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import lietorch
import torch
import torch.nn.functional as F
from .chol import block_solve, schur_solve
import geom.projective_ops as pops
from torch_scatter import scatter_sum
# 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 BA(target, weight, eta, poses, disps, intrinsics, ii, jj, fixedp=1, rig=1):
""" Full Bundle Adjustment """
B, P, ht, wd = disps.shape
N = ii.shape[0]
D = poses.manifold_dim
### 1: commpute jacobians and residuals ###
coords, valid, (Ji, Jj, Jz) = pops.projective_transform(
poses, disps, intrinsics, ii, jj, jacobian=True)
r = (target - coords).view(B, N, -1, 1)
w = .001 * (valid * weight).view(B, N, -1, 1)
### 2: construct linear system ###
Ji = Ji.reshape(B, N, -1, D)
Jj = Jj.reshape(B, N, -1, D)
wJiT = (w * Ji).transpose(2,3)
wJjT = (w * Jj).transpose(2,3)
Jz = Jz.reshape(B, N, ht*wd, -1)
Hii = torch.matmul(wJiT, Ji)
Hij = torch.matmul(wJiT, Jj)
Hji = torch.matmul(wJjT, Ji)
Hjj = torch.matmul(wJjT, Jj)
vi = torch.matmul(wJiT, r).squeeze(-1)
vj = torch.matmul(wJjT, r).squeeze(-1)
Ei = (wJiT.view(B,N,D,ht*wd,-1) * Jz[:,:,None]).sum(dim=-1)
Ej = (wJjT.view(B,N,D,ht*wd,-1) * Jz[:,:,None]).sum(dim=-1)
w = w.view(B, N, ht*wd, -1)
r = r.view(B, N, ht*wd, -1)
wk = torch.sum(w*r*Jz, dim=-1)
Ck = torch.sum(w*Jz*Jz, dim=-1)
kx, kk = torch.unique(ii, return_inverse=True)
M = kx.shape[0]
# only optimize keyframe poses
P = P // rig - fixedp
ii = ii // rig - fixedp
jj = jj // rig - fixedp
H = safe_scatter_add_mat(Hii, ii, ii, P, P) + \
safe_scatter_add_mat(Hij, ii, jj, P, P) + \
safe_scatter_add_mat(Hji, jj, ii, P, P) + \
safe_scatter_add_mat(Hjj, jj, jj, P, P)
E = safe_scatter_add_mat(Ei, ii, kk, P, M) + \
safe_scatter_add_mat(Ej, jj, kk, P, M)
v = safe_scatter_add_vec(vi, ii, P) + \
safe_scatter_add_vec(vj, jj, P)
C = safe_scatter_add_vec(Ck, kk, M)
w = safe_scatter_add_vec(wk, kk, M)
C = C + eta.view(*C.shape) + 1e-7
H = H.view(B, P, P, D, D)
E = E.view(B, P, M, D, ht*wd)
### 3: solve the system ###
dx, dz = schur_solve(H, E, C, v, w)
### 4: apply retraction ###
poses = pose_retr(poses, dx, torch.arange(P) + fixedp)
disps = disp_retr(disps, dz.view(B,-1,ht,wd), kx)
disps = torch.where(disps > 10, torch.zeros_like(disps), disps)
disps = disps.clamp(min=0.0)
return poses, disps
def MoBA(target, weight, eta, poses, disps, intrinsics, ii, jj, fixedp=1, rig=1):
""" Motion only bundle adjustment """
B, P, ht, wd = disps.shape
N = ii.shape[0]
D = poses.manifold_dim
### 1: commpute jacobians and residuals ###
coords, valid, (Ji, Jj, Jz) = pops.projective_transform(
poses, disps, intrinsics, ii, jj, jacobian=True)
r = (target - coords).view(B, N, -1, 1)
w = .001 * (valid * weight).view(B, N, -1, 1)
### 2: construct linear system ###
Ji = Ji.reshape(B, N, -1, D)
Jj = Jj.reshape(B, N, -1, D)
wJiT = (w * Ji).transpose(2,3)
wJjT = (w * Jj).transpose(2,3)
Hii = torch.matmul(wJiT, Ji)
Hij = torch.matmul(wJiT, Jj)
Hji = torch.matmul(wJjT, Ji)
Hjj = torch.matmul(wJjT, Jj)
vi = torch.matmul(wJiT, r).squeeze(-1)
vj = torch.matmul(wJjT, r).squeeze(-1)
# only optimize keyframe poses
P = P // rig - fixedp
ii = ii // rig - fixedp
jj = jj // rig - fixedp
H = safe_scatter_add_mat(Hii, ii, ii, P, P) + \
safe_scatter_add_mat(Hij, ii, jj, P, P) + \
safe_scatter_add_mat(Hji, jj, ii, P, P) + \
safe_scatter_add_mat(Hjj, jj, jj, P, P)
v = safe_scatter_add_vec(vi, ii, P) + \
safe_scatter_add_vec(vj, jj, P)
H = H.view(B, P, P, D, D)
### 3: solve the system ###
dx = block_solve(H, v)
### 4: apply retraction ###
poses = pose_retr(poses, dx, torch.arange(P) + fixedp)
return poses
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