Source code for kornia.geometry.depth

"""Module containing operators to work on RGB-Depth images."""
from typing import Union

import torch
import torch.nn.functional as F

from kornia.core import Module, Tensor, concatenate, tensor
from kornia.utils import create_meshgrid

from .camera import PinholeCamera, cam2pixel, pixel2cam, project_points, unproject_points
from .conversions import normalize_pixel_coordinates
from .linalg import compose_transformations, convert_points_to_homogeneous, inverse_transformation, transform_points

__all__ = ["depth_to_3d", "depth_to_normals", "warp_frame_depth", "depth_warp", "DepthWarper"]

[docs]def depth_to_3d(depth: Tensor, camera_matrix: Tensor, normalize_points: bool = False) -> Tensor:
"""Compute a 3d point per pixel given its depth value and the camera intrinsics.

Args:
depth: image tensor containing a depth value per pixel with shape :math:(B, 1, H, W).
camera_matrix: tensor containing the camera intrinsics with shape :math:(B, 3, 3).
normalize_points: whether to normalise the pointcloud. This must be set to True when the depth is
represented as the Euclidean ray length from the camera position.

Return:
tensor with a 3d point per pixel of the same resolution as the input :math:(B, 3, H, W).

Example:
>>> depth = torch.rand(1, 1, 4, 4)
>>> K = torch.eye(3)[None]
>>> depth_to_3d(depth, K).shape
torch.Size([1, 3, 4, 4])
"""
if not isinstance(depth, Tensor):
raise TypeError(f"Input depht type is not a Tensor. Got {type(depth)}.")

if not (len(depth.shape) == 4 and depth.shape[-3] == 1):
raise ValueError(f"Input depth musth have a shape (B, 1, H, W). Got: {depth.shape}")

if not isinstance(camera_matrix, Tensor):
raise TypeError(f"Input camera_matrix type is not a Tensor. " f"Got {type(camera_matrix)}.")

if not (len(camera_matrix.shape) == 3 and camera_matrix.shape[-2:] == (3, 3)):
raise ValueError(f"Input camera_matrix must have a shape (B, 3, 3). " f"Got: {camera_matrix.shape}.")

# create base coordinates grid
_, _, height, width = depth.shape
points_2d: Tensor = create_meshgrid(height, width, normalized_coordinates=False)  # 1xHxWx2
points_2d = points_2d.to(depth.device).to(depth.dtype)

# depth should come in Bx1xHxW
points_depth: Tensor = depth.permute(0, 2, 3, 1)  # 1xHxWx1

# project pixels to camera frame
camera_matrix_tmp: Tensor = camera_matrix[:, None, None]  # Bx1x1x3x3
points_3d: Tensor = unproject_points(
points_2d, points_depth, camera_matrix_tmp, normalize=normalize_points
)  # BxHxWx3

return points_3d.permute(0, 3, 1, 2)  # Bx3xHxW

[docs]def depth_to_normals(depth: Tensor, camera_matrix: Tensor, normalize_points: bool = False) -> Tensor:
"""Compute the normal surface per pixel.

Args:
depth: image tensor containing a depth value per pixel with shape :math:(B, 1, H, W).
camera_matrix: tensor containing the camera intrinsics with shape :math:(B, 3, 3).
normalize_points: whether to normalise the pointcloud. This must be set to True when the depth is
represented as the Euclidean ray length from the camera position.

Return:
tensor with a normal surface vector per pixel of the same resolution as the input :math:(B, 3, H, W).

Example:
>>> depth = torch.rand(1, 1, 4, 4)
>>> K = torch.eye(3)[None]
>>> depth_to_normals(depth, K).shape
torch.Size([1, 3, 4, 4])
"""
if not isinstance(depth, Tensor):
raise TypeError(f"Input depht type is not a Tensor. Got {type(depth)}.")

if not (len(depth.shape) == 4 and depth.shape[-3] == 1):
raise ValueError(f"Input depth musth have a shape (B, 1, H, W). Got: {depth.shape}")

if not isinstance(camera_matrix, Tensor):
raise TypeError(f"Input camera_matrix type is not a Tensor. " f"Got {type(camera_matrix)}.")

if not (len(camera_matrix.shape) == 3 and camera_matrix.shape[-2:] == (3, 3)):
raise ValueError(f"Input camera_matrix must have a shape (B, 3, 3). " f"Got: {camera_matrix.shape}.")

# compute the 3d points from depth
xyz: Tensor = depth_to_3d(depth, camera_matrix, normalize_points)  # Bx3xHxW

# compute the pointcloud spatial gradients

# compute normals

normals: Tensor = torch.cross(a, b, dim=1)  # Bx3xHxW
return F.normalize(normals, dim=1, p=2)

[docs]def warp_frame_depth(
image_src: Tensor, depth_dst: Tensor, src_trans_dst: Tensor, camera_matrix: Tensor, normalize_points: bool = False
) -> Tensor:
"""Warp a tensor from a source to destination frame by the depth in the destination.

Compute 3d points from the depth, transform them using given transformation, then project the point cloud to an
image plane.

Args:
image_src: image tensor in the source frame with shape :math:(B,D,H,W).
depth_dst: depth tensor in the destination frame with shape :math:(B,1,H,W).
src_trans_dst: transformation matrix from destination to source with shape :math:(B,4,4).
camera_matrix: tensor containing the camera intrinsics with shape :math:(B,3,3).
normalize_points: whether to normalise the pointcloud. This must be set to True when the depth
is represented as the Euclidean ray length from the camera position.

Return:
the warped tensor in the source frame with shape :math:(B,3,H,W).
"""
if not isinstance(image_src, Tensor):
raise TypeError(f"Input image_src type is not a Tensor. Got {type(image_src)}.")

if not len(image_src.shape) == 4:
raise ValueError(f"Input image_src musth have a shape (B, D, H, W). Got: {image_src.shape}")

if not isinstance(depth_dst, Tensor):
raise TypeError(f"Input depht_dst type is not a Tensor. Got {type(depth_dst)}.")

if not (len(depth_dst.shape) == 4 and depth_dst.shape[-3] == 1):
raise ValueError(f"Input depth_dst musth have a shape (B, 1, H, W). Got: {depth_dst.shape}")

if not isinstance(src_trans_dst, Tensor):
raise TypeError(f"Input src_trans_dst type is not a Tensor. " f"Got {type(src_trans_dst)}.")

if not (len(src_trans_dst.shape) == 3 and src_trans_dst.shape[-2:] == (4, 4)):
raise ValueError(f"Input src_trans_dst must have a shape (B, 4, 4). " f"Got: {src_trans_dst.shape}.")

if not isinstance(camera_matrix, Tensor):
raise TypeError(f"Input camera_matrix type is not a Tensor. " f"Got {type(camera_matrix)}.")

if not (len(camera_matrix.shape) == 3 and camera_matrix.shape[-2:] == (3, 3)):
raise ValueError(f"Input camera_matrix must have a shape (B, 3, 3). " f"Got: {camera_matrix.shape}.")
# unproject source points to camera frame
points_3d_dst: Tensor = depth_to_3d(depth_dst, camera_matrix, normalize_points)  # Bx3xHxW

# transform points from source to destination
points_3d_dst = points_3d_dst.permute(0, 2, 3, 1)  # BxHxWx3

# apply transformation to the 3d points
points_3d_src = transform_points(src_trans_dst[:, None], points_3d_dst)  # BxHxWx3

# project back to pixels
camera_matrix_tmp: Tensor = camera_matrix[:, None, None]  # Bx1x1xHxW
points_2d_src: Tensor = project_points(points_3d_src, camera_matrix_tmp)  # BxHxWx2

# normalize points between [-1 / 1]
height, width = depth_dst.shape[-2:]
points_2d_src_norm: Tensor = normalize_pixel_coordinates(points_2d_src, height, width)  # BxHxWx2

return F.grid_sample(image_src, points_2d_src_norm, align_corners=True)

class DepthWarper(Module):
r"""Warp a patch by depth.

.. math::
P_{src}^{\{dst\}} = K_{dst} * T_{src}^{\{dst\}}

I_{src} = \\omega(I_{dst}, P_{src}^{\{dst\}}, D_{src})

Args:
pinholes_dst: the pinhole models for the destination frame.
height: the height of the image to warp.
width: the width of the image to warp.
mode: interpolation mode to calculate output values 'bilinear' | 'nearest'.
padding_mode: padding mode for outside grid values 'zeros' | 'border' | 'reflection'.
align_corners: interpolation flag.
"""

def __init__(
self,
pinhole_dst: PinholeCamera,
height: int,
width: int,
mode: str = 'bilinear',
align_corners: bool = True,
):
super().__init__()
# constructor members
self.width: int = width
self.height: int = height
self.mode: str = mode
self.eps = 1e-6
self.align_corners: bool = align_corners

# state members
self._pinhole_dst: PinholeCamera = pinhole_dst
self._pinhole_src: Union[None, PinholeCamera] = None
self._dst_proj_src: Union[None, Tensor] = None

self.grid: Tensor = self._create_meshgrid(height, width)

@staticmethod
def _create_meshgrid(height: int, width: int) -> Tensor:
grid: Tensor = create_meshgrid(height, width, normalized_coordinates=False)  # 1xHxWx2
return convert_points_to_homogeneous(grid)  # append ones to last dim

def compute_projection_matrix(self, pinhole_src: PinholeCamera) -> 'DepthWarper':
r"""Compute the projection matrix from the source to destination frame."""
if not isinstance(self._pinhole_dst, PinholeCamera):
raise TypeError(
"Member self._pinhole_dst expected to be of class "
"PinholeCamera. Got {}".format(type(self._pinhole_dst))
)
if not isinstance(pinhole_src, PinholeCamera):
raise TypeError(
"Argument pinhole_src expected to be of class " "PinholeCamera. Got {}".format(type(pinhole_src))
)
# compute the relative pose between the non reference and the reference
# camera frames.
dst_trans_src: Tensor = compose_transformations(
self._pinhole_dst.extrinsics, inverse_transformation(pinhole_src.extrinsics)
)

# compute the projection matrix between the non reference cameras and
# the reference.
dst_proj_src: Tensor = torch.matmul(self._pinhole_dst.intrinsics, dst_trans_src)

# update class members
self._pinhole_src = pinhole_src
self._dst_proj_src = dst_proj_src
return self

def _compute_projection(self, x, y, invd):
if self._dst_proj_src is None or self._pinhole_src is None:

point = tensor([[[x], [y], [invd], [1.0]]], device=self._dst_proj_src.device, dtype=self._dst_proj_src.dtype)
flow = torch.matmul(self._dst_proj_src, point)
z = 1.0 / flow[:, 2]
x = flow[:, 0] * z
y = flow[:, 1] * z
return concatenate([x, y], 1)

def compute_subpixel_step(self) -> Tensor:
"""Compute the required inverse depth step to achieve sub pixel accurate sampling of the depth cost volume,
per camera.

Szeliski, Richard, and Daniel Scharstein. "Symmetric sub-pixel stereo matching." European Conference on Computer
Vision. Springer Berlin Heidelberg, 2002.
"""
delta_d = 0.01
xy_m1 = self._compute_projection(self.width / 2, self.height / 2, 1.0 - delta_d)
xy_p1 = self._compute_projection(self.width / 2, self.height / 2, 1.0 + delta_d)
dx = torch.norm((xy_p1 - xy_m1), 2, dim=-1) / 2.0
dxdd = dx / (delta_d)  # pixel*(1/meter)
# half pixel sampling, we're interested in the min for all cameras

def warp_grid(self, depth_src: Tensor) -> Tensor:
"""Compute a grid for warping a given the depth from the reference pinhole camera.

The function compute_projection_matrix has to be called beforehand in order to have precomputed the relative
projection matrices encoding the relative pose and the intrinsics between the reference and a non reference
camera.
"""
# TODO: add type and value checkings
if self._dst_proj_src is None or self._pinhole_src is None:

if len(depth_src.shape) != 4:
raise ValueError("Input depth_src has to be in the shape of " "Bx1xHxW. Got {}".format(depth_src.shape))

# unpack depth attributes
batch_size, _, _, _ = depth_src.shape
device: torch.device = depth_src.device
dtype: torch.dtype = depth_src.dtype

# expand the base coordinate grid according to the input batch size
pixel_coords: Tensor = self.grid.to(device=device, dtype=dtype).expand(batch_size, -1, -1, -1)  # BxHxWx3

# reproject the pixel coordinates to the camera frame
cam_coords_src: Tensor = pixel2cam(
depth_src, self._pinhole_src.intrinsics_inverse().to(device=device, dtype=dtype), pixel_coords
)  # BxHxWx3

# reproject the camera coordinates to the pixel
pixel_coords_src: Tensor = cam2pixel(
cam_coords_src, self._dst_proj_src.to(device=device, dtype=dtype)
)  # (B*N)xHxWx2

# normalize between -1 and 1 the coordinates
pixel_coords_src_norm: Tensor = normalize_pixel_coordinates(pixel_coords_src, self.height, self.width)
return pixel_coords_src_norm

def forward(self, depth_src: Tensor, patch_dst: Tensor) -> Tensor:
"""Warp a tensor from destination frame to reference given the depth in the reference frame.

Args:
depth_src: the depth in the reference frame. The tensor must have a shape :math:(B, 1, H, W).
patch_dst: the patch in the destination frame. The tensor must have a shape :math:(B, C, H, W).

Return:
the warped patch from destination frame to reference.

Shape:
- Output: :math:(N, C, H, W) where C = number of channels.

Example:
>>> # pinholes camera models
>>> pinhole_dst = PinholeCamera(torch.randn(1, 4, 4), torch.randn(1, 4, 4),
... torch.tensor([32]), torch.tensor([32]))
>>> pinhole_src = PinholeCamera(torch.randn(1, 4, 4), torch.randn(1, 4, 4),
... torch.tensor([32]), torch.tensor([32]))
>>> # create the depth warper, compute the projection matrix
>>> warper = DepthWarper(pinhole_dst, 32, 32)
>>> _ = warper.compute_projection_matrix(pinhole_src)
>>> # warp the destination frame to reference by depth
>>> depth_src = torch.ones(1, 1, 32, 32)  # Nx1xHxW
>>> image_dst = torch.rand(1, 3, 32, 32)  # NxCxHxW
>>> image_src = warper(depth_src, image_dst)  # NxCxHxW
"""
return F.grid_sample(
patch_dst,
self.warp_grid(depth_src),
mode=self.mode,
align_corners=self.align_corners,
)

def depth_warp(
pinhole_dst: PinholeCamera,
pinhole_src: PinholeCamera,
depth_src: Tensor,
patch_dst: Tensor,
height: int,
width: int,
align_corners: bool = True,
):
r"""Function that warps a tensor from destination frame to reference given the depth in the reference frame.

See :class:~kornia.geometry.warp.DepthWarper for details.

Example:
>>> # pinholes camera models
>>> pinhole_dst = PinholeCamera(torch.randn(1, 4, 4), torch.randn(1, 4, 4),
... torch.tensor([32]), torch.tensor([32]))
>>> pinhole_src = PinholeCamera(torch.randn(1, 4, 4), torch.randn(1, 4, 4),
... torch.tensor([32]), torch.tensor([32]))
>>> # warp the destination frame to reference by depth
>>> depth_src = torch.ones(1, 1, 32, 32)  # Nx1xHxW
>>> image_dst = torch.rand(1, 3, 32, 32)  # NxCxHxW
>>> image_src = depth_warp(pinhole_dst, pinhole_src, depth_src, image_dst, 32, 32)  # NxCxHxW
"""
warper = DepthWarper(pinhole_dst, height, width, align_corners=align_corners)
warper.compute_projection_matrix(pinhole_src)
return warper(depth_src, patch_dst)