Relevant bibliographies by topics / Geodesical projection

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  2. Dissertations / Theses
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  5. Conference papers

Academic literature on the topic 'Geodesical projection'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Geodesical projection"

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Bejan, Cornelia-Livia, and Simona-Luiza Druţǎ-Romaniuc. "F-geodesics on manifolds." Filomat 29, no. 10 (2015): 2367–79. http://dx.doi.org/10.2298/fil1510367b.

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The notion of F-geodesic, which is slightly different from that of F-planar curve (see [13], [17], and [18]), generalizes the magnetic curves, and implicitly the geodesics, by using any (1,1)-tensor field on the manifold (in particular the electro-magnetic field or the Lorentz force). We give several examples of F-geodesics and the characterizations of the F-geodesics w.r.t. Vranceanu connections on foliated manifolds and adapted connections on almost contact manifolds. We generalize the classical projective transformation, holomorphic-projective transformation and C-projective transformation, by considering a pair of symmetric connections which have the same F-geodesics. We deal with the transformations between such two connections, namely F-planar diffeomorphisms ([18]). We obtain a Weyl type tensor field, invariant under any F-planar diffeomorphism, on a 1-codimensional foliation.
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KIM, BYUNG HAK, IN-BAE KIM, and SADAHIRO MAEDA. "CHARACTERIZATIONS OF BERGER SPHERES FROM THE VIEWPOINT OF SUBMANIFOLD THEORY." Glasgow Mathematical Journal 62, no. 1 (March 1, 2019): 137–45. http://dx.doi.org/10.1017/s0017089519000016.

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AbstractIn this paper, Berger spheres are regarded as geodesic spheres with sufficiently big radii in a complex projective space. We characterize such real hypersurfaces by investigating their geodesics and contact structures from the viewpoint of submanifold theory.
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Le Donne, Enrico, and Roger Züst. "Space of signatures as inverse limits of Carnot groups." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 37. http://dx.doi.org/10.1051/cocv/2021040.

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We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
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Leininger, Christopher, Anna Lenzhen, and Kasra Rafi. "Limit sets of Teichmüller geodesics with minimal non-uniquely ergodic vertical foliation." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 737 (April 1, 2018): 1–32. http://dx.doi.org/10.1515/crelle-2015-0040.

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AbstractWe describe a method for constructing Teichmüller geodesics where the vertical foliation ν is minimal but is not uniquely ergodic and where we have a good understanding of the behavior of the Teichmüller geodesic. The construction depends on various parameters, and we show that one can adjust the parameters to ensure that the set of accumulation points of such a geodesic in the Thurston boundary is exactly the projective 1-simplex of all projective measured foliations that are topologically equivalent to ν. With further adjustment of the parameters, one can further assume that the transverse measure is an ergodic measure on the non-uniquely ergodic foliation ν.
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BUCATARU, IOAN, and ZOLTÁN MUZSNAY. "PROJECTIVE AND FINSLER METRIZABILITY: PARAMETERIZATION-RIGIDITY OF THE GEODESICS." International Journal of Mathematics 23, no. 09 (July 31, 2012): 1250099. http://dx.doi.org/10.1142/s0129167x12500991.

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In this work we show that for the geodesic spray S of a Finsler function F, the most natural projective deformation [Formula: see text] leads to a non-Finsler metrizable spray, for almost every value of λ ∈ ℝ. This result shows how rigid is the metrizablility property with respect to certain reparameterizations of the geodesics. As a consequence, we obtain that the projective class of an arbitrary spray contains infinitely many sprays that are not Finsler metrizable.
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Lenells, Jonatan. "Spheres, Kähler geometry and the Hunter–Saxton system." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2154 (June 8, 2013): 20120726. http://dx.doi.org/10.1098/rspa.2012.0726.

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Many important equations of mathematical physics arise geometrically as geodesic equations on Lie groups. In this paper, we study an example of a geodesic equation, the two-component Hunter–Saxton (2HS) system, which displays a number of unique geometric features. We show that 2HS describes the geodesic flow on a manifold, which is isometric to a subset of a sphere. Since the geodesics on a sphere are simply the great circles, this immediately yields explicit formulae for the solutions of 2HS. We also show that when restricted to functions of zero mean, 2HS reduces to the geodesic equation on an infinite-dimensional manifold, which admits a Kähler structure. We demonstrate that this manifold is in fact isometric to a subset of complex projective space, and that the above constructions provide an example of an infinite-dimensional Hopf fibration.
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ANDRUCHOW, ESTEBAN, and LÁZARO RECHT. "GRASSMANNIANS OF A FINITE ALGEBRA IN THE STRONG OPERATOR TOPOLOGY." International Journal of Mathematics 17, no. 04 (April 2006): 477–91. http://dx.doi.org/10.1142/s0129167x06003552.

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If [Formula: see text] is a type II1 von Neumann algebra with a faithful trace τ, we consider the set [Formula: see text] of self-adjoint projections of [Formula: see text] as a subset of the Hilbert space [Formula: see text]. We prove that though it is not a differentiable submanifold, the geodesics of the natural Levi–Civita connection given by the trace have minimal length. More precisely: the curves of the form γ(t) = eitxpe-itx with x* = x, pxp = (1 - p)x(1 - p) = 0 have minimal length when measured in the Hilbert space norm of [Formula: see text], provided that the operator norm ‖x‖ is less or equal than π/2. Moreover, any two projections which are unitary equivalent are joined by at least one such minimal geodesic, and only unitary equivalent projections can be joined by a smooth curve. Finally, we prove that these geodesics have also minimal length if one measures them with the Schatten k-norms of τ, ‖x‖k = τ((x* x)k/2)1/k, for all k ∈ ℝ, k ≥ 0. We also characterize curves of unitaries which have minimal length with these k-norms.
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Pędzich, Paweł, and Marta Kuźma. "Application of methods for area calculation of geodesic polygons on Polish administrative units." Geodesy and Cartography 61, no. 2 (November 1, 2012): 105–15. http://dx.doi.org/10.2478/v10277-012-0025-6.

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Abstract The paper presents methods of area calculation, which may be applied for big geodesic polygons on the ellipsoid. Proposal developed by the authors of this paper is discussed. The proposed methods are compared with other, alternative methods of area calculation of such polygons. Test calculations are performed for administrative units in Poland. The obtained results are also compared with areas of those units registered in statistical annals. Utilisation of the equal-area map projections of the ellipsoid onto a plane seems to be the best solution for the discussed task. In the case of small distances between points we may expect accurate results of calculations, since the area size is influenced by the projection reductions only, which are small in such cases. In some cases their influence on results of calculations may be neglected. Then, only re-calculation of co-ordinates from the GRS80 ellipsoid to the cartographic, equal-area projection is required.
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Williams, Roy. "Gnomonic Projection of the Surface of an Ellipsoid." Journal of Navigation 50, no. 2 (May 1997): 314–20. http://dx.doi.org/10.1017/s0373463300023936.

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When a surface is mapped onto a plane so that the image of a geodesic arc is a straight line on the plane then the mapping is known as a geodesic mapping. It is only possible to perform a geodesic mapping of a surface onto a plane when the surface has constant normal curvature. The normal curvature of a sphere of radius r at all points on the surface is I/r hence it is possible to map the surface of a sphere onto a plane using a geodesic mapping. The geodesic mapping of the surface of a sphere onto a plane is achieved by a gnomonic projection which is the projection of the surface of the sphere from its centre onto a tangent plane. There is no geodesic mapping of the ellipsoid of revolution or the spheroid onto a plane because the ellipsoid of revolution or the spheroid are not surfaces whose curvature is constant at all points. We can, however, still construct a projection of the surface of the ellipsoid from the centre of the body onto a tangent plane and we call this projection a gnomonic projection also.
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Podestà, Fabio. "Projective submersions." Bulletin of the Australian Mathematical Society 43, no. 2 (April 1991): 251–56. http://dx.doi.org/10.1017/s0004972700029014.

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We consider C∞ manifolds endowed with torsionfree affine connections and C∞ projective submersions between them which, by definition, map geodesics into geodesics up to parametrisation. After giving a differential characterisation of these mappings, we deal with the case when one of the given connections is projectively flat or satisfies certain conditions concerning its Ricci tensor; under these hypotheses we prove that the projective submersion is actually a covering.
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Dissertations / Theses on the topic "Geodesical projection"

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Réthoré, Christophe. "Approche textométrique et comparative du discours de segmentation du marché automobile : implications pour la traduction publicitaire anglais > français." Thesis, Bourgogne Franche-Comté, 2017. http://www.theses.fr/2017UBFCC032/document.

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Cette recherche est ancrée à la fois dans la statistique textuelle, et secondairement dans l’analyse du discours, avec une complémentarité quantitatif-qualitatif. L’état de la question présente une vue d’ensemble des recherches linguistiques sur la publicité – linguistique descriptive, analyse du discours, sémiologie/sémiotique et rhétorique/stylistique, en prenant pour point de départ le travail pionnier en linguistique descriptive de Leech (TheLanguage of Advertising, 1966) – et révèle plusieurs constats :1. les mots de la publicité constituent bien un discours spécialisé 2. la publicité ressemble à la fois à la poésie et à la langue courante 3. l’intertextualité et la participation active d’un récepteur ciblé sont deux données clés de la communication publicitaire 4. la langue publicitaire est émotionnelle, ambiguë, indirecte et implicite 5. de façon simpliste et ludique, la publicité nous dépeint un monde de bonheur parfait 6. simplicité et conventionnalisation du discours publicitaire, et invariants lexicaux. Pour répondre à certaines questions sur le discours, la langue, la communication et la traduction publicitaires, nous avons choisi une approche quantitative et l’approche lexicométrique (ou statistique textuelle, devenue récemment textométrie), développée notamment par le « groupe de Saint-Cloud » et ses collaborateurs, dont André Salem (concepteur de Lexico, le logiciel utilisé pour nos analyses). L'analyse lexicométrique est complétée par l'analyse factorielle des correspondances (AFC) et la méthode de projection géodésique de Viprey (avec le logiciel Astadiag). Grâce à un corpus parallèle (bitexte) d’environ 800 000 occurrences en anglais et un million en français (170 brochures publicitaires compilées à partir de sites Web canadiens de 20 marques, 10 constructeurs, 229 véhicules au total), nous avons réussi à déterminer un profil lexical distinct pour chacun des sept segments du marché automobile : AB, CD, EF, MPV (véhicules multifonctions), PK (pickups/camions), SP (voitures de sport) et SUV (VUS : véhicules utilitaires sports) et montré que dans l’ensemble, les publicités sont traduites assez littéralement
Our research is quantitative and qualitative, based on textometrics tools and discourse analysis. Our literature review surveyed linguistic studies of advertising, through different schools of thought : descriptive linguistics, discourse analysis, semiology, rhetorics/stylistics, starting with Leech’s founding work (The Language of Advertising, 1966), which led to several highlights : 1. advertising is indeed a specialty discourse, or a language for special purpose (LSP) 2. advertising shares some common features with both poetry and the language we speak everyday 3. intertextuality and active participation of the targeted reader are two key factors of advertising communication 4. the language of advertising is emotional, ambiguous, indirect and implicit 5. in a simple and playful way, advertising depicts a perfect, happy world 6. simplicity and conventionalization of the advertising discourse, with lexical constants.To find answers to some of our questions on the advertising discourse, language, communication and translation, we selected a quantitative approach, i.e., the lexicometric methodology (statistical linguistics, more recently called textometry) developed by the Saint-Cloud (France) group, including André Salem (founder and developer of Lexico,which we used to analyze our corpus). Our lexicometric analysis is complemented by a classic factor analysis (FCA)and Viprey’s geodesical projection method (with the Astadiag software). With our parallel corpus of roughly 800,000 tokens in English and one million in French (170 advertising brochures downloaded from 20 brands/10carmakers’ Canadian websites, for a total of 229 vehicles), we found distinct lexical profiles for each of the seven carmarket segments: AB, CD, EF, MPV, PK (pickup trucks), SP (sports cars) and SUV. We also showed that overall,advertisements are translated rather literally
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Draper, Christopher Peter William. "The geodesic Gauss map of spheres and complex projective space." Thesis, University of York, 2015. http://etheses.whiterose.ac.uk/11542/.

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For an isometrically immersed submanifold, the spherical Gauss map is the induced immersion of the unit normal bundle into the unit tangent bundle. Compact rank one symmetric spaces have the distinguishing feature that their geodesics are closed with the same period, and so we can define the manifold of geodesics as the quotient of the unit tangent bundle by geodesic flow. Through this quotient we define the geodesic Gauss map to be the Lagrangian immersion given by the projection of the spherical Gauss map. In this thesis we establish relationships between the minimality of isometrically immersed submanifolds of the sphere and complex projective space and the minimality of the geodesic Gauss map with respect to the Kähler-Einstein metric on the manifold of geodesics. In particular, we establish that for an isometrically immersed holomorphic submanifold of complex projective space, its geodesic Gauss map is minimal Lagrangian if it has conformal shape form.
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Cuevas, Santamaría Sergio Axel. "My MFA Experience." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524073680662621.

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Ochoa, Mayorga Victor Manuel. "Geometric approach to multi-scale 3D gesture comparison." Phd thesis, 2010. http://hdl.handle.net/10048/1530.

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The present dissertation develops an invariant framework for 3D gesture comparison studies. 3D gesture comparison without Lagrangian models is challenging not only because of the lack of prediction provided by physics, but also because of a dual geometry representation, spatial dimensionality and non-linearity associated to 3D-kinematics. In 3D spaces, it is difficult to compare curves without an alignment operator since it is likely that discrete curves are not synchronized and do not share a common point in space. One has to assume that each and every single trajectory in the space is unique. The common answer is to assert the similitude between two or more trajectories as estimating an average distance error from the aligned curves, provided that the alignment operator is found. In order to avoid the alignment problem, the method uses differential geometry for position and orientation curves. Differential geometry not only reduces the spatial dimensionality but also achieves view invariance. However, the nonlinear signatures may be unbounded or singular. Yet, it is shown that pattern recognition between intrinsic signatures using correlations is robust for position and orientation alike. A new mapping for orientation sequences is introduced in order to treat quaternion and Euclidean intrinsic signatures alike. The new mapping projects a 4D-hyper-sphere for orientations onto a 3D-Euclidean volume. The projection uses the quaternion invariant distance to map rotation sequences into 3D-Euclidean curves. However, quaternion spaces are sectional discrete spaces. The significance is that continuous rotation functions can be only approximated for small angles. Rotation sequences with large angle variations can only be interpolated in discrete sections. The current dissertation introduces two multi-scale approaches that improve numerical stability and bound the signal energy content of the intrinsic signatures. The first is a multilevel least squares curve fitting method similar to Haar wavelet. The second is a geodesic distance anisotropic kernel filter. The methodology testing is carried out on 3D-gestures for obstetrics training. The study quantitatively assess the process of skill acquisition and transfer of manipulating obstetric forceps gestures. The results show that the multi-scale correlations with intrinsic signatures track and evaluate gesture differences between experts and trainees.
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Books on the topic "Geodesical projection"

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Divide spheres: Geodesics and the orderly subdivision of the sphere. Boca Raton: A K Peters/CRC Press, 2012.

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Book chapters on the topic "Geodesical projection"

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Järvenpää, Maarit. "Projections of Measures Invariant Under the Geodesic Flow." In Further Developments in Fractals and Related Fields, 153–60. Boston: Birkhäuser Boston, 2013. http://dx.doi.org/10.1007/978-0-8176-8400-6_8.

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Estévez, Pablo A., Andrés M. Chong, Claudio M. Held, and Claudio A. Perez. "Nonlinear Projection Using Geodesic Distances and the Neural Gas Network." In Artificial Neural Networks – ICANN 2006, 464–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11840817_49.

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Bekkers, Erik J., Remco Duits, Alexey Mashtakov, and Yuri Sachkov. "Vessel Tracking via Sub-Riemannian Geodesics on the Projective Line Bundle." In Lecture Notes in Computer Science, 773–81. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68445-1_89.

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Kimura, Yasunori. "Convex Minimization Problems on Geodesic Spaces and the Shrinking Projection Method with Errors." In Springer Proceedings in Mathematics & Statistics, 197–206. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5455-1_16.

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Allen, James, Nikhil Karkera, and Lijun Yin. "3D Facial Feature Detection Using Iso-Geodesic Stripes and Shape-Index Based Integral Projection." In Advances in Visual Computing, 148–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-24031-7_15.

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D'Agostino, Susan. "Conclusion." In How to Free Your Inner Mathematician, 293–98. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198843597.003.0048.

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This book offers a survey of mathematical topics. However, there is much more for you to explore. Catastrophe theory, the Chinese Remainder Theorem, combinatorics, and complex analysis. Equivalence relations, Euclid’s elements, and Euler’s formula. The Fields Medal and Four-color Theorem. Galois theory, the gambler’s fallacy, geodesic domes, the geometry of spacetime, and group theory. The Ham Sandwich Theorem. Isomorphisms. Linear algebra. The Mandelbrot set, mathematical induction, matrices, and the monster group. The parallel postulate, Pascal’s triangle, perfect numbers, permutation groups, pi, the Poincare Conjecture, projective geometry, public-key cryptography, and Pythagoras’ Theorem. Quaternions. Regression analysis. Set theory, squaring the circle, and surreal numbers. Truth tables, turning machines, and turning a sphere inside out. Venn diagrams. Wavelets. Zero. The list never ends....
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Conference papers on the topic "Geodesical projection"

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Góes, Daniel A., and Nelson D. A. Mascarenhas. "Low-Dose Computed Tomography Filtering Using Geodesic Distances." In Conference on Graphics, Patterns and Images. Sociedade Brasileira de Computação, 2020. http://dx.doi.org/10.5753/sibgrapi.est.2020.12983.

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Due to the concerns related to patient exposure to X-ray, the dosage used in computed tomography must be reduced (Low-dose Computed Tomography - LDCT). One of the effects of LDCT is the degradation in the quality of the final reconstructed image. In this work, we propose a method of filtering LDCT sinograms that are subject to signal-dependent Poisson noise. To filter this type of noise, we use a Bayesian approach, changing the Non-local Means (NLM) algorithm to use geodesic stochastic distances for Gamma distribution, the conjugate prior to Poisson, as a similarity metric between each projection point. Among the geodesic distances evaluated, we found a closed solution for the Shannon entropy for Gamma distributions. We compare our method with the following methods based on NLM: PoissonNLM, Stochastic Poisson NLM, Stochastic Gamma NLM and the original NLM after Anscombe transform. We also compare with BM3D after Anscombe transform. Comparisons are made on the final images reconstructed by the Filtered-Back Projection (FBP) and Projection onto Convex Sets (POCS) methods using the metrics PSNR and SSIM.
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Hall, Graham. "Einstein’s Geodesic Postulate, Projective Relatedness and Weyl’s Projective Tensor." In 14th Regional Conference on Mathematical Physics. WORLD SCIENTIFIC, 2018. http://dx.doi.org/10.1142/9789813224971_0004.

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Bai, Xiaoming, Baocai Yin, Qin Shi, and Yanfeng Sun. "Face Recognition Based on Geodesic Preserving Projection Algorithm with 3D Morphable Model." In 2006 5th IEEE International Conference on Cognitive Informatics. IEEE, 2006. http://dx.doi.org/10.1109/coginf.2006.365602.

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Li Yang. "K-edge connected neighborhood graph for geodesic distance estimation and nonlinear data projection." In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. IEEE, 2004. http://dx.doi.org/10.1109/icpr.2004.1334057.

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Mahmoudi, Mona, Pierre Vandergheynst, and Matteo Sorci. "On the estimation of geodesic paths on sampled manifolds under random projections." In 2008 15th IEEE International Conference on Image Processing. IEEE, 2008. http://dx.doi.org/10.1109/icip.2008.4712136.

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ADACHI, Toshiaki. "EXTRINSIC CIRCULAR TRAJECTORIES ON GEODESIC SPHERES IN A COMPLEX PROJECTIVE SPACE." In Proceedings of the International Workshop in Honor of S Maeda's 60th Birthday. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814566285_0005.

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Vrahatis, Aristidis G., Sotiris K. Tasoulis, Georgios N. Dimitrakopoulos, and Vassilis P. Plagianakos. "Visualizing High-Dimensional Single-Cell RNA-seq Data via Random Projections and Geodesic Distances." In 2019 IEEE Conference on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB). IEEE, 2019. http://dx.doi.org/10.1109/cibcb.2019.8791482.

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