# @lint-ignore-every LICENSELINT
# Adapted from https://github.com/lioryariv/idr
# Copyright (c) 2020 Lior Yariv
# pyre-unsafe
from typing import Any, Callable, Tuple
import torch
import torch.nn as nn
from pytorch3d.implicitron.tools.config import Configurable
[docs]
class RayTracing(Configurable, nn.Module):
"""
Finds the intersection points of rays with the implicit surface defined
by a signed distance function (SDF). The algorithm follows the pipeline:
1. Initialise start and end points on rays by the intersections with
the circumscribing sphere.
2. Run sphere tracing from both ends.
3. Divide the untraced segments of non-convergent rays into uniform
intervals and find the one with the sign transition.
4. Run the secant method to estimate the point of the sign transition.
Args:
object_bounding_sphere: The radius of the initial sphere circumscribing
the object.
sdf_threshold: Absolute SDF value small enough for the sphere tracer
to consider it a surface.
line_search_step: Length of the backward correction on sphere tracing
iterations.
line_step_iters: Number of backward correction iterations.
sphere_tracing_iters: Maximum number of sphere tracing iterations
(the actual number of iterations may be smaller if all ray
intersections are found).
n_steps: Number of intervals sampled for unconvergent rays.
n_secant_steps: Number of iterations in the secant algorithm.
"""
object_bounding_sphere: float = 1.0
sdf_threshold: float = 5.0e-5
line_search_step: float = 0.5
line_step_iters: int = 1
sphere_tracing_iters: int = 10
n_steps: int = 100
n_secant_steps: int = 8
[docs]
def forward(
self,
sdf: Callable[[torch.Tensor], torch.Tensor],
cam_loc: torch.Tensor,
object_mask: torch.BoolTensor,
ray_directions: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""
Args:
sdf: A callable that takes a (N, 3) tensor of points and returns
a tensor of (N,) SDF values.
cam_loc: A tensor of (B, N, 3) ray origins.
object_mask: A (N, 3) tensor of indicators whether a sampled pixel
corresponds to the rendered object or background.
ray_directions: A tensor of (B, N, 3) ray directions.
Returns:
curr_start_points: A tensor of (B*N, 3) found intersection points
with the implicit surface.
network_object_mask: A tensor of (B*N,) indicators denoting whether
intersections were found.
acc_start_dis: A tensor of (B*N,) distances from the ray origins
to intersrection points.
"""
batch_size, num_pixels, _ = ray_directions.shape
device = cam_loc.device
sphere_intersections, mask_intersect = _get_sphere_intersection(
cam_loc, ray_directions, r=self.object_bounding_sphere
)
(
curr_start_points,
unfinished_mask_start,
acc_start_dis,
acc_end_dis,
min_dis,
max_dis,
) = self.sphere_tracing(
batch_size,
num_pixels,
sdf,
cam_loc,
ray_directions,
mask_intersect,
sphere_intersections,
)
network_object_mask = acc_start_dis < acc_end_dis
# The non convergent rays should be handled by the sampler
sampler_mask = unfinished_mask_start
sampler_net_obj_mask = torch.zeros_like(
sampler_mask, dtype=torch.bool, device=device
)
if sampler_mask.sum() > 0:
sampler_min_max = torch.zeros((batch_size, num_pixels, 2), device=device)
sampler_min_max.reshape(-1, 2)[sampler_mask, 0] = acc_start_dis[
sampler_mask
]
sampler_min_max.reshape(-1, 2)[sampler_mask, 1] = acc_end_dis[sampler_mask]
sampler_pts, sampler_net_obj_mask, sampler_dists = self.ray_sampler(
sdf, cam_loc, object_mask, ray_directions, sampler_min_max, sampler_mask
)
curr_start_points[sampler_mask] = sampler_pts[sampler_mask]
acc_start_dis[sampler_mask] = sampler_dists[sampler_mask]
network_object_mask[sampler_mask] = sampler_net_obj_mask[sampler_mask]
if not self.training:
return curr_start_points, network_object_mask, acc_start_dis
# in case we are training, we are updating curr_start_points and acc_start_dis for
ray_directions = ray_directions.reshape(-1, 3)
mask_intersect = mask_intersect.reshape(-1)
# pyre-fixme[9]: object_mask has type `BoolTensor`; used as `Tensor`.
object_mask = object_mask.reshape(-1)
in_mask = ~network_object_mask & object_mask & ~sampler_mask
out_mask = ~object_mask & ~sampler_mask
mask_left_out = (in_mask | out_mask) & ~mask_intersect
if (
mask_left_out.sum() > 0
): # project the origin to the not intersect points on the sphere
cam_left_out = cam_loc.reshape(-1, 3)[mask_left_out]
rays_left_out = ray_directions[mask_left_out]
acc_start_dis[mask_left_out] = -torch.bmm(
rays_left_out.view(-1, 1, 3), cam_left_out.view(-1, 3, 1)
).squeeze()
curr_start_points[mask_left_out] = (
cam_left_out + acc_start_dis[mask_left_out].unsqueeze(1) * rays_left_out
)
mask = (in_mask | out_mask) & mask_intersect
if mask.sum() > 0:
min_dis[network_object_mask & out_mask] = acc_start_dis[
network_object_mask & out_mask
]
min_mask_points, min_mask_dist = self.minimal_sdf_points(
sdf, cam_loc, ray_directions, mask, min_dis, max_dis
)
curr_start_points[mask] = min_mask_points
acc_start_dis[mask] = min_mask_dist
return curr_start_points, network_object_mask, acc_start_dis
[docs]
def sphere_tracing(
self,
batch_size: int,
num_pixels: int,
sdf: Callable[[torch.Tensor], torch.Tensor],
cam_loc: torch.Tensor,
ray_directions: torch.Tensor,
mask_intersect: torch.Tensor,
sphere_intersections: torch.Tensor,
) -> Tuple[Any, Any, Any, Any, Any, Any]:
"""
Run sphere tracing algorithm for max iterations
from both sides of unit sphere intersection
Args:
batch_size:
num_pixels:
sdf:
cam_loc:
ray_directions:
mask_intersect:
sphere_intersections:
Returns:
curr_start_points:
unfinished_mask_start:
acc_start_dis:
acc_end_dis:
min_dis:
max_dis:
"""
device = cam_loc.device
sphere_intersections_points = (
cam_loc[..., None, :]
+ sphere_intersections[..., None] * ray_directions[..., None, :]
)
unfinished_mask_start = mask_intersect.reshape(-1).clone()
unfinished_mask_end = mask_intersect.reshape(-1).clone()
# Initialize start current points
curr_start_points = torch.zeros(batch_size * num_pixels, 3, device=device)
curr_start_points[unfinished_mask_start] = sphere_intersections_points[
:, :, 0, :
].reshape(-1, 3)[unfinished_mask_start]
acc_start_dis = torch.zeros(batch_size * num_pixels, device=device)
acc_start_dis[unfinished_mask_start] = sphere_intersections.reshape(-1, 2)[
unfinished_mask_start, 0
]
# Initialize end current points
curr_end_points = torch.zeros(batch_size * num_pixels, 3, device=device)
curr_end_points[unfinished_mask_end] = sphere_intersections_points[
:, :, 1, :
].reshape(-1, 3)[unfinished_mask_end]
acc_end_dis = torch.zeros(batch_size * num_pixels, device=device)
acc_end_dis[unfinished_mask_end] = sphere_intersections.reshape(-1, 2)[
unfinished_mask_end, 1
]
# Initialise min and max depth
min_dis = acc_start_dis.clone()
max_dis = acc_end_dis.clone()
# Iterate on the rays (from both sides) till finding a surface
iters = 0
# TODO: sdf should also pass info about batches
next_sdf_start = torch.zeros_like(acc_start_dis)
next_sdf_start[unfinished_mask_start] = sdf(
curr_start_points[unfinished_mask_start]
)
next_sdf_end = torch.zeros_like(acc_end_dis)
next_sdf_end[unfinished_mask_end] = sdf(curr_end_points[unfinished_mask_end])
while True:
# Update sdf
curr_sdf_start = torch.zeros_like(acc_start_dis)
curr_sdf_start[unfinished_mask_start] = next_sdf_start[
unfinished_mask_start
]
curr_sdf_start[curr_sdf_start <= self.sdf_threshold] = 0
curr_sdf_end = torch.zeros_like(acc_end_dis)
curr_sdf_end[unfinished_mask_end] = next_sdf_end[unfinished_mask_end]
curr_sdf_end[curr_sdf_end <= self.sdf_threshold] = 0
# Update masks
unfinished_mask_start = unfinished_mask_start & (
curr_sdf_start > self.sdf_threshold
)
unfinished_mask_end = unfinished_mask_end & (
curr_sdf_end > self.sdf_threshold
)
if (
unfinished_mask_start.sum() == 0 and unfinished_mask_end.sum() == 0
) or iters == self.sphere_tracing_iters:
break
iters += 1
# Make step
# Update distance
acc_start_dis = acc_start_dis + curr_sdf_start
acc_end_dis = acc_end_dis - curr_sdf_end
# Update points
curr_start_points = (
cam_loc
+ acc_start_dis.reshape(batch_size, num_pixels, 1) * ray_directions
).reshape(-1, 3)
curr_end_points = (
cam_loc
+ acc_end_dis.reshape(batch_size, num_pixels, 1) * ray_directions
).reshape(-1, 3)
# Fix points which wrongly crossed the surface
next_sdf_start = torch.zeros_like(acc_start_dis)
next_sdf_start[unfinished_mask_start] = sdf(
curr_start_points[unfinished_mask_start]
)
next_sdf_end = torch.zeros_like(acc_end_dis)
next_sdf_end[unfinished_mask_end] = sdf(
curr_end_points[unfinished_mask_end]
)
not_projected_start = next_sdf_start < 0
not_projected_end = next_sdf_end < 0
not_proj_iters = 0
while (
not_projected_start.sum() > 0 or not_projected_end.sum() > 0
) and not_proj_iters < self.line_step_iters:
# Step backwards
acc_start_dis[not_projected_start] -= (
(1 - self.line_search_step) / (2**not_proj_iters)
) * curr_sdf_start[not_projected_start]
curr_start_points[not_projected_start] = (
cam_loc
+ acc_start_dis.reshape(batch_size, num_pixels, 1) * ray_directions
).reshape(-1, 3)[not_projected_start]
acc_end_dis[not_projected_end] += (
(1 - self.line_search_step) / (2**not_proj_iters)
) * curr_sdf_end[not_projected_end]
curr_end_points[not_projected_end] = (
cam_loc
+ acc_end_dis.reshape(batch_size, num_pixels, 1) * ray_directions
).reshape(-1, 3)[not_projected_end]
# Calc sdf
next_sdf_start[not_projected_start] = sdf(
curr_start_points[not_projected_start]
)
next_sdf_end[not_projected_end] = sdf(
curr_end_points[not_projected_end]
)
# Update mask
not_projected_start = next_sdf_start < 0
not_projected_end = next_sdf_end < 0
not_proj_iters += 1
unfinished_mask_start = unfinished_mask_start & (
acc_start_dis < acc_end_dis
)
unfinished_mask_end = unfinished_mask_end & (acc_start_dis < acc_end_dis)
return (
curr_start_points,
unfinished_mask_start,
acc_start_dis,
acc_end_dis,
min_dis,
max_dis,
)
[docs]
def ray_sampler(
self,
sdf: Callable[[torch.Tensor], torch.Tensor],
cam_loc: torch.Tensor,
object_mask: torch.Tensor,
ray_directions: torch.Tensor,
sampler_min_max: torch.Tensor,
sampler_mask: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
"""
Sample the ray in a given range and run secant on rays which have sign transition.
Args:
sdf:
cam_loc:
object_mask:
ray_directions:
sampler_min_max:
sampler_mask:
Returns:
"""
batch_size, num_pixels, _ = ray_directions.shape
device = cam_loc.device
n_total_pxl = batch_size * num_pixels
sampler_pts = torch.zeros(n_total_pxl, 3, device=device)
sampler_dists = torch.zeros(n_total_pxl, device=device)
intervals_dist = torch.linspace(0, 1, steps=self.n_steps, device=device).view(
1, 1, -1
)
pts_intervals = sampler_min_max[:, :, 0].unsqueeze(-1) + intervals_dist * (
sampler_min_max[:, :, 1] - sampler_min_max[:, :, 0]
).unsqueeze(-1)
points = (
cam_loc[..., None, :]
+ pts_intervals[..., None] * ray_directions[..., None, :]
)
# Get the non convergent rays
mask_intersect_idx = torch.nonzero(sampler_mask).flatten()
points = points.reshape((-1, self.n_steps, 3))[sampler_mask, :, :]
pts_intervals = pts_intervals.reshape((-1, self.n_steps))[sampler_mask]
sdf_val_all = []
for pnts in torch.split(points.reshape(-1, 3), 100000, dim=0):
sdf_val_all.append(sdf(pnts))
sdf_val = torch.cat(sdf_val_all).reshape(-1, self.n_steps)
tmp = torch.sign(sdf_val) * torch.arange(
self.n_steps, 0, -1, device=device, dtype=torch.float32
).reshape(1, self.n_steps)
# Force argmin to return the first min value
sampler_pts_ind = torch.argmin(tmp, -1)
sampler_pts[mask_intersect_idx] = points[
torch.arange(points.shape[0]), sampler_pts_ind, :
]
sampler_dists[mask_intersect_idx] = pts_intervals[
torch.arange(pts_intervals.shape[0]), sampler_pts_ind
]
true_surface_pts = object_mask.reshape(-1)[sampler_mask]
net_surface_pts = sdf_val[torch.arange(sdf_val.shape[0]), sampler_pts_ind] < 0
# take points with minimal SDF value for P_out pixels
p_out_mask = ~(true_surface_pts & net_surface_pts)
n_p_out = p_out_mask.sum()
if n_p_out > 0:
out_pts_idx = torch.argmin(sdf_val[p_out_mask, :], -1)
sampler_pts[mask_intersect_idx[p_out_mask]] = points[p_out_mask, :, :][
# pyre-fixme[6]: For 1st param expected `Union[bool, float, int]`
# but got `Tensor`.
torch.arange(n_p_out),
out_pts_idx,
:,
]
sampler_dists[mask_intersect_idx[p_out_mask]] = pts_intervals[
p_out_mask,
:,
# pyre-fixme[6]: For 1st param expected `Union[bool, float, int]` but
# got `Tensor`.
][torch.arange(n_p_out), out_pts_idx]
# Get Network object mask
sampler_net_obj_mask = sampler_mask.clone()
sampler_net_obj_mask[mask_intersect_idx[~net_surface_pts]] = False
# Run Secant method
secant_pts = (
net_surface_pts & true_surface_pts if self.training else net_surface_pts
)
n_secant_pts = secant_pts.sum()
if n_secant_pts > 0:
# Get secant z predictions
z_high = pts_intervals[
torch.arange(pts_intervals.shape[0]), sampler_pts_ind
][secant_pts]
sdf_high = sdf_val[torch.arange(sdf_val.shape[0]), sampler_pts_ind][
secant_pts
]
z_low = pts_intervals[secant_pts][
# pyre-fixme[6]: For 1st param expected `Union[bool, float, int]`
# but got `Tensor`.
torch.arange(n_secant_pts),
sampler_pts_ind[secant_pts] - 1,
]
sdf_low = sdf_val[secant_pts][
# pyre-fixme[6]: For 1st param expected `Union[bool, float, int]`
# but got `Tensor`.
torch.arange(n_secant_pts),
sampler_pts_ind[secant_pts] - 1,
]
cam_loc_secant = cam_loc.reshape(-1, 3)[mask_intersect_idx[secant_pts]]
ray_directions_secant = ray_directions.reshape((-1, 3))[
mask_intersect_idx[secant_pts]
]
z_pred_secant = self.secant(
sdf_low,
sdf_high,
z_low,
z_high,
cam_loc_secant,
ray_directions_secant,
# pyre-fixme[6]: For 7th param expected `Module` but got `(Tensor)
# -> Tensor`.
sdf,
)
# Get points
sampler_pts[mask_intersect_idx[secant_pts]] = (
cam_loc_secant + z_pred_secant.unsqueeze(-1) * ray_directions_secant
)
sampler_dists[mask_intersect_idx[secant_pts]] = z_pred_secant
return sampler_pts, sampler_net_obj_mask, sampler_dists
[docs]
def secant(
self,
sdf_low: torch.Tensor,
sdf_high: torch.Tensor,
z_low: torch.Tensor,
z_high: torch.Tensor,
cam_loc: torch.Tensor,
ray_directions: torch.Tensor,
sdf: nn.Module,
) -> torch.Tensor:
"""
Runs the secant method for interval [z_low, z_high] for n_secant_steps
"""
z_pred = -sdf_low * (z_high - z_low) / (sdf_high - sdf_low) + z_low
for _ in range(self.n_secant_steps):
p_mid = cam_loc + z_pred.unsqueeze(-1) * ray_directions
sdf_mid = sdf(p_mid)
ind_low = sdf_mid > 0
if ind_low.sum() > 0:
z_low[ind_low] = z_pred[ind_low]
sdf_low[ind_low] = sdf_mid[ind_low]
ind_high = sdf_mid < 0
if ind_high.sum() > 0:
z_high[ind_high] = z_pred[ind_high]
sdf_high[ind_high] = sdf_mid[ind_high]
z_pred = -sdf_low * (z_high - z_low) / (sdf_high - sdf_low) + z_low
return z_pred
[docs]
def minimal_sdf_points(
self,
sdf: Callable[[torch.Tensor], torch.Tensor],
cam_loc: torch.Tensor,
ray_directions: torch.Tensor,
mask: torch.Tensor,
min_dis: torch.Tensor,
max_dis: torch.Tensor,
) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Find points with minimal SDF value on rays for P_out pixels
"""
n_mask_points = mask.sum()
n = self.n_steps
steps = torch.empty(n, device=cam_loc.device).uniform_(0.0, 1.0)
mask_max_dis = max_dis[mask].unsqueeze(-1)
mask_min_dis = min_dis[mask].unsqueeze(-1)
steps = (
# pyre-fixme[6]: For 1st param expected `int` but got `Tensor`.
steps.unsqueeze(0).repeat(n_mask_points, 1) * (mask_max_dis - mask_min_dis)
+ mask_min_dis
)
mask_points = cam_loc.reshape(-1, 3)[mask]
mask_rays = ray_directions[mask, :]
mask_points_all = mask_points.unsqueeze(1).repeat(1, n, 1) + steps.unsqueeze(
-1
) * mask_rays.unsqueeze(1).repeat(1, n, 1)
points = mask_points_all.reshape(-1, 3)
mask_sdf_all = []
for pnts in torch.split(points, 100000, dim=0):
mask_sdf_all.append(sdf(pnts))
mask_sdf_all = torch.cat(mask_sdf_all).reshape(-1, n)
min_vals, min_idx = mask_sdf_all.min(-1)
min_mask_points = mask_points_all.reshape(-1, n, 3)[
# pyre-fixme[6]: For 2nd param expected `Union[bool, float, int]` but
# got `Tensor`.
torch.arange(0, n_mask_points),
min_idx,
]
# pyre-fixme[6]: For 2nd param expected `Union[bool, float, int]` but got
# `Tensor`.
min_mask_dist = steps.reshape(-1, n)[torch.arange(0, n_mask_points), min_idx]
return min_mask_points, min_mask_dist
# TODO: support variable origins
def _get_sphere_intersection(
cam_loc: torch.Tensor, ray_directions: torch.Tensor, r: float = 1.0
) -> Tuple[torch.Tensor, torch.Tensor]:
# Input: n_images x 3 ; n_images x n_rays x 3
# Output: n_images * n_rays x 2 (close and far) ; n_images * n_rays
n_imgs, n_pix, _ = ray_directions.shape
device = cam_loc.device
# cam_loc = cam_loc.unsqueeze(-1)
# ray_cam_dot = torch.bmm(ray_directions, cam_loc).squeeze()
ray_cam_dot = (ray_directions * cam_loc).sum(-1) # n_images x n_rays
# pyre-fixme[58]: `**` is not supported for operand types `Tensor` and `int`.
under_sqrt = ray_cam_dot**2 - (cam_loc.norm(2, dim=-1) ** 2 - r**2)
under_sqrt = under_sqrt.reshape(-1)
mask_intersect = under_sqrt > 0
sphere_intersections = torch.zeros(n_imgs * n_pix, 2, device=device)
sphere_intersections[mask_intersect] = torch.sqrt(
under_sqrt[mask_intersect]
).unsqueeze(-1) * torch.tensor([-1.0, 1.0], device=device)
sphere_intersections[mask_intersect] -= ray_cam_dot.reshape(-1)[
mask_intersect
].unsqueeze(-1)
sphere_intersections = sphere_intersections.reshape(n_imgs, n_pix, 2)
sphere_intersections = sphere_intersections.clamp_min(0.0)
mask_intersect = mask_intersect.reshape(n_imgs, n_pix)
return sphere_intersections, mask_intersect