Image Processing Reference

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Table 2

Correspondence distances and average marker error for four variants of ICP

Correspondence Distance [mm] Marker Error [number of unit]

ID

E

NH

SM

DM

E

NH

SM

DM

1

0.26

0.18

0.25

0.58

12.42

10.81

4.45

0.76

2

0.12

0.27

0.33

0.87

7.02

6.28

2.12

1.49

3

0.04

0.03

0.03

1.7

2.57

2.9

1.86

0.44

4

0.14

0.22

0.15

0.88

4.3

4.63

3.6

0.72

5

0.04

0.07

0.1

0.1

4.05

2.61

3.11

4.69

6

0.16

0.07

0.06

0.53

2.25

1.89

0.75

0.09

E, the Euclidean distance; NH, normal vectors with initial rigid registration; SM, static; DM, dynamic markers vectors.

4 Discussion and conclusions

The implemented nonrigid ICP algorithm showed average residual distance of 0.68 mm (Euc-

lidean distance not included). A further analysis of registration accuracy was focused on ind-

ing correspondence problem. Four methods for this problem were tested: Euclidean distance

treated as base line, normal shooting with initial rigid registration—marker-based Horn al-

gorithm, static marker vectors (computing only one at the beginning of registration process),

and dynamic marker vectors (computing in every iteration). For “near” cloud, where stiffness

vector is constant for almost every iterations in nonrigid ICP, Euclidean distance is good

enough. Unlike “near” clouds, “far” clouds, where stiffness vectors are changing for few iter-

ations, Euclidean distance seems to be not enough. There are a lot of gaps in registered source

not only used in computing transformation step but also in computing correspondences step

for each iteration, correspondence assignment error of points nearest to the markers decreased

from 5.4 to 2.0 of confused neighbors. Normal shooting approach was also evaluated, but res-

ults were worse than other cases, while combination normal shooting and initial rigid regis-

tration significantly improved results (
Figure 2
). To use Horn algorithm at least three noncol-

linear corresponding points in source and target should be known. It helps to overcome the

problem of the relative displacement of the source and target point clouds, which is not taking

into account when Euclidean distance is used.

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