mask=smooth_mask,
return_relative_depth_error=return_relative_depth_error,
depth_interpolation_mode="nearest-exact",
relative_depth_error_threshold=relative_depth_error_threshold,
)
nearest_valid_bilinear_invalid = (~valid_bilinear).logical_and(valid_nearest)
warp = warp_bilinear.clone()
warp[nearest_valid_bilinear_invalid] = warp_nearest[
nearest_valid_bilinear_invalid
]
valid = valid_bilinear | valid_nearest
return valid, warp
kpts0_depth = F.grid_sample(
depth0[:, None],
kpts0[:, :, None],
mode=depth_interpolation_mode,
align_corners=False,
)[:, 0, :, 0]
kpts0 = torch.stack(
(w * (kpts0[..., 0] + 1) / 2, h * (kpts0[..., 1] + 1) / 2), dim=-1
) # [-1+1/h, 1-1/h] -> [0.5, h-0.5]
# Sample depth, get calculable_mask on depth != 0
nonzero_mask = kpts0_depth != 0
# Unproject
kpts0_h = (
torch.cat([kpts0, torch.ones_like(kpts0[:, :, [0]])], dim=-1)
* kpts0_depth[..., None]
) # (N, L, 3)
kpts0_n = K0.inverse() @ kpts0_h.transpose(2, 1) # (N, 3, L)
kpts0_cam = kpts0_n
# Rigid Transform
w_kpts0_cam = T_0to1[:, :3, :3] @ kpts0_cam + T_0to1[:, :3, [3]] # (N, 3, L)
w_kpts0_depth_computed = w_kpts0_cam[:, 2, :]
# Project
w_kpts0_h = (K1 @ w_kpts0_cam).transpose(2, 1) # (N, L, 3)
w_kpts0 = w_kpts0_h[:, :, :2] / (
w_kpts0_h[:, :, [2]] + 1e-4
) # (N, L, 2), +1e-4 to avoid zero depth
# Covisible Check
h, w = depth1.shape[1:3]
covisible_mask = (
(w_kpts0[:, :, 0] > 0)
* (w_kpts0[:, :, 0] < w - 1)
* (w_kpts0[:, :, 1] > 0)
* (w_kpts0[:, :, 1] < h - 1)
)
w_kpts0 = torch.stack(
(2 * w_kpts0[..., 0] / w - 1, 2 * w_kpts0[..., 1] / h - 1), dim=-1
) # from [0.5,h-0.5] -> [-1+1/h, 1-1/h]
# w_kpts0[~covisible_mask, :] = -5 # xd
w_kpts0_depth = F.grid_sample(
depth1[:, None],
w_kpts0[:, :, None],
mode=depth_interpolation_mode,
align_corners=False,
)[:, 0, :, 0]
relative_depth_error = (
(w_kpts0_depth - w_kpts0_depth_computed) / w_kpts0_depth
).abs()
if not smooth_mask:
consistent_mask = relative_depth_error < relative_depth_error_threshold
else:
consistent_mask = (-relative_depth_error / smooth_mask).exp()
valid_mask = nonzero_mask * covisible_mask * consistent_mask
if return_relative_depth_error:
return relative_depth_error, w_kpts0
else:
return valid_mask, w_kpts0
imagenet_mean = torch.tensor([0.485, 0.456, 0.406])
imagenet_std = torch.tensor([0.229, 0.224, 0.225])
def numpy_to_pil(x: np.ndarray):
"""
Args:
x: Assumed to be of shape (h,w,c)
"""
if isinstance(x, torch.Tensor):
x = x.detach().cpu().numpy()
if x.max() <= 1.01:
x *= 255
x = x.astype(np.uint8)
return Image.fromarray(x)
def tensor_to_pil(x, unnormalize=False):
if unnormalize:
x = x * (imagenet_std[:, None, None].to(x.device)) + (
imagenet_mean[:, None, None].to(x.device)
)
x = x.detach().permute(1, 2, 0).cpu().numpy()
x = np.clip(x, 0.0, 1.0)
return numpy_to_pil(x)
def to_cuda(batch):
for key, value in batch.items():
if isinstance(value, torch.Tensor):
batch[key] = value.cuda()
return batch
def to_cpu(batch):
for key, value in batch.items():
if isinstance(value, torch.Tensor):
batch[key] = value.cpu()
return batch
def get_pose(calib):
w, h = np.array(calib["imsize"])[0]
return np.array(calib["K"]), np.array(calib["R"]), np.array(calib["T"]).T, h, w
def compute_relative_pose(R1, t1, R2, t2):
rots = R2 @ (R1.T)
trans = -rots @ t1 + t2
return rots, trans
@torch.no_grad()
def reset_opt(opt):
for group in opt.param_groups:
for p in group["params"]:
if p.requires_grad:
state = opt.state[p]
# State initialization
# Exponential moving average of gradient values
state["exp_avg"] = torch.zeros_like(p)
# Exponential moving average of squared gradient values
state["exp_avg_sq"] = torch.zeros_like(p)
# Exponential moving average of gradient difference
state["exp_avg_diff"] = torch.zeros_like(p)
def flow_to_pixel_coords(flow, h1, w1):
flow = torch.stack(
(
w1 * (flow[..., 0] + 1) / 2,
h1 * (flow[..., 1] + 1) / 2,
),
axis=-1,
)
return flow
def flow_to_normalized_coords(flow, h1, w1):
flow = torch.stack(
(
2 * (flow[..., 0]) / w1 - 1,
2 * (flow[..., 1]) / h1 - 1,
),
axis=-1,
)
return flow
def warp_to_pixel_coords(warp, h1, w1, h2, w2):
warp1 = warp[..., :2]
warp1 = torch.stack(
(
w1 * (warp1[..., 0] + 1) / 2,
h1 * (warp1[..., 1] + 1) / 2,
),
axis=-1,
)
warp2 = warp[..., 2:]
warp2 = torch.stack(
(
w2 * (warp2[..., 0] + 1) / 2,
h2 * (warp2[..., 1] + 1) / 2,
),
axis=-1,
)
return torch.cat((warp1, warp2), dim=-1)
def signed_point_line_distance(point, line, eps: float = 1e-9):
r"""Return the distance from points to lines.
Args:
point: (possibly homogeneous) points :math:`(*, N, 2 or 3)`.
line: lines coefficients :math:`(a, b, c)` with shape :math:`(*, N, 3)`, where :math:`ax + by + c = 0`.
eps: Small constant for safe sqrt.
Returns:
the computed distance with shape :math:`(*, N)`.
"""
if not point.shape[-1] in (2, 3):
raise ValueError(f"pts must be a (*, 2 or 3) tensor. Got {point.shape}")
if not line.shape[-1] == 3:
raise ValueError(f"lines must be a (*, 3) tensor. Got {line.shape}")
numerator = (
line[..., 0] * point[..., 0] + line[..., 1] * point[..., 1] + line[..., 2]
)
denominator = line[..., :2].norm(dim=-1)
return numerator / (denominator + eps)
def signed_left_to_right_epipolar_distance(pts1, pts2, Fm):
r"""Return one-sided epipolar distance for correspondences given the fundamental matrix.
This method measures the distance from points in the right images to the epilines
of the corresponding points in the left images as they reflect in the right images.
Args:
pts1: correspondences from the left images with shape
:math:`(*, N, 2 or 3)`. If they are not homogeneous, converted automatically.
pts2: correspondences from the right images with shape
:math:`(*, N, 2 or 3)`. If they are not homogeneous, converted automatically.
Fm: Fundamental matrices with shape :math:`(*, 3, 3)`. Called Fm to
avoid ambiguity with torch.nn.functional.
Returns:
the computed Symmetrical distance with shape :math:`(*, N)`.
"""
import kornia
if (len(Fm.shape) < 3) or not Fm.shape[-2:] == (3, 3):
raise ValueError(f"Fm must be a (*, 3, 3) tensor. Got {Fm.shape}")
if pts1.shape[-1] == 2:
pts1 = kornia.geometry.convert_points_to_homogeneous(pts1)
F_t = Fm.transpose(dim0=-2, dim1=-1)
line1_in_2 = pts1 @ F_t
return signed_point_line_distance(pts2, line1_in_2)
def get_grid(b, h, w, device):
grid = torch.meshgrid(
*[torch.linspace(-1 + 1 / n, 1 - 1 / n, n, device=device) for n in (b, h, w)]
)
grid = torch.stack((grid[2], grid[1]), dim=-1).reshape(b, h, w, 2)
return grid
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