A new version of Bishop frame and an application to spherical images

被引：83

作者：

Yilmaz, Sueha ^{[1
]}

Turgut, Melih ^{[1
]}

机构：

[1] Dokuz Eylul Univ, Buca Educ Fac, Dept Math, TR-35160 Buca Izmir, Turkey

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 371卷 / 02期

关键词：

Classical differential geometry; Spherical images; Bishop frame; General helix; Slant helix; Euclidean space; ALTERNATIVE MOVING FRAME; SLANT HELICES; MINKOWSKI; CURVES;

D O I：

10.1016/j.jmaa.2010.06.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we introduce a new version of Bishop frame using a common vector field as binormal vector field of a regular curve and call this frame as "Type-2 Bishop Frame" Thereafter, by translating type-2 Bishop frame vectors to the center of unit sphere of three-dimensional Euclidean space, we introduce new spherical images and call them as type-2 Bishop spherical images. Frenet-Serret apparatus of these new spherical Images are obtained in terms of base curve's type-2 Bishop invariants. Additionally, we express some interesting relations and illustrate two examples of our main results. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：764 / 776

页数：13

共 50 条

[31] A New Quaternion Valued Frame of Curves with an Application
Cansu, Gizem
Yayli, Yusuf
Gok, Ismail
FILOMAT, 2021, 35 (01) : 315 - 330
[32] Some curve pairs according to types of Bishop frame
YILMAZ, Beyhan
AIMS MATHEMATICS, 2021, 6 (05): : 4463 - 4473
[33] A new method for spherical object detection and its application to computer aided detection of pulmonary nodules in CT images
Zhang, Xiangwei
Stockel, Jonathan
Wolf, Matthias
Cathier, Pascal
McLennan, Geoffrey
Hoffman, Eric A.
Sonka, Milan
MEDICAL IMAGE COMPUTING AND COMPUTER-ASSISTED INTERVENTION - MICCAI 2007, PT 1, PROCEEDINGS, 2007, 4791 : 842 - +
[34] Glenoid spherical orientation and version
Lewis, Gregory S.
Armstrong, April D.
JOURNAL OF SHOULDER AND ELBOW SURGERY, 2011, 20 (01) : 3 - 11
[35] NONCOMPACT VERSION OF CHOGUET-BISHOP-DELEEUW THEOREM
POLONSKII, YA
IZVESTIYA VYSSHIKH UCHEBNYKH ZAVEDENII MATEMATIKA, 1991, (06): : 45 - 48
[36] THE RELATION BETWEEN FRENET FRAME OF THE NATURAL LIFT CURVE AND BISHOP FRAME OF THE CURVE br
Ergun, Evren
JOURNAL OF SCIENCE AND ARTS, 2022, (04): : 979 - 990
[37] A new modified version of the HDWTSVD coding system for monochromatic images
Ochoa, Humberto
Mireles, Jose
Rao, K.R.
WSEAS Transactions on Systems, 2006, 5 (05): : 1190 - 1195
[38] There is no operatorwise version of the Bishop-Phelps-Bollobas property
Dantas, Sheldon
Kadets, Vladimir
Kim, Sun Kwang
Lee, Han Ju
Martin, Miguel
LINEAR & MULTILINEAR ALGEBRA, 2020, 68 (09): : 1767 - 1778
[39] A new version of Visual tool for estimating the fractal dimension of images
Grossu I.V.
Felea D.
Besliu C.
Jipa Al.
Bordeianu C.C.
Stan E.
Esanu T.
Computer Physics Communications, 2010, 181 (04) : 831 - 832
[40] A New Spherical Mixture Model for Head Detection in Depth Images
Brazey, Denis
Portier, Bruno
SIAM JOURNAL ON IMAGING SCIENCES, 2014, 7 (04): : 2423 - 2447

← 1 2 3 4 5 →