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Image generator for tabular data based on non-Euclidean metrics for CNN-based classification. [PDF]
PLoS OneLin YR, Wu HM.
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ACM Transactions on Graphics, 2010
Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend ...
Bailin Deng +2 more
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Geodesic curves in surfaces are not only minimizers of distance, but they are also the curves of zero geodesic (sideways) curvature. It turns out that this property makes patterns of geodesics the basic geometric entity when dealing with the cladding of a freeform surface with wooden panels which do not bend ...
Bailin Deng +2 more
exaly +5 more sources
Hamilton–Jacobi formalism for geodesics and geodesic deviations
Journal of Mathematical Physics, 1989A formalism of integrating the equations of geodesics and of geodesic deviation is examined based upon the Hamilton–Jacobi equation for geodesics. The latter equation has been extended to the case of geodesic deviation and theorems analogous to Jacobi’s theorem on the complete integral has been proved.
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Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 2020
Together with the curse of dimensionality, nonlinear dependencies in large data sets persist as major challenges in data mining tasks. A reliable way to accurately preserve nonlinear structure is to compute geodesic distances between data points. Manifold learning methods, such as Isomap, aim to preserve geodesic distances in a Riemannian manifold ...
Meghana Madhyastha +6 more
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Together with the curse of dimensionality, nonlinear dependencies in large data sets persist as major challenges in data mining tasks. A reliable way to accurately preserve nonlinear structure is to compute geodesic distances between data points. Manifold learning methods, such as Isomap, aim to preserve geodesic distances in a Riemannian manifold ...
Meghana Madhyastha +6 more
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Geodesics and Almost Geodesics Curves
Results in Mathematics, 2018An \textit{almost geodesic} of an affine connection \(\nabla\) on a manifold is a curve \(x(t)\) in the manifold so that \[ \nabla^2_{\dot{x}}\dot{x}=a\nabla_{\dot{x}} \dot{x}+b\dot{x}, \] for some real-valued continuous functions \(a(t)\), \(b(t)\).
Olga Belova +2 more
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Geodesic as Limit of Geodesics on PL-Surfaces
2008We study the problem of convergence of geodesics on PL-surfaces and in particular on subdivision surfaces. More precisely, if a sequence (Tn)n∈N of PL-surfaces converges in distance and in normals to a smooth surface S and if Cn is a geodesic of Tn (i.e.
André Lieutier, Boris Thibert
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Geodesic compatibility and integrability of geodesic flows
Journal of Mathematical Physics, 2003We give a natural geometric condition called geodesic compatibility that implies the existence of integrals in involution of the geodesic flow of a pseudo-Riemannian metric. We prove that if two metrics satisfy the condition of geodesic compatibility then we can produce a hierarchy of metrics that also satisfy this condition. A lot of metrics studed in
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Analysis and Applications, 2003
We consider a subRiemannian geometry induced by a step 3 subelliptic partial differential operator in ℝ3. Our main result is the characterization of a canonical submanifold through the origin, all of whose points are connected to the origin by infinitely many (subRiemannian) geodesics.
Greiner, Peter, Calin, Ovidiu
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We consider a subRiemannian geometry induced by a step 3 subelliptic partial differential operator in ℝ3. Our main result is the characterization of a canonical submanifold through the origin, all of whose points are connected to the origin by infinitely many (subRiemannian) geodesics.
Greiner, Peter, Calin, Ovidiu
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