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# Copyright (c) Meta Platforms, Inc. and affiliates.
# All rights reserved.
#
# This source code is licensed under the license found in the
# LICENSE file in the root directory of this source tree.
#
# Modified from https://github.com/facebookresearch/vggt
from typing import Tuple, Union
import torch
import torch.nn.functional as F
def get_2d_sincos_pos_embed(
embed_dim: int, grid_size: Union[int, Tuple[int, int]], return_grid=False
) -> torch.Tensor:
"""
This function initializes a grid and generates a 2D positional embedding using sine and cosine functions.
It is a wrapper of get_2d_sincos_pos_embed_from_grid.
Args:
- embed_dim: The embedding dimension.
- grid_size: The grid size.
Returns:
- pos_embed: The generated 2D positional embedding.
"""
if isinstance(grid_size, tuple):
grid_size_h, grid_size_w = grid_size
else:
grid_size_h = grid_size_w = grid_size
grid_h = torch.arange(grid_size_h, dtype=torch.float)
grid_w = torch.arange(grid_size_w, dtype=torch.float)
grid = torch.meshgrid(grid_w, grid_h, indexing="xy")
grid = torch.stack(grid, dim=0)
grid = grid.reshape([2, 1, grid_size_h, grid_size_w])
pos_embed = get_2d_sincos_pos_embed_from_grid(embed_dim, grid)
if return_grid:
return (
pos_embed.reshape(1, grid_size_h, grid_size_w, -1).permute(0, 3, 1, 2),
grid,
)
return pos_embed.reshape(1, grid_size_h, grid_size_w, -1).permute(0, 3, 1, 2)
def get_2d_sincos_pos_embed_from_grid(
embed_dim: int, grid: torch.Tensor
) -> torch.Tensor:
"""
This function generates a 2D positional embedding from a given grid using sine and cosine functions.
Args:
- embed_dim: The embedding dimension.
- grid: The grid to generate the embedding from.
Returns:
- emb: The generated 2D positional embedding.
"""
assert embed_dim % 2 == 0
# use half of dimensions to encode grid_h
emb_h = get_1d_sincos_pos_embed_from_grid(embed_dim // 2, grid[0]) # (H*W, D/2)
emb_w = get_1d_sincos_pos_embed_from_grid(embed_dim // 2, grid[1]) # (H*W, D/2)
emb = torch.cat([emb_h, emb_w], dim=2) # (H*W, D)
return emb
def get_1d_sincos_pos_embed_from_grid(
embed_dim: int, pos: torch.Tensor
) -> torch.Tensor:
"""
This function generates a 1D positional embedding from a given grid using sine and cosine functions.
Args:
- embed_dim: The embedding dimension.
- pos: The position to generate the embedding from.
Returns:
- emb: The generated 1D positional embedding.
"""
assert embed_dim % 2 == 0
omega = torch.arange(embed_dim // 2, dtype=torch.double)
omega /= embed_dim / 2.0
omega = 1.0 / 10000**omega # (D/2,)
pos = pos.reshape(-1) # (M,)
out = torch.einsum("m,d->md", pos, omega) # (M, D/2), outer product
emb_sin = torch.sin(out) # (M, D/2)
emb_cos = torch.cos(out) # (M, D/2)
emb = torch.cat([emb_sin, emb_cos], dim=1) # (M, D)
return emb[None].float()
def get_2d_embedding(xy: torch.Tensor, C: int, cat_coords: bool = True) -> torch.Tensor:
"""
This function generates a 2D positional embedding from given coordinates using sine and cosine functions.
Args:
- xy: The coordinates to generate the embedding from.
- C: The size of the embedding.
- cat_coords: A flag to indicate whether to concatenate the original coordinates to the embedding.
Returns:
- pe: The generated 2D positional embedding.
"""
B, N, D = xy.shape
assert D == 2
x = xy[:, :, 0:1]
y = xy[:, :, 1:2]
div_term = (
torch.arange(0, C, 2, device=xy.device, dtype=torch.float32) * (1000.0 / C)
).reshape(1, 1, int(C / 2))
pe_x = torch.zeros(B, N, C, device=xy.device, dtype=torch.float32)
pe_y = torch.zeros(B, N, C, device=xy.device, dtype=torch.float32)
pe_x[:, :, 0::2] = torch.sin(x * div_term)
pe_x[:, :, 1::2] = torch.cos(x * div_term)
pe_y[:, :, 0::2] = torch.sin(y * div_term)
pe_y[:, :, 1::2] = torch.cos(y * div_term)
pe = torch.cat([pe_x, pe_y], dim=2) # (B, N, C*3)
if cat_coords:
pe = torch.cat([xy, pe], dim=2) # (B, N, C*3+3)
return pe
def bilinear_sampler(input, coords, align_corners=True, padding_mode="border"):
r"""Sample a tensor using bilinear interpolation
`bilinear_sampler(input, coords)` samples a tensor :attr:`input` at
coordinates :attr:`coords` using bilinear interpolation. It is the same
as `torch.nn.functional.grid_sample()` but with a different coordinate
convention.
The input tensor is assumed to be of shape :math:`(B, C, H, W)`, where
:math:`B` is the batch size, :math:`C` is the number of channels,
:math:`H` is the height of the image, and :math:`W` is the width of the
image. The tensor :attr:`coords` of shape :math:`(B, H_o, W_o, 2)` is
interpreted as an array of 2D point coordinates :math:`(x_i,y_i)`.
Alternatively, the input tensor can be of size :math:`(B, C, T, H, W)`,
in which case sample points are triplets :math:`(t_i,x_i,y_i)`. Note
that in this case the order of the components is slightly different
from `grid_sample()`, which would expect :math:`(x_i,y_i,t_i)`.
If `align_corners` is `True`, the coordinate :math:`x` is assumed to be
in the range :math:`[0,W-1]`, with 0 corresponding to the center of the
left-most image pixel :math:`W-1` to the center of the right-most
pixel.
If `align_corners` is `False`, the coordinate :math:`x` is assumed to
be in the range :math:`[0,W]`, with 0 corresponding to the left edge of
the left-most pixel :math:`W` to the right edge of the right-most
pixel.
Similar conventions apply to the :math:`y` for the range
:math:`[0,H-1]` and :math:`[0,H]` and to :math:`t` for the range
:math:`[0,T-1]` and :math:`[0,T]`.
Args:
input (Tensor): batch of input images.
coords (Tensor): batch of coordinates.
align_corners (bool, optional): Coordinate convention. Defaults to `True`.
padding_mode (str, optional): Padding mode. Defaults to `"border"`.
Returns:
Tensor: sampled points.
"""
coords = coords.detach().clone()
############################################################
# IMPORTANT:
coords = coords.to(input.device).to(input.dtype)
############################################################
sizes = input.shape[2:]
assert len(sizes) in [2, 3]
if len(sizes) == 3:
# t x y -> x y t to match dimensions T H W in grid_sample
coords = coords[..., [1, 2, 0]]
if align_corners:
scale = torch.tensor(
[2 / max(size - 1, 1) for size in reversed(sizes)],
device=coords.device,
dtype=coords.dtype,
)
else:
scale = torch.tensor(
[2 / size for size in reversed(sizes)],
device=coords.device,
dtype=coords.dtype,
)
coords.mul_(scale) # coords = coords * scale
coords.sub_(1) # coords = coords - 1
return F.grid_sample(
input, coords, align_corners=align_corners, padding_mode=padding_mode
)
def sample_features4d(input, coords):
r"""Sample spatial features
`sample_features4d(input, coords)` samples the spatial features
:attr:`input` represented by a 4D tensor :math:`(B, C, H, W)`.
The field is sampled at coordinates :attr:`coords` using bilinear
interpolation. :attr:`coords` is assumed to be of shape :math:`(B, R,
2)`, where each sample has the format :math:`(x_i, y_i)`. This uses the
same convention as :func:`bilinear_sampler` with `align_corners=True`.
The output tensor has one feature per point, and has shape :math:`(B,
R, C)`.
Args:
input (Tensor): spatial features.
coords (Tensor): points.
Returns:
Tensor: sampled features.
"""
B, _, _, _ = input.shape
# B R 2 -> B R 1 2
coords = coords.unsqueeze(2)
# B C R 1
feats = bilinear_sampler(input, coords)
return feats.permute(0, 2, 1, 3).view(
B, -1, feats.shape[1] * feats.shape[3]
) # B C R 1 -> B R C
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