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# Copyright 2023 Bingxin Ke, ETH Zurich. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# --------------------------------------------------------------------------
# If you find this code useful, we kindly ask you to cite our paper in your work.
# Please find bibtex at: https://github.com/prs-eth/Marigold#-citation
# More information about the method can be found at https://marigoldmonodepth.github.io
# --------------------------------------------------------------------------
from functools import partial
from typing import Optional, Tuple
import numpy as np
import torch
from .image_util import get_tv_resample_method, resize_max_res
def inter_distances(tensors: torch.Tensor):
"""
To calculate the distance between each two depth maps.
"""
distances = []
for i, j in torch.combinations(torch.arange(tensors.shape[0])):
arr1 = tensors[i : i + 1]
arr2 = tensors[j : j + 1]
distances.append(arr1 - arr2)
dist = torch.concatenate(distances, dim=0)
return dist
def ensemble_depth(
depth: torch.Tensor,
scale_invariant: bool = True,
shift_invariant: bool = True,
output_uncertainty: bool = False,
reduction: str = "median",
regularizer_strength: float = 0.02,
max_iter: int = 2,
tol: float = 1e-3,
max_res: int = 1024,
) -> Tuple[torch.Tensor, Optional[torch.Tensor]]:
"""
Ensembles depth maps represented by the `depth` tensor with expected shape `(B, 1, H, W)`, where B is the
number of ensemble members for a given prediction of size `(H x W)`. Even though the function is designed for
depth maps, it can also be used with disparity maps as long as the input tensor values are non-negative. The
alignment happens when the predictions have one or more degrees of freedom, that is when they are either
affine-invariant (`scale_invariant=True` and `shift_invariant=True`), or just scale-invariant (only
`scale_invariant=True`). For absolute predictions (`scale_invariant=False` and `shift_invariant=False`)
alignment is skipped and only ensembling is performed.
Args:
depth (`torch.Tensor`):
Input ensemble depth maps.
scale_invariant (`bool`, *optional*, defaults to `True`):
Whether to treat predictions as scale-invariant.
shift_invariant (`bool`, *optional*, defaults to `True`):
Whether to treat predictions as shift-invariant.
output_uncertainty (`bool`, *optional*, defaults to `False`):
Whether to output uncertainty map.
reduction (`str`, *optional*, defaults to `"median"`):
Reduction method used to ensemble aligned predictions. The accepted values are: `"mean"` and
`"median"`.
regularizer_strength (`float`, *optional*, defaults to `0.02`):
Strength of the regularizer that pulls the aligned predictions to the unit range from 0 to 1.
max_iter (`int`, *optional*, defaults to `2`):
Maximum number of the alignment solver steps. Refer to `scipy.optimize.minimize` function, `options`
argument.
tol (`float`, *optional*, defaults to `1e-3`):
Alignment solver tolerance. The solver stops when the tolerance is reached.
max_res (`int`, *optional*, defaults to `1024`):
Resolution at which the alignment is performed; `None` matches the `processing_resolution`.
Returns:
A tensor of aligned and ensembled depth maps and optionally a tensor of uncertainties of the same shape:
`(1, 1, H, W)`.
"""
if depth.dim() != 4 or depth.shape[1] != 1:
raise ValueError(f"Expecting 4D tensor of shape [B,1,H,W]; got {depth.shape}.")
if reduction not in ("mean", "median"):
raise ValueError(f"Unrecognized reduction method: {reduction}.")
if not scale_invariant and shift_invariant:
raise ValueError("Pure shift-invariant ensembling is not supported.")
def init_param(depth: torch.Tensor):
init_min = depth.reshape(ensemble_size, -1).min(dim=1).values
init_max = depth.reshape(ensemble_size, -1).max(dim=1).values
if scale_invariant and shift_invariant:
init_s = 1.0 / (init_max - init_min).clamp(min=1e-6)
init_t = -init_s * init_min
param = torch.cat((init_s, init_t)).cpu().numpy()
elif scale_invariant:
init_s = 1.0 / init_max.clamp(min=1e-6)
param = init_s.cpu().numpy()
else:
raise ValueError("Unrecognized alignment.")
return param
def align(depth: torch.Tensor, param: np.ndarray) -> torch.Tensor:
if scale_invariant and shift_invariant:
s, t = np.split(param, 2)
s = torch.from_numpy(s).to(depth).view(ensemble_size, 1, 1, 1)
t = torch.from_numpy(t).to(depth).view(ensemble_size, 1, 1, 1)
out = depth * s + t
elif scale_invariant:
s = torch.from_numpy(param).to(depth).view(ensemble_size, 1, 1, 1)
out = depth * s
else:
raise ValueError("Unrecognized alignment.")
return out
def ensemble(
depth_aligned: torch.Tensor, return_uncertainty: bool = False
) -> Tuple[torch.Tensor, Optional[torch.Tensor]]:
uncertainty = None
if reduction == "mean":
prediction = torch.mean(depth_aligned, dim=0, keepdim=True)
if return_uncertainty:
uncertainty = torch.std(depth_aligned, dim=0, keepdim=True)
elif reduction == "median":
prediction = torch.median(depth_aligned, dim=0, keepdim=True).values
if return_uncertainty:
uncertainty = torch.median(
torch.abs(depth_aligned - prediction), dim=0, keepdim=True
).values
else:
raise ValueError(f"Unrecognized reduction method: {reduction}.")
return prediction, uncertainty
def cost_fn(param: np.ndarray, depth: torch.Tensor) -> float:
cost = 0.0
depth_aligned = align(depth, param)
for i, j in torch.combinations(torch.arange(ensemble_size)):
diff = depth_aligned[i] - depth_aligned[j]
cost += (diff**2).mean().sqrt().item()
if regularizer_strength > 0:
prediction, _ = ensemble(depth_aligned, return_uncertainty=False)
err_near = (0.0 - prediction.min()).abs().item()
err_far = (1.0 - prediction.max()).abs().item()
cost += (err_near + err_far) * regularizer_strength
return cost
def compute_param(depth: torch.Tensor):
import scipy
depth_to_align = depth.to(torch.float32)
if max_res is not None and max(depth_to_align.shape[2:]) > max_res:
depth_to_align = resize_max_res(
depth_to_align, max_res, get_tv_resample_method("nearest-exact")
)
param = init_param(depth_to_align)
res = scipy.optimize.minimize(
partial(cost_fn, depth=depth_to_align),
param,
method="BFGS",
tol=tol,
options={"maxiter": max_iter, "disp": False},
)
return res.x
requires_aligning = scale_invariant or shift_invariant
ensemble_size = depth.shape[0]
if requires_aligning:
param = compute_param(depth)
depth = align(depth, param)
depth, uncertainty = ensemble(depth, return_uncertainty=output_uncertainty)
depth_max = depth.max()
if scale_invariant and shift_invariant:
depth_min = depth.min()
elif scale_invariant:
depth_min = 0
else:
raise ValueError("Unrecognized alignment.")
depth_range = (depth_max - depth_min).clamp(min=1e-6)
depth = (depth - depth_min) / depth_range
if output_uncertainty:
uncertainty /= depth_range
return depth, uncertainty # [1,1,H,W], [1,1,H,W]
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