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

2010 ◽  
Vol 371 (2) ◽  
pp. 764-776 ◽  
Author(s):  
Süha Yılmaz ◽  
Melih Turgut
Keyword(s):  
Bishop Frame ◽  
Spherical Images

Relation between Darboux and type-2 Bishop frames in Euclidean space

2016 ◽  
Vol 13 (07) ◽  
pp. 1650101 ◽  
Author(s):  
Amine Yilmaz ◽  
Emin Özyilmaz
Keyword(s):  
Euclidean Space ◽  
Transition Matrix ◽  
Geodesic Curvature ◽  
Spherical Image ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Spherical Images

In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.

An application of N-Bishop frame to spherical images for direction curves

2017 ◽  
Vol 14 (11) ◽  
pp. 1750162 ◽  
Author(s):  
Ozgur Keskin ◽  
Yusuf Yayli
Keyword(s):  
Unit Sphere ◽  
Integral Curve ◽  
Normal Direction ◽  
Bishop Frame ◽  
Integral Curves ◽  
Spherical Images

In this paper, we first introduce [Formula: see text]-Bishop frame for a normal direction curve which is defined as an integral curve of the principal normal of a curve. We express this new frame and its properties. Afterwards, we obtain new spherical images by translating [Formula: see text]-Bishop frame vectors to the center of unit sphere [Formula: see text] in [Formula: see text]. Then, these new spherical images are called [Formula: see text]-Bishop spherical images. Additionally, we compute the Frénet–Serret equations of these new spherical images. Moreover, we show that integral curves of [Formula: see text]-Bishop spherical images of slant helices are also slant helices. Finally, we present some illustrated examples.

scholarly journals Cusps of Bishop Spherical Indicatrixes and Their Visualizations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Haiming Liu ◽  
Donghe Pei
Keyword(s):  
Space Curve ◽  
Singular Points ◽  
Bishop Frame ◽  
Spherical Images

The main result of this paper is using Bishop Frame and “Type-2 Bishop Frame” to study the cusps of Bishop spherical images and type-2 Bishop spherical images which are deeply related to a space curve and to make them visualized by computer. We find that the singular points of the Bishop spherical images and type-2 Bishop spherical images correspond to the point where Bishop curvatures and type-2 Bishop curvatures vanished and their derivatives are not equal to zero. As applications and illustration of the main results, two examples are given.

Methods for constructing virtual panoramic tours

2020 ◽  
Author(s):  
Elizaveta Koptenok ◽  
Natalia Lagereva ◽  
Arsenii Savenko ◽  
Ilia Fomin
Keyword(s):  
Real Estate ◽  
Web Service ◽  
Virtual Museums ◽  
Implementation Method ◽  
Spherical Images

The article discusses the existing methods for building virtual panoramic tours. A proprietary implementation method based on the Yandex JS API technology is proposed. The designed web service allows to automatically create virtual panoramic tours from a collection of panoramic spherical images "in one click", in contrast to the considered analogues. The developed technology should be used for educational purposes, for example, for the implementation of virtual museums, as well as on real estate trading platforms to increase ad views and improve sales.

Biomass estimates derived from sector subsampling of 360° spherical images

2021 ◽  
Author(s):  
Xiao Dai ◽  
Mark J Ducey ◽  
Haozhou Wang ◽  
Ting-Ru Yang ◽  
Yung-Han Hsu ◽  
...  
Keyword(s):  
Basal Area ◽  
Sampling Errors ◽  
Eastern Canada ◽  
Individual Tree ◽  
Inventory Costs ◽  
Standard Error Estimation ◽  
The Mean ◽  
Biomass Ratio ◽  
Spherical Images ◽  
Additional Level

Abstract Efficient subsampling designs reduce forest inventory costs by focusing sampling efforts on more variable forest attributes. Sector subsampling is an efficient and accurate alternative to big basal area factor (big BAF) sampling to estimate the mean basal area to biomass ratio. In this study, we apply sector subsampling of spherical images to estimate aboveground biomass and compare our image-based estimates with field data collected from three early spacing trials on western Newfoundland Island in eastern Canada. The results show that sector subsampling of spherical images produced increased sampling errors of 0.3–3.4 per cent with only about 60 trees measured across 30 spherical images compared with about 4000 trees measured in the field. Photo-derived basal area was underestimated because of occluded trees; however, we implemented an additional level of subsampling, collecting field-based basal area counts, to correct for bias due to occluded trees. We applied Bruce’s formula for standard error estimation to our three-level hierarchical subsampling scheme and showed that Bruce’s formula is generalizable to any dimension of hierarchical subsampling. Spherical images are easily and quickly captured in the field using a consumer-grade 360° camera and sector subsampling, including all individual tree measurements, were obtained using a custom-developed python software package. The system is an efficient and accurate photo-based alternative to field-based big BAF subsampling.

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