IEICE TRANSACTIONS on Fundamentals
Efficient Approximate 3-Dimensional Point Set Matching Using Root-Mean-Square Deviation Score
Summary :
In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.9 pp.1159-1170
- Publication Date
- 2019/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E102.A.1159
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Optimization
Authors
Yoichi SASAKI
Hokkaido University
Tetsuo SHIBUYA
University of Tokyo
Kimihito ITO
Hokkaido University
Hiroki ARIMURA
Hokkaido University
Keyword
Latest Issue
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Yoichi SASAKI, Tetsuo SHIBUYA, Kimihito ITO, Hiroki ARIMURA, "Efficient Approximate 3-Dimensional Point Set Matching Using Root-Mean-Square Deviation Score" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 9, pp. 1159-1170, September 2019, doi: 10.1587/transfun.E102.A.1159.
Abstract: In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1159/_p
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@ARTICLE{e102-a_9_1159,
author={Yoichi SASAKI, Tetsuo SHIBUYA, Kimihito ITO, Hiroki ARIMURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Efficient Approximate 3-Dimensional Point Set Matching Using Root-Mean-Square Deviation Score},
year={2019},
volume={E102-A},
number={9},
pages={1159-1170},
abstract={In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.},
keywords={},
doi={10.1587/transfun.E102.A.1159},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - Efficient Approximate 3-Dimensional Point Set Matching Using Root-Mean-Square Deviation Score
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1159
EP - 1170
AU - Yoichi SASAKI
AU - Tetsuo SHIBUYA
AU - Kimihito ITO
AU - Hiroki ARIMURA
PY - 2019
DO - 10.1587/transfun.E102.A.1159
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2019
AB - In this paper, we study the approximate point set matching (APSM) problem with minimum RMSD score under translation, rotation, and one-to-one correspondence in d-dimension. Since most of the previous works about APSM problems use similality scores that do not especially care about one-to-one correspondence between points, such as Hausdorff distance, we cannot easily apply previously proposed methods to our APSM problem. So, we focus on speed-up of exhaustive search algorithms that can find all approximate matches. First, we present an efficient branch-and-bound algorithm using a novel lower bound function of the minimum RMSD score for the enumeration version of APSM problem. Then, we modify this algorithm for the optimization version. Next, we present another algorithm that runs fast with high probability when a set of parameters are fixed. Experimental results on both synthetic datasets and real 3-D molecular datasets showed that our branch-and-bound algorithm achieved significant speed-up over the naive algorithm still keeping the advantage of generating all answers.
ER -
English
