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geometry.py
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geometry.py
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import numpy as np
import torch
from torch.nn import functional as F
import util
def compute_normal_map(x_img, y_img, z, intrinsics):
cam_coords = lift(x_img, y_img, z, intrinsics)
cam_coords = util.lin2img(cam_coords)
shift_left = cam_coords[:, :, 2:, :]
shift_right = cam_coords[:, :, :-2, :]
shift_up = cam_coords[:, :, :, 2:]
shift_down = cam_coords[:, :, :, :-2]
diff_hor = F.normalize(shift_right - shift_left, dim=1)[:, :, :, 1:-1]
diff_ver = F.normalize(shift_up - shift_down, dim=1)[:, :, 1:-1, :]
cross = torch.cross(diff_hor, diff_ver, dim=1)
return cross
def get_ray_directions_cam(uv, intrinsics):
'''Translates meshgrid of uv pixel coordinates to normalized directions of rays through these pixels,
in camera coordinates.
'''
batch_size, num_samples, _ = uv.shape
x_cam = uv[:, :, 0].view(batch_size, -1)
y_cam = uv[:, :, 1].view(batch_size, -1)
z_cam = torch.ones((batch_size, num_samples)).cuda()
pixel_points_cam = lift(x_cam, y_cam, z_cam, intrinsics=intrinsics, homogeneous=False) # (batch_size, -1, 4)
ray_dirs = F.normalize(pixel_points_cam, dim=2)
return ray_dirs
def reflect_vector_on_vector(vector_to_reflect, reflection_axis):
refl = F.normalize(vector_to_reflect.cuda())
ax = F.normalize(reflection_axis.cuda())
r = 2 * (ax * refl).sum(dim=1, keepdim=True) * ax - refl
return r
def parse_intrinsics(intrinsics):
intrinsics = intrinsics.cuda()
fx = intrinsics[:, 0, 0]
fy = intrinsics[:, 1, 1]
cx = intrinsics[:, 0, 2]
cy = intrinsics[:, 1, 2]
return fx, fy, cx, cy
def expand_as(x, y):
if len(x.shape) == len(y.shape):
return x
for i in range(len(y.shape) - len(x.shape)):
x = x.unsqueeze(-1)
return x
def lift(x, y, z, intrinsics, homogeneous=False):
'''
:param self:
:param x: Shape (batch_size, num_points)
:param y:
:param z:
:param intrinsics:
:return:
'''
fx, fy, cx, cy = parse_intrinsics(intrinsics)
x_lift = (x - expand_as(cx, x)) / expand_as(fx, x) * z
y_lift = (y - expand_as(cy, y)) / expand_as(fy, y) * z
if homogeneous:
return torch.stack((x_lift, y_lift, z, torch.ones_like(z).cuda()), dim=-1)
else:
return torch.stack((x_lift, y_lift, z), dim=-1)
def project(x, y, z, intrinsics):
'''
:param self:
:param x: Shape (batch_size, num_points)
:param y:
:param z:
:param intrinsics:
:return:
'''
fx, fy, cx, cy = parse_intrinsics(intrinsics)
x_proj = expand_as(fx, x) * x / z + expand_as(cx, x)
y_proj = expand_as(fy, y) * y / z + expand_as(cy, y)
return torch.stack((x_proj, y_proj, z), dim=-1)
def world_from_xy_depth(xy, depth, cam2world, intrinsics):
'''Translates meshgrid of xy pixel coordinates plus depth to world coordinates.
'''
batch_size, _, _ = cam2world.shape
x_cam = xy[:, :, 0].view(batch_size, -1)
y_cam = xy[:, :, 1].view(batch_size, -1)
z_cam = depth.view(batch_size, -1)
pixel_points_cam = lift(x_cam, y_cam, z_cam, intrinsics=intrinsics, homogeneous=True) # (batch_size, -1, 4)
# permute for batch matrix product
pixel_points_cam = pixel_points_cam.permute(0, 2, 1)
world_coords = torch.bmm(cam2world, pixel_points_cam).permute(0, 2, 1)[:, :, :3] # (batch_size, -1, 3)
return world_coords
def project_point_on_line(projection_point, line_direction, point_on_line, dim):
'''Projects a batch of points on a batch of lines as defined by their direction and a point on each line. '''
assert torch.allclose((line_direction ** 2).sum(dim=dim, keepdim=True).cuda(), torch.Tensor([1]).cuda())
return point_on_line + ((projection_point - point_on_line) * line_direction).sum(dim=dim,
keepdim=True) * line_direction
def get_ray_directions(xy, cam2world, intrinsics):
'''Translates meshgrid of xy pixel coordinates to normalized directions of rays through these pixels.
'''
batch_size, num_samples, _ = xy.shape
z_cam = torch.ones((batch_size, num_samples)).cuda()
pixel_points = world_from_xy_depth(xy, z_cam, intrinsics=intrinsics, cam2world=cam2world) # (batch, num_samples, 3)
cam_pos = cam2world[:, :3, 3]
ray_dirs = pixel_points - cam_pos[:, None, :] # (batch, num_samples, 3)
ray_dirs = F.normalize(ray_dirs, dim=2)
return ray_dirs
def depth_from_world(world_coords, cam2world):
batch_size, num_samples, _ = world_coords.shape
points_hom = torch.cat((world_coords, torch.ones((batch_size, num_samples, 1)).cuda()),
dim=2) # (batch, num_samples, 4)
# permute for bmm
points_hom = points_hom.permute(0, 2, 1)
points_cam = torch.inverse(cam2world).bmm(points_hom) # (batch, 4, num_samples)
depth = points_cam[:, 2, :][:, :, None] # (batch, num_samples, 1)
return depth