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inverse_warp.py
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inverse_warp.py
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# Author: Anurag Ranjan
# Copyright (c) 2019, Anurag Ranjan
# All rights reserved.
# based on github.com/ClementPinard/SfMLearner-Pytorch
from __future__ import division
import torch
from torch.autograd import Variable
pixel_coords = None
def set_id_grid(depth):
global pixel_coords
b, h, w = depth.size()
i_range = Variable(torch.arange(0, h).view(1, h, 1).expand(1,h,w)).type_as(depth) # [1, H, W]
j_range = Variable(torch.arange(0, w).view(1, 1, w).expand(1,h,w)).type_as(depth) # [1, H, W]
ones = Variable(torch.ones(1,h,w)).type_as(depth)
pixel_coords = torch.stack((j_range, i_range, ones), dim=1) # [1, 3, H, W]
def check_sizes(input, input_name, expected):
condition = [input.ndimension() == len(expected)]
for i,size in enumerate(expected):
if size.isdigit():
condition.append(input.size(i) == int(size))
assert(all(condition)), "wrong size for {}, expected {}, got {}".format(input_name, 'x'.join(expected), list(input.size()))
def pixel2cam(depth, intrinsics_inv):
global pixel_coords
"""Transform coordinates in the pixel frame to the camera frame.
Args:
depth: depth maps -- [B, H, W]
intrinsics_inv: intrinsics_inv matrix for each element of batch -- [B, 3, 3]
Returns:
array of (u,v,1) cam coordinates -- [B, 3, H, W]
"""
b, h, w = depth.size()
if (pixel_coords is None) or pixel_coords.size(2) != h or pixel_coords.size(3) != w:
set_id_grid(depth)
current_pixel_coords = pixel_coords[:,:,:h,:w].expand(b,3,h,w).contiguous().view(b, 3, -1) # [B, 3, H*W]
cam_coords = intrinsics_inv.bmm(current_pixel_coords).view(b, 3, h, w)
return cam_coords * depth.unsqueeze(1)
def cam2pixel(cam_coords, proj_c2p_rot, proj_c2p_tr, padding_mode):
"""Transform coordinates in the camera frame to the pixel frame.
Args:
cam_coords: pixel coordinates defined in the first camera coordinates system -- [B, 4, H, W]
proj_c2p_rot: rotation matrix of cameras -- [B, 3, 4]
proj_c2p_tr: translation vectors of cameras -- [B, 3, 1]
Returns:
array of [-1,1] coordinates -- [B, 2, H, W]
"""
b, _, h, w = cam_coords.size()
cam_coords_flat = cam_coords.view(b, 3, -1) # [B, 3, H*W]
if proj_c2p_rot is not None:
pcoords = proj_c2p_rot.bmm(cam_coords_flat)
else:
pcoords = cam_coords_flat
if proj_c2p_tr is not None:
pcoords = pcoords + proj_c2p_tr # [B, 3, H*W]
X = pcoords[:, 0]
Y = pcoords[:, 1]
Z = pcoords[:, 2].clamp(min=1e-3)
X_norm = 2*(X / Z)/(w-1) - 1 # Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1) [B, H*W]
Y_norm = 2*(Y / Z)/(h-1) - 1 # Idem [B, H*W]
if padding_mode == 'zeros':
X_mask = ((X_norm > 1)+(X_norm < -1)).detach()
X_norm[X_mask] = 2 # make sure that no point in warped image is a combinaison of im and gray
Y_mask = ((Y_norm > 1)+(Y_norm < -1)).detach()
Y_norm[Y_mask] = 2
pixel_coords = torch.stack([X_norm, Y_norm], dim=2) # [B, H*W, 2]
return pixel_coords.view(b,h,w,2)
def euler2mat(angle):
"""Convert euler angles to rotation matrix.
Reference: https://github.com/pulkitag/pycaffe-utils/blob/master/rot_utils.py#L174
Args:
angle: rotation angle along 3 axis (in radians) -- size = [B, 3]
Returns:
Rotation matrix corresponding to the euler angles -- size = [B, 3, 3]
"""
B = angle.size(0)
x, y, z = angle[:,0], angle[:,1], angle[:,2]
cosz = torch.cos(z)
sinz = torch.sin(z)
zeros = z.detach()*0
ones = zeros.detach()+1
zmat = torch.stack([cosz, -sinz, zeros,
sinz, cosz, zeros,
zeros, zeros, ones], dim=1).view(B, 3, 3)
cosy = torch.cos(y)
siny = torch.sin(y)
ymat = torch.stack([cosy, zeros, siny,
zeros, ones, zeros,
-siny, zeros, cosy], dim=1).view(B, 3, 3)
cosx = torch.cos(x)
sinx = torch.sin(x)
xmat = torch.stack([ones, zeros, zeros,
zeros, cosx, -sinx,
zeros, sinx, cosx], dim=1).view(B, 3, 3)
rotMat = xmat.bmm(ymat).bmm(zmat)
return rotMat
def quat2mat(quat):
"""Convert quaternion coefficients to rotation matrix.
Args:
quat: first three coeff of quaternion of rotation. fourht is then computed to have a norm of 1 -- size = [B, 3]
Returns:
Rotation matrix corresponding to the quaternion -- size = [B, 3, 3]
"""
norm_quat = torch.cat([quat[:,:1].detach()*0 + 1, quat], dim=1)
norm_quat = norm_quat/norm_quat.norm(p=2, dim=1, keepdim=True)
w, x, y, z = norm_quat[:,0], norm_quat[:,1], norm_quat[:,2], norm_quat[:,3]
B = quat.size(0)
w2, x2, y2, z2 = w.pow(2), x.pow(2), y.pow(2), z.pow(2)
wx, wy, wz = w*x, w*y, w*z
xy, xz, yz = x*y, x*z, y*z
rotMat = torch.stack([w2 + x2 - y2 - z2, 2*xy - 2*wz, 2*wy + 2*xz,
2*wz + 2*xy, w2 - x2 + y2 - z2, 2*yz - 2*wx,
2*xz - 2*wy, 2*wx + 2*yz, w2 - x2 - y2 + z2], dim=1).view(B, 3, 3)
return rotMat
def pose_vec2mat(vec, rotation_mode='euler'):
"""
Convert 6DoF parameters to transformation matrix.
Args:s
vec: 6DoF parameters in the order of tx, ty, tz, rx, ry, rz -- [B, 6]
Returns:
A transformation matrix -- [B, 3, 4]
"""
translation = vec[:, :3].unsqueeze(-1) # [B, 3, 1]
rot = vec[:,3:]
if rotation_mode == 'euler':
rot_mat = euler2mat(rot) # [B, 3, 3]
elif rotation_mode == 'quat':
rot_mat = quat2mat(rot) # [B, 3, 3]
transform_mat = torch.cat([rot_mat, translation], dim=2) # [B, 3, 4]
return transform_mat
def flow_warp(img, flow, padding_mode='zeros'):
"""
Inverse warp a source image to the target image plane.
Args:
img: the source image (where to sample pixels) -- [B, 3, H, W]
flow: flow map of the target image -- [B, 2, H, W]
Returns:
Source image warped to the target image plane
"""
check_sizes(img, 'img', 'BCHW')
check_sizes(flow, 'flow', 'B2HW')
bs, _, h, w = flow.size()
u = flow[:,0,:,:]
v = flow[:,1,:,:]
grid_x = Variable(torch.arange(0, w).view(1, 1, w).expand(1,h,w), requires_grad=False).type_as(u).expand_as(u) # [bs, H, W]
grid_y = Variable(torch.arange(0, h).view(1, h, 1).expand(1,h,w), requires_grad=False).type_as(v).expand_as(v) # [bs, H, W]
X = grid_x + u
Y = grid_y + v
X = 2*(X/(w-1.0) - 0.5)
Y = 2*(Y/(h-1.0) - 0.5)
grid_tf = torch.stack((X,Y), dim=3)
img_tf = torch.nn.functional.grid_sample(img, grid_tf, padding_mode=padding_mode)
return img_tf
def pose2flow(depth, pose, intrinsics, intrinsics_inv, rotation_mode='euler', padding_mode=None):
"""
Converts pose parameters to rigid optical flow
"""
check_sizes(depth, 'depth', 'BHW')
check_sizes(pose, 'pose', 'B6')
check_sizes(intrinsics, 'intrinsics', 'B33')
check_sizes(intrinsics_inv, 'intrinsics', 'B33')
assert(intrinsics_inv.size() == intrinsics.size())
bs, h, w = depth.size()
grid_x = Variable(torch.arange(0, w).view(1, 1, w).expand(1,h,w), requires_grad=False).type_as(depth).expand_as(depth) # [bs, H, W]
grid_y = Variable(torch.arange(0, h).view(1, h, 1).expand(1,h,w), requires_grad=False).type_as(depth).expand_as(depth) # [bs, H, W]
cam_coords = pixel2cam(depth, intrinsics_inv) # [B,3,H,W]
pose_mat = pose_vec2mat(pose, rotation_mode) # [B,3,4]
# Get projection matrix for tgt camera frame to source pixel frame
proj_cam_to_src_pixel = intrinsics.bmm(pose_mat) # [B, 3, 4]
src_pixel_coords = cam2pixel(cam_coords, proj_cam_to_src_pixel[:,:,:3], proj_cam_to_src_pixel[:,:,-1:], padding_mode) # [B,H,W,2]
X = (w-1)*(src_pixel_coords[:,:,:,0]/2.0 + 0.5) - grid_x
Y = (h-1)*(src_pixel_coords[:,:,:,1]/2.0 + 0.5) - grid_y
return torch.stack((X,Y), dim=1)
def flow2oob(flow):
check_sizes(flow, 'flow', 'B2HW')
bs, _, h, w = flow.size()
u = flow[:,0,:,:]
v = flow[:,1,:,:]
grid_x = Variable(torch.arange(0, w).view(1, 1, w).expand(1,h,w), requires_grad=False).type_as(u).expand_as(u) # [bs, H, W]
grid_y = Variable(torch.arange(0, h).view(1, h, 1).expand(1,h,w), requires_grad=False).type_as(v).expand_as(v) # [bs, H, W]
X = grid_x + u
Y = grid_y + v
X = 2*(X/(w-1.0) - 0.5)
Y = 2*(Y/(h-1.0) - 0.5)
oob = (X.abs()>1).add(Y.abs()>1)>0
return oob
def occlusion_mask(grid, depth):
check_sizes(img, 'grid', 'BHW2')
check_sizes(depth, 'depth', 'BHW')
mask = grid
return mask
def inverse_warp(img, depth, pose, intrinsics, intrinsics_inv, rotation_mode='euler', padding_mode='zeros'):
"""
Inverse warp a source image to the target image plane.
Args:
img: the source image (where to sample pixels) -- [B, 3, H, W]
depth: depth map of the target image -- [B, H, W]
pose: 6DoF pose parameters from target to source -- [B, 6]
intrinsics: camera intrinsic matrix -- [B, 3, 3]
intrinsics_inv: inverse of the intrinsic matrix -- [B, 3, 3]
Returns:
Source image warped to the target image plane
"""
# print(pose)
check_sizes(img, 'img', 'B3HW')
check_sizes(depth, 'depth', 'BHW')
check_sizes(pose, 'pose', 'B6')
check_sizes(intrinsics, 'intrinsics', 'B33')
check_sizes(intrinsics_inv, 'intrinsics', 'B33')
assert(intrinsics_inv.size() == intrinsics.size())
batch_size, _, img_height, img_width = img.size()
cam_coords = pixel2cam(depth, intrinsics_inv) # [B,3,H,W]
pose_mat = pose_vec2mat(pose, rotation_mode) # [B,3,4]
# Get projection matrix for tgt camera frame to source pixel frame
proj_cam_to_src_pixel = intrinsics.bmm(pose_mat) # [B, 3, 4]
src_pixel_coords = cam2pixel(cam_coords, proj_cam_to_src_pixel[:,:,:3], proj_cam_to_src_pixel[:,:,-1:], padding_mode) # [B,H,W,2]
projected_img = torch.nn.functional.grid_sample(img, src_pixel_coords, padding_mode=padding_mode)
return projected_img