Large Common Plansets4Points Congruent Sets for Point Cloud Registration
Abstract
:1. Introduction
2. Related Work
 Initialize registration parameters (Rotation, Translation, Scale) and registration error.
 For each point in the P, find the corresponding closest point in Q.
 Compute registration parameters, given the point correspondences obtained in step 2.
 Apply the alignment to P
 Compute the registration error between the currently aligned P and Q
 If error > threshold and max iterations has not been reached return to step 2 with new P.
 $numberAlignPoints=0$
 Select a set of 4 coplanar points B in S
 Find the congruent bases U of B into T within an approximation level $\delta >0$
 For each ${U}_{i}$$\in U$ find the best rigid transform ${G}_{i}$, ${G}_{i}\left(Ui\right)=B$
 Find ${Q}_{i}\subseteq T$, such that $d({G}_{i}\left({Q}_{i}\right),S)\le \delta $
 If ${Q}_{i}>numberAlignPoints$ then $numberAlignPoints$=${Q}_{i}$ and $rigidTransform={G}_{i}$
 Repeat the process from step 2 L times
 return $rigidTransform$
3. Large Common Plansets4PCS (LCP4PCS)
 In cases where the overlap levels between the entities to be merged are very low. A relatively large increase in the number of maximum iterations sometimes leads to good results. However, the execution time increases considerably.
 In cases where overlapping portions between the point clouds to be merged are concentrated in a relatively small part of the entities. An increase in the number of iterations does not improve the results.
Algorithm 1 LCP4PCS Given two point clouds P and Q in arbitrary initial positions, $\delta \in ]0;1]$ an approximation level, $\beta \in ]0;1]$ an overlapping threshold and $L>0$ a maximal iteration. 

4. Experiments and Results
4.1. Data and Implementation
4.2. Tests and Comparisons
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Dataset  Scan1  Scan2  Time(s)  

Number Segments before Fusion  Number Segments after Fusion  Number Segments before Fusion  Number Segments after Fusion  Time before Fusion  Time after Fusion  
Camertronix  27  14  11  8  179  107 
Valentino  34  21  19  14  75  44 
Charlottebügerturm  43  25  37  22  162  91 
Buro  32  9  11  6  173  98 
Flurzimmer  27  18  6  5  74  49 
Dataset  Size(x1000)  4PCS  LCP4PCS  

Scan1  Scan2  Aligned Samples (%)  Time (s)  Aligned Samples (%)  Number Aligned Segments  Time (s)  
Camertronix  1,708,126  1,281,042  528  141  17.2  3  107 
Valentino  82,259  75,533  507  108  223  2  44 
Charlottebürgerturm  1,218,731  1,132,942  998  165  208  8  91 
Buro  1,447,277  1,051,268  673  125  191  2  98 
Flurzimmer  95,804  89,378  494  93  157  2  49 
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Fotsing, C.; Nziengam, N.; Bobda, C. Large Common Plansets4Points Congruent Sets for Point Cloud Registration. ISPRS Int. J. GeoInf. 2020, 9, 647. https://doi.org/10.3390/ijgi9110647
Fotsing C, Nziengam N, Bobda C. Large Common Plansets4Points Congruent Sets for Point Cloud Registration. ISPRS International Journal of GeoInformation. 2020; 9(11):647. https://doi.org/10.3390/ijgi9110647
Chicago/Turabian StyleFotsing, Cedrique, Nafissetou Nziengam, and Christophe Bobda. 2020. "Large Common Plansets4Points Congruent Sets for Point Cloud Registration" ISPRS International Journal of GeoInformation 9, no. 11: 647. https://doi.org/10.3390/ijgi9110647