Easy and Fast Reconstruction of a 3D Avatar with an RGB-D Sensor

. 2017 May 12;17(5):1113. doi: 10.3390/s17051113

Algorithm 1: Non-rigid alignment for two point clouds in neighboring views.

1:
point cloud Q:= down-sampled P1 (50 mm)
2:
point cloud S1:= down-sampled P1 (15 mm), point cloud S2 := down-sampled P2 (15 mm)
3:
new embedded deformation graph G with G.node_amount = Q.point_amount
4:
for i:= 1 to Q.point_amount
5:
G.node[i].xyz := Q.point[i].xyz
6:
G.node[i].translation_matrix:= 3 × 1 zero matrix
7:
G.node[i].rotation_matrix:= 3 × 3 identity matrix
8:
end for
9:
while not reach max iteration times or stop condition
10:
for i:= 1 to S1.point_amount
11:
S1.point[i].correspondence:= corresponding point in S2
12:
end for
13:
matrix X:= all rotation matrix and translation matrix in G
14:
new Gauss-Newton iterator (X = arg min ( $w_{1} E_{r i g i d} + w_{2} E_{s m o o t h} + w_{3} E_{c o r}$ ))
15:
new matrix f
16:
while not satisfy precision requirement
17:
compute matrix f according to $w_{1} E_{r i g i d} + w_{2} E_{s m o o t h} + w_{3} E_{c o r}$

f^Tf = $2 (w_{1} E_{r i g i d} + w_{2} E_{s m o o t h} + w_{3} E_{c o r})$
18:
matrix J := jacobian_matrix(f)
19:
Cholesky_Decompositon.solve_linear_equation

Obtain the iteration $h_{k + 1} = h_{k} + Δ h$ where J^TJ Δh_k = −J^Tf
20:
X:= X + h
21:
Update E;
22:
end while
23:
deform P1 with G
24:
end while