Monge Hypersurfaces in Euclidean 4-Space with Density

Altin, Mustafa; Kazan, Ahmet; Karadağ, H. Bayram

doi:10.2339/politeknik.634175

Cited by 6 publications

(5 citation statements)

References 21 publications

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“…The determinant of the Hessian matrix expresses the positive or negative value of the curvature of the surface. The geometrical labeling and classification of the image surface are carried out with the signs of surface curvatures [48]- [50].…”

Section: A Hessian Matrixmentioning

confidence: 99%

Multi-Resolution Intrinsic Texture Geometry-Based Local Binary Pattern for Texture Classification

Alpaslan

Hanbay

2020

IEEE Access

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In this paper, we propose a new hybrid Local Binary Pattern (LBP) based on Hessian matrix and Attractive Center-Symmetric LBP (ACS-LBP), called Hess-ACS-LBP. The Hessian matrix provides the directional derivative information of different texture regions, while ACS-LBP reveals the local texture features efficiently. To obtain the macro-and micro-structure textural changes, Hessian matrix is calculated in a multiscale schema. Multiscale Hessian matrix presents the intrinsic local geometry of the texture changes. The magnitude information of the Hessian matrix is used in the ACS-LBP method. A cross-scale joint coding strategy is used to construct Hess-ACS-LBP descriptor. Finally, histogram concatenation is carried out. Extensive experiments on eight texture databases of CUReT, USPTex, KTH-TIPS2b, MondialMarmi, OuTeX TC_00013, XU HR, ALOT and STex validate the efficiency of the proposed method. The proposed Hess-ACS-LBP method achieves about 20% improvement over the original LBP method and 1%-11% improvement over the other state-of-the-art hand-crafted LBP methods in terms of classification accuracy. Besides, the experimental results show that the proposed method achieves up to 32% better results than the state-of-the-art deep learning based methods. Especially, the performance of the proposed method on ALOT and STex datasets containing many classes is remarkable. INDEX TERMS Hessian matrix, feature extraction, local binary patterns, texture classification.

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Section: A Hessian Matrixmentioning

confidence: 99%

Multi-Resolution Intrinsic Texture Geometry-Based Local Binary Pattern for Texture Classification

Alpaslan

Hanbay

2020

IEEE Access

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“…In [31], weighted minimal translation surfaces in the Galilean 3-space with log-linear density have been classified and in [19], weighted minimal and weighted flat surfaces of revolution in Galilean 3-space with density 2 + 2 + 2 have been investigated. Also, Altın and his friends have studied ruled surfaces and rotational surfaces in different spaces with density, in recent years (see [18,[35][36][37][38]).…”

Section: Introductionmentioning

confidence: 99%

Rotational Hypersurfaces in Euclidean 4-Space with Density

Altin

2022

Politeknik Dergisi

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“…Furthermore, the differential geometry of different types of (hyper)surfaces in 4-D spaces has been a popular topic for geometers, recently, [17,[28][29][30][31][32][33][34][35], and etc. If Ω: U ⊂ E 3 → E 4 is a hypersurface in E 4 parametrized by: ( )…”

Section: Introductionmentioning

confidence: 99%

Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

Kazan

2022

THERM SCI

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In the present study, we deal with canal hypersurfaces according to extended Darboux frame field of second kind in Euclidean 4-space (E4) and in this context, firstly we obtain the Gaussian, mean and principal curvatures of the canal hypersurface according to extended Darboux frame field of second kind and give some results for flatness and minimality of these hypersurfaces in E4. Also, we give some results for Weingarten canal hypersurfaces according to extended Darboux frame field of second kind in E4 and finally, we construct an example.

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Monge Hypersurfaces in Euclidean 4-Space with Density

Cited by 6 publications

References 21 publications

Multi-Resolution Intrinsic Texture Geometry-Based Local Binary Pattern for Texture Classification

Multi-Resolution Intrinsic Texture Geometry-Based Local Binary Pattern for Texture Classification

Rotational Hypersurfaces in Euclidean 4-Space with Density

Canal hypersurfaces according to one of the extended Darboux frame field in Euclidean 4-space

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