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import torch
from torch_scatter import scatter_sum
from . import fastba
from . import lietorch
from .lietorch import SE3
from .utils import Timer
from . import projective_ops as pops
class CholeskySolver(torch.autograd.Function):
@staticmethod
def forward(ctx, H, b):
# don't crash training if cholesky decomp fails
U, info = torch.linalg.cholesky_ex(H)
if torch.any(info):
ctx.failed = True
return torch.zeros_like(b)
xs = torch.cholesky_solve(b, U)
ctx.save_for_backward(U, xs)
ctx.failed = False
return xs
@staticmethod
def backward(ctx, grad_x):
if ctx.failed:
return None, None
U, xs = ctx.saved_tensors
dz = torch.cholesky_solve(grad_x, U)
dH = -torch.matmul(xs, dz.transpose(-1,-2))
return dH, dz
# utility functions for scattering ops
def safe_scatter_add_mat(A, ii, jj, n, m):
v = (ii >= 0) & (jj >= 0) & (ii < n) & (jj < m)
return scatter_sum(A[:,v], ii[v]*m + jj[v], dim=1, dim_size=n*m)
def safe_scatter_add_vec(b, ii, n):
v = (ii >= 0) & (ii < n)
return scatter_sum(b[:,v], ii[v], dim=1, dim_size=n)
# apply retraction operator to inv-depth maps
def disp_retr(disps, dz, ii):
ii = ii.to(device=dz.device)
return disps + scatter_sum(dz, ii, dim=1, dim_size=disps.shape[1])
# apply retraction operator to poses
def pose_retr(poses, dx, ii):
ii = ii.to(device=dx.device)
return poses.retr(scatter_sum(dx, ii, dim=1, dim_size=poses.shape[1]))
def block_matmul(A, B):
""" block matrix multiply """
b, n1, m1, p1, q1 = A.shape
b, n2, m2, p2, q2 = B.shape
A = A.permute(0, 1, 3, 2, 4).reshape(b, n1*p1, m1*q1)
B = B.permute(0, 1, 3, 2, 4).reshape(b, n2*p2, m2*q2)
return torch.matmul(A, B).reshape(b, n1, p1, m2, q2).permute(0, 1, 3, 2, 4)
def block_solve(A, B, ep=1.0, lm=1e-4):
""" block matrix solve """
b, n1, m1, p1, q1 = A.shape
b, n2, m2, p2, q2 = B.shape
A = A.permute(0, 1, 3, 2, 4).reshape(b, n1*p1, m1*q1)
B = B.permute(0, 1, 3, 2, 4).reshape(b, n2*p2, m2*q2)
A = A + (ep + lm * A) * torch.eye(n1*p1, device=A.device)
X = CholeskySolver.apply(A, B)
return X.reshape(b, n1, p1, m2, q2).permute(0, 1, 3, 2, 4)
def block_show(A):
import matplotlib.pyplot as plt
b, n1, m1, p1, q1 = A.shape
A = A.permute(0, 1, 3, 2, 4).reshape(b, n1*p1, m1*q1)
plt.imshow(A[0].detach().cpu().numpy())
plt.show()
def BA(poses, patches, intrinsics, targets, weights, lmbda, ii, jj, kk, bounds, ep=100.0, PRINT=False, fixedp=1, structure_only=False):
""" bundle adjustment """
b = 1
n = max(ii.max().item(), jj.max().item()) + 1
coords, v, (Ji, Jj, Jz) = \
pops.transform(poses, patches, intrinsics, ii, jj, kk, jacobian=True)
p = coords.shape[3]
r = targets - coords[...,p//2,p//2,:]
v *= (r.norm(dim=-1) < 250).float()
in_bounds = \
(coords[...,p//2,p//2,0] > bounds[0]) & \
(coords[...,p//2,p//2,1] > bounds[1]) & \
(coords[...,p//2,p//2,0] < bounds[2]) & \
(coords[...,p//2,p//2,1] < bounds[3])
v *= in_bounds.float()
if PRINT:
print((r * v[...,None]).norm(dim=-1).mean().item())
r = (v[...,None] * r).unsqueeze(dim=-1)
weights = (v[...,None] * weights).unsqueeze(dim=-1)
wJiT = (weights * Ji).transpose(2,3)
wJjT = (weights * Jj).transpose(2,3)
wJzT = (weights * Jz).transpose(2,3)
Bii = torch.matmul(wJiT, Ji)
Bij = torch.matmul(wJiT, Jj)
Bji = torch.matmul(wJjT, Ji)
Bjj = torch.matmul(wJjT, Jj)
Eik = torch.matmul(wJiT, Jz)
Ejk = torch.matmul(wJjT, Jz)
vi = torch.matmul(wJiT, r)
vj = torch.matmul(wJjT, r)
# fix first pose
ii = ii.clone()
jj = jj.clone()
n = n - fixedp
ii = ii - fixedp
jj = jj - fixedp
kx, kk = torch.unique(kk, return_inverse=True, sorted=True)
m = len(kx)
B = safe_scatter_add_mat(Bii, ii, ii, n, n).view(b, n, n, 6, 6) + \
safe_scatter_add_mat(Bij, ii, jj, n, n).view(b, n, n, 6, 6) + \
safe_scatter_add_mat(Bji, jj, ii, n, n).view(b, n, n, 6, 6) + \
safe_scatter_add_mat(Bjj, jj, jj, n, n).view(b, n, n, 6, 6)
E = safe_scatter_add_mat(Eik, ii, kk, n, m).view(b, n, m, 6, 1) + \
safe_scatter_add_mat(Ejk, jj, kk, n, m).view(b, n, m, 6, 1)
C = safe_scatter_add_vec(torch.matmul(wJzT, Jz), kk, m)
v = safe_scatter_add_vec(vi, ii, n).view(b, n, 1, 6, 1) + \
safe_scatter_add_vec(vj, jj, n).view(b, n, 1, 6, 1)
w = safe_scatter_add_vec(torch.matmul(wJzT, r), kk, m)
if isinstance(lmbda, torch.Tensor):
lmbda = lmbda.reshape(*C.shape)
Q = 1.0 / (C + lmbda)
### solve w/ schur complement ###
EQ = E * Q[:,None]
if structure_only or n == 0:
dZ = (Q * w).view(b, -1, 1, 1)
else:
S = B - block_matmul(EQ, E.permute(0,2,1,4,3))
y = v - block_matmul(EQ, w.unsqueeze(dim=2))
dX = block_solve(S, y, ep=ep, lm=1e-4)
dZ = Q * (w - block_matmul(E.permute(0,2,1,4,3), dX).squeeze(dim=-1))
dX = dX.view(b, -1, 6)
dZ = dZ.view(b, -1, 1, 1)
x, y, disps = patches.unbind(dim=2)
disps = disp_retr(disps, dZ, kx).clamp(min=1e-3, max=10.0)
patches = torch.stack([x, y, disps], dim=2)
if not structure_only and n > 0:
poses = pose_retr(poses, dX, fixedp + torch.arange(n))
return poses, patches
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