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Fast and efficient calculations of structural invariants of chirality.

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Title: Fast and efficient calculations of structural invariants of chirality.
Authors: Zhang, He1,2 (AUTHOR) zhanghe@ict.ac.cn, Mo, Hanlin1,2 (AUTHOR), Hao, You1,2 (AUTHOR), Li, Qi1,2 (AUTHOR), Li, Shirui1,2 (AUTHOR), Li, Hua1,2 (AUTHOR)
Source: Pattern Recognition Letters. Dec2019, Vol. 128, p270-277. 8p.
Subjects: Chirality, Generating functions, Mathematical invariants, Chirality of nuclear particles, Symmetry
Abstract: • Chiral invariants before and after reflection are opposite to each other. • Brief form, low time complexity (O (n)), order and degree are no more than four. • Determining the global symmetry plane and coping with false zeros problems. Chirality describes the structural properties or configuration of an object, and it plays an important role in fields such as physics, chemistry and biology. It is critical to identify achiral objects and determine symmetry plane of them in shape analysis, and chiral invariants play essential role in above tasks. However, chiral invariants are often complex and time-consuming to calculate in practical applications. In this paper, we present five chiral invariants based on the concept of generating functions. Three of the five chiral invariants decode the expression of a chiral index, and they are the core part of this chiral index. In addition, this paper provides three new chiral invariants. These five chiral invariants have three characteristics: (1) Their results on the shape before and after the reflection transformation are opposite to each other. (2) The five chiral invariants have brief form and low time complexity (O (n)), the order and degree of them are not more than four. (3) They can be used to determine the global symmetry plane of reflection symmetry objects, and they help to deal with false zeros problem. The five chiral invariants give the invariants under reflection transformation from the geometrical point of view, and the experimental results show that they are effective and efficient. In conclusion, our invariants can be used for determining archiral objects and mutual symmetry shape, as well as for determining symmetry plane of reflection symmetry objects. [ABSTRACT FROM AUTHOR]
Copyright of Pattern Recognition Letters is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 139767190
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
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  Data: Fast and efficient calculations of structural invariants of chirality.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+He%22">Zhang, He</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zhanghe@ict.ac.cn</i><br /><searchLink fieldCode="AR" term="%22Mo%2C+Hanlin%22">Mo, Hanlin</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hao%2C+You%22">Hao, You</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Qi%22">Li, Qi</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Shirui%22">Li, Shirui</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Hua%22">Li, Hua</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Pattern+Recognition+Letters%22">Pattern Recognition Letters</searchLink>. Dec2019, Vol. 128, p270-277. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Chirality%22">Chirality</searchLink><br /><searchLink fieldCode="DE" term="%22Generating+functions%22">Generating functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+invariants%22">Mathematical invariants</searchLink><br /><searchLink fieldCode="DE" term="%22Chirality+of+nuclear+particles%22">Chirality of nuclear particles</searchLink><br /><searchLink fieldCode="DE" term="%22Symmetry%22">Symmetry</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: • Chiral invariants before and after reflection are opposite to each other. • Brief form, low time complexity (O (n)), order and degree are no more than four. • Determining the global symmetry plane and coping with false zeros problems. Chirality describes the structural properties or configuration of an object, and it plays an important role in fields such as physics, chemistry and biology. It is critical to identify achiral objects and determine symmetry plane of them in shape analysis, and chiral invariants play essential role in above tasks. However, chiral invariants are often complex and time-consuming to calculate in practical applications. In this paper, we present five chiral invariants based on the concept of generating functions. Three of the five chiral invariants decode the expression of a chiral index, and they are the core part of this chiral index. In addition, this paper provides three new chiral invariants. These five chiral invariants have three characteristics: (1) Their results on the shape before and after the reflection transformation are opposite to each other. (2) The five chiral invariants have brief form and low time complexity (O (n)), the order and degree of them are not more than four. (3) They can be used to determine the global symmetry plane of reflection symmetry objects, and they help to deal with false zeros problem. The five chiral invariants give the invariants under reflection transformation from the geometrical point of view, and the experimental results show that they are effective and efficient. In conclusion, our invariants can be used for determining archiral objects and mutual symmetry shape, as well as for determining symmetry plane of reflection symmetry objects. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Pattern Recognition Letters is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.patrec.2019.09.010
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      – Code: eng
        Text: English
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        PageCount: 8
        StartPage: 270
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      – SubjectFull: Chirality
        Type: general
      – SubjectFull: Generating functions
        Type: general
      – SubjectFull: Mathematical invariants
        Type: general
      – SubjectFull: Chirality of nuclear particles
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      – SubjectFull: Symmetry
        Type: general
    Titles:
      – TitleFull: Fast and efficient calculations of structural invariants of chirality.
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            NameFull: Zhang, He
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            NameFull: Mo, Hanlin
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            NameFull: Hao, You
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            NameFull: Li, Shirui
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            – D: 01
              M: 12
              Text: Dec2019
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              Y: 2019
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              Value: 128
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