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import numpy as np
import torch
from my3d import unproject
def subpixel_rays_from_img(H, W, K, c2w_pose, normalize_dir=True, f=8):
assert c2w_pose[3, 3] == 1.
H, W = H * f, W * f
n = H * W
ys, xs = np.meshgrid(range(H), range(W), indexing="ij")
xy_coords = np.stack([xs, ys], axis=-1).reshape(n, 2)
top_left = np.array([-0.5, -0.5]) + 1 / (2 * f)
xy_coords = top_left + xy_coords / f
ro = c2w_pose[:, -1]
pts = unproject(K, xy_coords, depth=1)
pts = pts @ c2w_pose.T
rd = pts - ro
rd = rd[:, :3]
if normalize_dir:
rd = rd / np.linalg.norm(rd, axis=-1, keepdims=True)
ro = np.tile(ro[:3], (n, 1))
return ro, rd
def rays_from_img(H, W, K, c2w_pose, normalize_dir=True):
assert c2w_pose[3, 3] == 1.
n = H * W
ys, xs = np.meshgrid(range(H), range(W), indexing="ij")
xy_coords = np.stack([xs, ys], axis=-1).reshape(n, 2)
ro = c2w_pose[:, -1]
pts = unproject(K, xy_coords, depth=1)
pts = pts @ c2w_pose.T
rd = pts - ro # equivalently can subtract [0,0,0,1] before pose transform
rd = rd[:, :3]
if normalize_dir:
rd = rd / np.linalg.norm(rd, axis=-1, keepdims=True)
ro = np.tile(ro[:3], (n, 1))
return ro, rd
def ray_box_intersect(ro, rd, aabb):
"""
Intersection of ray with axis-aligned bounding box
This routine works for arbitrary dimensions; commonly d = 2 or 3
only works for numpy, not torch (which has slightly diff api for min, max, and clone)
Args:
ro: [n, d] ray origin
rd: [n, d] ray direction (assumed to be already normalized;
if not still fine, meaning of t as time of flight holds true)
aabb: [d, 2] bbox bound on each dim
Return:
is_intersect: [n,] of bool, whether the particular ray intersects the bbox
t_min: [n,] ray entrance time
t_max: [n,] ray exit time
"""
n = ro.shape[0]
d = aabb.shape[0]
assert aabb.shape == (d, 2)
assert ro.shape == (n, d) and rd.shape == (n, d)
rd = rd.copy()
rd[rd == 0] = 1e-6 # avoid div overflow; logically safe to give it big t
ro = ro.reshape(n, d, 1)
rd = rd.reshape(n, d, 1)
ts = (aabb - ro) / rd # [n, d, 2]
t_min = ts.min(-1).max(-1) # [n,] last of entrance
t_max = ts.max(-1).min(-1) # [n,] first of exit
is_intersect = t_min < t_max
return is_intersect, t_min, t_max
def as_torch_tsrs(device, *args):
ret = []
for elem in args:
target_dtype = torch.float32 if np.issubdtype(elem.dtype, np.floating) else None
ret.append(
torch.as_tensor(elem, dtype=target_dtype, device=device)
)
return ret
def group_mask_filter(mask, *items):
return [elem[mask] for elem in items]
def mask_back_fill(tsr, N, inds, base_value=1.0):
shape = [N, *tsr.shape[1:]]
canvas = base_value * np.ones_like(tsr, shape=shape)
canvas[inds] = tsr
return canvas
def render_one_view(model, aabb, H, W, K, pose):
N = H * W
bs = max(W * 5, 4096) # render 5 rows; original batch size 4096, now 4000;
ro, rd = rays_from_img(H, W, K, pose)
ro, rd, t_min, t_max, intsct_inds = scene_box_filter(ro, rd, aabb)
n = len(ro)
# print(f"{n} vs {N}") # n can be smaller than N since some rays do not intsct aabb
# n = n // 1 # actual number of rays to render; only needed for fast debugging
dev = model.device
ro, rd, t_min, t_max = as_torch_tsrs(dev, ro, rd, t_min, t_max)
rgbs = torch.zeros(n, 3, device=dev)
depth = torch.zeros(n, 1, device=dev)
with torch.no_grad():
for i in range(int(np.ceil(n / bs))):
s = i * bs
e = min(n, s + bs)
_rgbs, _depth, _ = render_ray_bundle(
model, ro[s:e], rd[s:e], t_min[s:e], t_max[s:e]
)
rgbs[s:e] = _rgbs
depth[s:e] = _depth
rgbs, depth = rgbs.cpu().numpy(), depth.cpu().numpy()
base_color = 1.0 # empty region needs to be white
rgbs = mask_back_fill(rgbs, N, intsct_inds, base_color).reshape(H, W, 3)
depth = mask_back_fill(depth, N, intsct_inds, base_color).reshape(H, W)
return rgbs, depth
def scene_box_filter(ro, rd, aabb):
N = len(ro)
_, t_min, t_max = ray_box_intersect(ro, rd, aabb)
# do not render what's behind the ray origin
t_min, t_max = np.maximum(t_min, 0), np.maximum(t_max, 0)
# can test intersect logic by reducing the focal length
is_intsct = t_min < t_max
ro, rd, t_min, t_max = group_mask_filter(is_intsct, ro, rd, t_min, t_max)
intsct_inds = np.arange(N)[is_intsct]
return ro, rd, t_min, t_max, intsct_inds
def render_ray_bundle(model, ro, rd, t_min, t_max):
"""
The working shape is (k, n, 3) where k is num of samples per ray, n the ray batch size
During integration the reduction is applied on k
chain of filtering
starting with ro, rd (from cameras), and a scene bbox
- rays that do not intersect scene bbox; sample pts that fall outside the bbox
- samples that do not fall within alpha mask
- samples whose densities are very low; no need to compute colors on them
"""
num_samples, step_size = model.get_num_samples((t_max - t_min).max())
# print(num_samples)
n, k = len(ro), num_samples
# print(n,k)
ticks = step_size * torch.arange(k, device=ro.device)
ticks = ticks.view(k, 1, 1)
t_min = t_min.view(n, 1)
# t_min = t_min + step_size * torch.rand_like(t_min) # NOTE seems useless
t_max = t_max.view(n, 1)
dists = t_min + ticks # [n, 1], [k, 1, 1] -> [k, n, 1]
pts = ro + rd * dists # [n, 3], [n, 3], [k, n, 1] -> [k, n, 3]
mask = (ticks < (t_max - t_min)).squeeze(-1) # [k, 1, 1], [n, 1] -> [k, n, 1] -> [k, n]
smp_pts = pts[mask]
if model.alphaMask is not None:
alphas = model.alphaMask.sample_alpha(smp_pts)
alpha_mask = alphas > 0
mask[mask.clone()] = alpha_mask
smp_pts = pts[mask]
σ = torch.zeros(k, n, device=ro.device)
σ[mask] = model.compute_density_feats(smp_pts)
weights = volume_rend_weights(σ, step_size)
mask = weights > model.ray_march_weight_thres
smp_pts = pts[mask]
app_feats = model.compute_app_feats(smp_pts)
# viewdirs = rd.view(1, n, 3).expand(k, n, 3)[mask] # ray dirs for each point
# additional wild factors here as in nerf-w; wild factors are optimizable
c_dim = app_feats.shape[-1]
colors = torch.zeros(k, n, c_dim, device=ro.device)
colors[mask] = model.feats2color(app_feats)
weights = weights.view(k, n, 1) # can be used to compute other expected vals e.g. depth
bg_weight = 1. - weights.sum(dim=0) # [n, 1]
rgbs = (weights * colors).sum(dim=0) # [n, 3]
if model.blend_bg_texture:
uv = spherical_xyz_to_uv(rd)
bg_feats = model.compute_bg(uv)
bg_color = model.feats2color(bg_feats)
rgbs = rgbs + bg_weight * bg_color
else:
rgbs = rgbs + bg_weight * 1. # blend white bg color
# print(rgbs.shape)
# rgbs = rgbs.clamp(0, 1) # don't clamp since this is can be SD latent features
E_dists = (weights * dists).sum(dim=0)
bg_dist = 10. # blend bg distance; just don't make it too large
E_dists = E_dists + bg_weight * bg_dist
return rgbs, E_dists, weights.squeeze(-1)
def spherical_xyz_to_uv(xyz):
# xyz is Tensor of shape [N, 3], uv in [-1, 1]
x, y, z = xyz.t() # [N]
xy = (x ** 2 + y ** 2) ** 0.5
u = torch.atan2(xy, z) / torch.pi # [N]
v = torch.atan2(y, x) / (torch.pi * 2) + 0.5 # [N]
uv = torch.stack([u, v], -1) # [N, 2]
uv = uv * 2 - 1 # [0, 1] -> [-1, 1]
return uv
def volume_rend_weights(σ, dist):
α = 1 - torch.exp(-σ * dist)
T = torch.ones_like(α)
T[1:] = (1 - α).cumprod(dim=0)[:-1]
assert (T >= 0).all()
weights = α * T
return weights
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