File size: 4,611 Bytes
b7eedf7
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
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