# REGISTRATION OF 3D - PATTERNS AND SHAPES WITH CHARACTERISTIC POINTS

### Darko Dimitrov, Christian Knauer, Klaus Kriegel

#### 2006

#### Abstract

We study approximation algorithms for a matching problem that is motivated by medical applications. Given a small set of points P ⊂ R3 and a surface S, the optimal matching of P with S is represented by a rigid transformation which maps P as ‘close as possible’ to S. Previous solutions either require polynomial runtime of high degree or they make use of heuristic techniques which could be trapped in some local minimum. We propose a modification of the problem setting by introducing small subsets of so called characteristic points Pc ⊆ P and Sc ⊆ S, and assuming that points from Pc must be matched with points from Sc. We focus our attention on the first nontrivial case that occurs if |Pc | = 2, and show that this restriction results in new fast and reliable algorithms for the matching problem. In contrast to heuristic approaches our algorithm provides guarantees on the approximation factor of the matching. Experimental results are provided for surfaces reconstructed from real and synthetic data.

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#### Paper Citation

#### in Harvard Style

Dimitrov D., Knauer C. and Kriegel K. (2006). **REGISTRATION OF 3D - PATTERNS AND SHAPES WITH CHARACTERISTIC POINTS** . In *Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,* ISBN 972-8865-40-6, pages 393-400. DOI: 10.5220/0001368303930400

#### in Bibtex Style

@conference{visapp06,

author={Darko Dimitrov and Christian Knauer and Klaus Kriegel},

title={REGISTRATION OF 3D - PATTERNS AND SHAPES WITH CHARACTERISTIC POINTS},

booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,},

year={2006},

pages={393-400},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001368303930400},

isbn={972-8865-40-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP,

TI - REGISTRATION OF 3D - PATTERNS AND SHAPES WITH CHARACTERISTIC POINTS

SN - 972-8865-40-6

AU - Dimitrov D.

AU - Knauer C.

AU - Kriegel K.

PY - 2006

SP - 393

EP - 400

DO - 10.5220/0001368303930400