Relevant bibliographies by topics / Riemannian metric and distance

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Riemannian metric and distance'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Riemannian metric and distance"

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Xie, Ying Hong, and Cheng Dong Wu. "Study on the Comparison of Two Metrics Used in the Fields of Object Tracking." Applied Mechanics and Materials 483 (December 2013): 419–22. http://dx.doi.org/10.4028/www.scientific.net/amm.483.419.

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The paper researches on the comparison of two metrics methods under Riemannian metric and under Log-Euclidean metric respectively. Firstly, Experiments are done for comparing the distance and mean values worked out under the two metrics. And the time required for computing under these two metrics is also shown. Lastly, the two methods are applied to the field of image tracking. The performance of the two methods is compared, and the time required for tracking each frame is gained. Experiments results show that the two methods can gain similar distance and mean values, and similar tracking resu
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Sanjay, Kumar. "Statistical features on Riemannian Manifold." MATHEMATICS EDUCATION LVIII, no. 2, June 2024 (2024): 10–22. https://doi.org/10.5281/zenodo.13855976.

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<em> &nbsp;Manifold are fundamental structures in different geometry. A smooth manifold with a metric is called a Riemannian Manifold. A connected Riemannian manifold carries the structure of metric space where distance function is the arc length of minimizing geodesic. In this paper, we consider finite dimensional manifold with a Riemannian metric as the basic structure. Based on this metric, we develop the notion of mean value, and covariance matrix of a random element, normal law mahalanobis distance and x2 test. &nbsp; &nbsp;</em>
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Mahamane, Saminou Ali, Hassirou Mouhamadou, and Mahaman Bazanfare. "Geodesically Complete Lie Algebroid." British Journal of Mathematics & Computer Science 22, no. 5 (2017): 1–12. https://doi.org/10.9734/BJMCS/2017/34009.

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In this paper we introduce the notion of geodesically complete Lie algebroid. We give a Riemannian distance on the connected base manifold of a Riemannian Lie algebroid. We also prove that the distance is equivalent to natural one if the base manifold was endowed with Riemannian metric. We obtain Hopf Rinow type theorem in the case of transitive Riemannian Lie algebroid, and give a characterization of the connected base manifold of a geodesically complete Lie algebroid.
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Rylov, Yuri A. "Geometry without topology as a new conception of geometry." International Journal of Mathematics and Mathematical Sciences 30, no. 12 (2002): 733–60. http://dx.doi.org/10.1155/s0161171202012243.

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A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two points). Such geometric concepts as dimension, manifold, metric tensor, curve are fundamental in the Riemannian conception of geometry, and they are derivative in the T-geometric one. T-geometry is the simplest geometric conception (essentially, only finite point sets are investigated) and simultaneously, it is the most general one. It is insensitive to the s
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Ho, Pei-Ming. "Riemannian Geometry on Quantum Spaces." International Journal of Modern Physics A 12, no. 05 (1997): 923–43. http://dx.doi.org/10.1142/s0217751x97000694.

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An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space.
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Correa, Cleber Souza, Thiago Braido Nogueira de Melo, and Diogo Machado Custódio. "The Alpha Group Tensorial Metric." Revista Brasileira de História da Matemática 24, no. 48 (2024): 51–57. http://dx.doi.org/10.47976/rbhm2024v24n4851-57.

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The Alpha Group is an abstract geometry group in R4. The way it was conceived allows a new interpretation of the structure of hypercomplex space with a new geometry and spatial topology, and a meaning for the geometric representation of R4 space to infinity. Therefore, it has been described as the tensorial metric formula in the Alpha Group. It will be shown that the Riemannian and Euclidean distance metrics between infinitesimal surfaces are represented as special cases of the metric of the Alpha group.
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Mönkkönen, Keijo. "Boundary rigidity for Randers metrics." Annales Fennici Mathematici 47, no. 1 (2021): 89–102. http://dx.doi.org/10.54330/afm.112492.

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&#x0D; If a non-reversible Finsler norm is the sum of a reversible Finsler norm and a closed 1-form, then one can uniquely recover the 1-form up to potential fields from the boundary distance data. We also show a boundary rigidity result for Randers metrics where the reversible Finsler norm is induced by a Riemannian metric which is boundary rigid. Our theorems generalize Riemannian boundary rigidity results to some non-reversible Finsler manifolds. We provide an application to seismology where the seismic wave propagates in a moving medium.
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Stojisavljević, Vukašin, and Jun Zhang. "Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics." International Journal of Mathematics 32, no. 07 (2021): 2150040. http://dx.doi.org/10.1142/s0129167x21500403.

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We use persistence modules and their corresponding barcodes to quantitatively distinguish between different fiberwise star-shaped domains in the cotangent bundle of a fixed manifold. The distance between two fiberwise star-shaped domains is measured by a nonlinear version of the classical Banach–Mazur distance, called symplectic Banach–Mazur distance and denoted by [Formula: see text]. The relevant persistence modules come from filtered symplectic homology and are stable with respect to [Formula: see text]. Our main focus is on the space of unit codisc bundles of orientable surfaces of positiv
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Beem, John K., and Paul E. Ehrlich. "Geodesic completeness and stability." Mathematical Proceedings of the Cambridge Philosophical Society 102, no. 2 (1987): 319–28. http://dx.doi.org/10.1017/s0305004100067347.

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A (connected) Riemannian manifold M is geodesically complete (i.e. each geodesic may be extended to a geodesic with domain ( −∞, + ∞)) iff, as a metric space under the induced Riemannian distance function, M is Cauchy complete ([12], p. 138). Furthermore, all compact Riemannian manifolds are complete. On the other hand, compact pseudo-Riemannian manifolds exist which are not geodesically complete. For example Fierz and Jost[8] have constructed incomplete metrics of the form 2dx dy + h dy2 on T2. Furthermore, Williams [16] has shown that geodesic completeness may fail to be stable for pseudo-Ri
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Fang, Yong, and Patrick Foulon. "On Finsler manifolds of negative flag curvature." Journal of Topology and Analysis 07, no. 03 (2015): 483–504. http://dx.doi.org/10.1142/s1793525315500181.

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One of the key differences between Finsler metrics and Riemannian metrics is the non-reversibility, i.e. given two points p and q, the Finsler distance d(p, q) is not necessarily equal to d(q, p). In this paper, we build the main tools to investigate the non-reversibility in the context of large-scale geometry of uniform Finsler Cartan–Hadamard manifolds. In the second part of this paper, we use the large-scale geometry to prove the following dynamical theorem: Let φ be the geodesic flow of a closed negatively curved Finsler manifold. If its Anosov splitting is C2, then its cohomological press
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Dissertations / Theses on the topic "Riemannian metric and distance"

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Suzuki, Kohei. "Convergence of stochastic processes on varying metric spaces." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215281.

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Palmer, Ian Christian. "Riemannian geometry of compact metric spaces." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34744.

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A construction is given for which the Hausdorff measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorff measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorff and box dimensions differ---in particular, it does n
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Choy, Tze Leung. "Sparse distance metric learning." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:a98695a3-0a60-448f-9ec0-63da3c37f7fa.

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A good distance metric can improve the accuracy of a nearest neighbour classifier. Xing et al. (2002) proposed distance metric learning to find a linear transformation of the data so that observations of different classes are better separated. For high-dimensional problems where many un-informative variables are present, it is attractive to select a sparse distance metric, both to increase predictive accuracy but also to aid interpretation of the result. In this thesis, we investigate three different types of sparsity assumption for distance metric learning and show that sparse recovery is pos
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Chang, Hong. "Semi-supervised distance metric learning /." View abstract or full-text, 2006. http://library.ust.hk/cgi/db/thesis.pl?COMP%202006%20CHANG.

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Christiansen, Tom. "Stochastic calculus in Riemannian polyhedra and martingales in metric spaces." [S.l.] : [s.n.], 2007. http://deposit.ddb.de/cgi-bin/dokserv?idn=983734232.

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Alekseevsky, Dmitri, Andreas Kriegl, Mark Losik, Peter W. Michor, and Peter Michor@esi ac at. "The Riemannian Geometry of Orbit Spaces. The Metric, Geodesics, and." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi997.ps.

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Persson, Nicklas. "Shortest paths and geodesics in metric spaces." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-66732.

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This thesis is divided into three part, the first part concerns metric spaces and specically length spaces where the existence of shortest path between points is the main focus. In the second part, an example of a length space, the Riemannian geometry will be given. Here both a classical approach to Riemannian geometry will be given together with specic results when considered as a metric space. In the third part, the Finsler geometry will be examined both with a classical approach and trying to deal with it as a metric space.
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Fuschino, Andrea. "Deep Meta Metric Learning via Learnable Distance." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.

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In this thesis work, we propose a Deep Metric Learning method via learnable distance to solve image retrieval problems. Unlike the conventional approaches where a certain predefined distance is used (such as the most commonly Euclidean distance) to compute the dissimilarity between embeddings, what we propose is to learn this distance with a neural network. This learned distance has the objective of performing better than a certain target distance (such as the Euclidean distance), trying to put the examples belonging to the same class closer and the examples belonging to different classes fart
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Law, Marc Teva. "Distance metric learning for image and webpage comparison." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066019/document.

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Cette thèse se focalise sur l'apprentissage de distance pour la comparaison d'images ou de pages Web. Les distances (ou métriques) sont exploitées dans divers contextes de l'apprentissage automatique et de la vision artificielle tels que la recherche des k plus proches voisins, le partitionnement, les machines à vecteurs de support, la recherche d'information/images, la visualisation etc. Nous nous intéressons dans cette thèse à l'apprentissage de fonction de distance paramétrée par une matrice symétrique semi-définie positive. Ce modèle, appelé (par abus) apprentissage de distance de Mahalano
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Law, Marc Teva. "Distance metric learning for image and webpage comparison." Electronic Thesis or Diss., Paris 6, 2015. http://www.theses.fr/2015PA066019.

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Cette thèse se focalise sur l'apprentissage de distance pour la comparaison d'images ou de pages Web. Les distances (ou métriques) sont exploitées dans divers contextes de l'apprentissage automatique et de la vision artificielle tels que la recherche des k plus proches voisins, le partitionnement, les machines à vecteurs de support, la recherche d'information/images, la visualisation etc. Nous nous intéressons dans cette thèse à l'apprentissage de fonction de distance paramétrée par une matrice symétrique semi-définie positive. Ce modèle, appelé (par abus) apprentissage de distance de Mahalano
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Books on the topic "Riemannian metric and distance"

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Gromov, Mikhael. Metric structures for Riemannian and non-Riemannian spaces. Birkhäuser, 1999.

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Grove, Karsten. Riemannian geometry: A metric entrance. University of Aarhus, Dept. of Mathemtics, 1999.

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1954-, Walschap Gerard, and SpringerLink (Online service), eds. Metric foliations and curvature. Birkhäuser, 2009.

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Washington, Allyn J. Basic technical mathematics with calculus. 5th ed. Addison-Wesley, 1990.

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Washington, Allyn J. Basic technical mathematics with calculus. 8th ed. Pearson/Addison-Wesley, 2005.

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Washington, Allyn J. Basic technical mathematics with calculus. 6th ed. Addison-Wesley, 1995.

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Washington, Allyn J. Basic technical mathematics with calculus. 5th ed. Benjamin/Cummings Pub. Co., 1990.

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Washington, Allyn J. Basic technical mathematics with calculus. 7th ed. Addison-Wesley, 2000.

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Washington, Allyn J. Basic technical mathematics with calculus. 4th ed. Benjamin/Cummings Pub. Co., 1985.

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Washington, Allyn J. Basic technical mathematics with calculus. 4th ed. Benjamin/Cummings Pub. Co., 1985.

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Book chapters on the topic "Riemannian metric and distance"

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Yessenbayev, Zhandos, and Zhanibek Kozhirbayev. "Use of Riemannian Distance Metric to Verify Topological Similarity of Acoustic and Text Domains." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-72350-6_25.

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Deza, Michel Marie, and Elena Deza. "Riemannian and Hermitian Metrics." In Encyclopedia of Distances. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44342-2_7.

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Deza, Michel Marie, and Elena Deza. "Riemannian and Hermitian Metrics." In Encyclopedia of Distances. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-30958-8_7.

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Deza, Michel Marie, and Elena Deza. "Riemannian and Hermitian Metrics." In Encyclopedia of Distances. Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-52844-0_7.

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A’Campo, Norbert. "Surfaces with Riemannian Metric." In Topological, Differential and Conformal Geometry of Surfaces. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89032-2_8.

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Sormani, Christina. "How Riemannian Manifolds Converge." In Metric and Differential Geometry. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0257-4_4.

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Todorčević, Vesna. "Distance Ratio Metric." In Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22591-9_4.

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Udrişte, Constantin. "Metric Properties of Riemannian Manifolds." In Convex Functions and Optimization Methods on Riemannian Manifolds. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8390-9_1.

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Kalita, Bhaben Chandra. "Riemannian Metric and Fundamental Tensors." In Tensor Calculus and Applications. CRC Press, 2019. http://dx.doi.org/10.1201/9780429028670-3.

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Tromba, Anthony J. "Properties of the Weil-Petersson Metric." In Teichmüller Theory in Riemannian Geometry. Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8613-0_6.

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Conference papers on the topic "Riemannian metric and distance"

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Jawanpuria, Pratik, Dai Shi, Bamdev Mishra, and Junbin Gao. "A Riemannian Approach to Ground Metric Learning for Optimal Transport." In ICASSP 2025 - 2025 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2025. https://doi.org/10.1109/icassp49660.2025.10890250.

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Zhu, Pengfei, Hao Cheng, Qinghua Hu, Qilong Wang, and Changqing Zhang. "Towards Generalized and Efficient Metric Learning on Riemannian Manifold." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/449.

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Modeling data as points on non-linear Riemannian manifold has attracted increasing attentions in many computer vision tasks, especially visual recognition. Learning an appropriate metric on Riemannian manifold plays a key role in achieving promising performance. For widely used symmetric positive definite (SPD) manifold and Grassmann manifold, most of existing metric learning methods are designed for one manifold, and are not straightforward for the other one. Furthermore, optimizations in previous methods usually rely on computationally expensive iterations. To address above limitations, this
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Zhang, Yi, and Kwun-Lon Ting. "Point-Line Distance Under Riemannian Metrics." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84637.

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A point-line is the combination of a directed line and an endpoint on the line. A pair of point-line positions corresponds to a point-line displacement, which is known to be associated with a set of rigid body displacements whose screw axes are distributed on a cylindroid. Different associated rigid body displacements generally correspond to different distances under Riemannian metrics on the manifold of SE(3). A unique measure of distance between a pair of point-line positions is desirable in engineering applications. In this paper, the distance between two point-line positions is investigate
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Casana-Eslava, Raul V., Jose D. Martin-Guerrero, Sandra Ortega-Martorell, Paulo J. Lisboa, and Ian H. Jarman. "Scalable implementation of measuring distances in a Riemannian manifold based on the Fisher Information metric." In 2019 International Joint Conference on Neural Networks (IJCNN). IEEE, 2019. http://dx.doi.org/10.1109/ijcnn.2019.8851870.

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Du, Yali, Chang Xu, and Dacheng Tao. "Collaborative Rating Allocation." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/224.

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This paper studies the collaborative rating allocation problem, in which each user has limited ratings on all items. These users are termed ``energy limited''. Different from existing methods which treat each rating independently, we investigate the geometric properties of a user's rating vector, and design a matrix completion method on the simplex. In this method, a user's rating vector is estimated by the combination of user profiles as basis points on the simplex. Instead of using Euclidean metric, a non-linear pull-back distance measurement from the sphere is adopted since it can depict th
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Wereszczyński, Kamil, Agnieszka Michalczuk, Michał Staniszewski, Henryk Josiński, Adam Świtoński, and Konrad Wojciechowski. "Metric tensor for Riemannian classifier." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992573.

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Li, Yangyang, and Ruqian Lu. "Riemannian Metric Learning based on Curvature Flow." In 2018 24th International Conference on Pattern Recognition (ICPR). IEEE, 2018. http://dx.doi.org/10.1109/icpr.2018.8546317.

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Liu, Meizhu, and Baba C. Vemuri. "RBoost: Riemannian distance based regularized Boosting." In 2011 8th IEEE International Symposium on Biomedical Imaging (ISBI 2011). IEEE, 2011. http://dx.doi.org/10.1109/isbi.2011.5872763.

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Sanfelice, Ricardo G., and Laurent Praly. "Nonlinear observer design with an appropriate Riemannian metric." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400714.

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Ncube, Sentibaleng, and Anuj Srivastava. "A novel Riemannian metric for analyzing HARDI data." In SPIE Medical Imaging, edited by Benoit M. Dawant and David R. Haynor. SPIE, 2011. http://dx.doi.org/10.1117/12.878100.

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Reports on the topic "Riemannian metric and distance"

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Altay, Sezgin. Nets of Asymptotic Lines in a Riemannian Hypersurface with Non-Symmetric Metric Connection. GIQ, 2012. http://dx.doi.org/10.7546/giq-4-2003-127-134.

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Lee, Jung-Eun, Rong Jin, and Anil K. Jain. Ranked-Based Distance Metric Learning: An Application to Image Retrieval. Defense Technical Information Center, 2008. http://dx.doi.org/10.21236/ada500953.

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Traina, Caetano, Traina Jr., Faloutsos Agma J., and Christos. Distance Exponent: A New Concept for Selectivity Estimation in Metric Trees. Defense Technical Information Center, 1999. http://dx.doi.org/10.21236/ada363780.

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Basri, Ronen, and Daphna Weinshall. Distance Metric between 3D Models and 2D Images for Recognition and Classification. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada260069.

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