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**Harvard**

Utriainen, T. (2010) *Least squares rigid body fitting of point-sets with unknown correspondences*. Göteborg : Chalmers University of Technology (Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, nr: 3091).

** BibTeX **

@book{

Utriainen2010,

author={Utriainen, Tapani},

title={Least squares rigid body fitting of point-sets with unknown correspondences},

isbn={978-91-7385-410-8},

abstract={The problem addressed here is: given points
u_1,...,u_n and v_1,...,v_n, find a translation t, a rotation R, a scale factor s, and an one-to-one correspondence pi(), that minimize the least squares error:
error = min_{t,R,s,pi} \sum_{i=1}^n ||s R u_i - v_{pi(i)} + t||_2^2
When the point-to-point correspondences are not known beforehand, and are to be determined as a part of the problem, no polynomial time algorithm with a performance guarantee has been described in the literature.
This thesis proves that near-optimal solutions can be calculated in polynomial time for both two- and three-dimensional point-sets.
In two dimensions this is done by transforming the problem to a vector-weighted bipartite matching problem (VWBM), and devising fully polynomial time approximation schemes (FPTAS) for it. It is discussed why an approximation scheme for a VWBM is not necessarily an approximation scheme for the two-dimensional point-matching problem. It is demonstrated that a global optimum for the two-dimensional problem can be computed in practice.
In three dimensions, the problem of least squares fitting point-sets is transformed to an eigenvalue maximization problem. An FPTAS is presented for the eigenvalue maximization problem, but similiarily to the two-dimensional case, that FPTAS is not necessarily one for the 3-D point-matching problem. Further, it is demonstrated that the presented algorithms are able to calculate
near-optimal solutions in practice.
},

publisher={Institutionen för data- och informationsteknik, Datavetenskap, Algoritmer (Chalmers), Chalmers tekniska högskola,},

place={Göteborg},

year={2010},

series={Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 3091Technical report D - Department of Computer Science and Engineering, Chalmers University of Technology and Göteborg University, no: 70},

note={129},

}

** RefWorks **

RT Dissertation/Thesis

SR Print

ID 121598

A1 Utriainen, Tapani

T1 Least squares rigid body fitting of point-sets with unknown correspondences

YR 2010

SN 978-91-7385-410-8

AB The problem addressed here is: given points
u_1,...,u_n and v_1,...,v_n, find a translation t, a rotation R, a scale factor s, and an one-to-one correspondence pi(), that minimize the least squares error:
error = min_{t,R,s,pi} \sum_{i=1}^n ||s R u_i - v_{pi(i)} + t||_2^2
When the point-to-point correspondences are not known beforehand, and are to be determined as a part of the problem, no polynomial time algorithm with a performance guarantee has been described in the literature.
This thesis proves that near-optimal solutions can be calculated in polynomial time for both two- and three-dimensional point-sets.
In two dimensions this is done by transforming the problem to a vector-weighted bipartite matching problem (VWBM), and devising fully polynomial time approximation schemes (FPTAS) for it. It is discussed why an approximation scheme for a VWBM is not necessarily an approximation scheme for the two-dimensional point-matching problem. It is demonstrated that a global optimum for the two-dimensional problem can be computed in practice.
In three dimensions, the problem of least squares fitting point-sets is transformed to an eigenvalue maximization problem. An FPTAS is presented for the eigenvalue maximization problem, but similiarily to the two-dimensional case, that FPTAS is not necessarily one for the 3-D point-matching problem. Further, it is demonstrated that the presented algorithms are able to calculate
near-optimal solutions in practice.

PB Institutionen för data- och informationsteknik, Datavetenskap, Algoritmer (Chalmers), Chalmers tekniska högskola,

T3 Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, no: 3091Technical report D - Department of Computer Science and Engineering, Chalmers University of Technology and Göteborg University, no: 70

LA eng

OL 30