Relevant bibliographies by topics / Viewpoint Equivariance

Academic literature on the topic 'Viewpoint Equivariance'

Author: Grafiati
Published: 11 March 2023

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Journal articles on the topic "Viewpoint Equivariance"

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HOU, ZUOLIANG. "EQUIVARIANT COHOMOLOGY AND HOLOMORPHIC INVARIANT." Communications in Contemporary Mathematics 10, no. 03 (June 2008): 433–47. http://dx.doi.org/10.1142/s0219199708002843.

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Using equivariant cohomology, we construct a family of holomorphic invariants which include the famous Futaki invariant and its generalization to singular variety as special cases. We are also using this viewpoint to compute the generalized Futaki invariant for complete intersections.
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Takata, Doman. "LT-equivariant index from the viewpoint of KK-theory." Journal of Geometry and Physics 150 (April 2020): 103591. http://dx.doi.org/10.1016/j.geomphys.2019.103591.

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Fraser, Maia. "Contact non-squeezing at large scale in ℝ2n × S1." International Journal of Mathematics 27, no. 13 (December 2016): 1650107. http://dx.doi.org/10.1142/s0129167x1650107x.

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We define a [Formula: see text]-equivariant version of the cylindrical contact homology used by Eliashberg–Kim–Polterovich [11] to prove contact non-squeezing for prequantized integer-capacity balls [Formula: see text], [Formula: see text] and we use it to extend their result to all [Formula: see text]. Specifically, we prove if [Formula: see text] there is no [Formula: see text], the group of compactly supported contactomorphisms of [Formula: see text] which squeezes [Formula: see text] into itself, i.e. maps the closure of [Formula: see text] into [Formula: see text]. A sheaf theoretic proof of non-existence of corresponding [Formula: see text], the identity component of [Formula: see text], is due to Chiu [7] it is not known if this is strictly weaker. Our construction has the advantage of retaining the contact homological viewpoint of Eliashberg–Kim–Polterovich and its potential for application in prequantizations of other Liouville manifolds. It makes use of the [Formula: see text]-action generated by a vertical [Formula: see text]-shift but can also be related, for prequantized balls, to the [Formula: see text]-equivariant contact homology developed by Milin [16] in her proof of orderability of lens spaces.
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PELAYO, ALVARO, and SUSAN TOLMAN. "Fixed points of symplectic periodic flows." Ergodic Theory and Dynamical Systems 31, no. 4 (June 16, 2010): 1237–47. http://dx.doi.org/10.1017/s0143385710000295.

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AbstractThe study of fixed points is a classical subject in geometry and dynamics. If the circle acts in a Hamiltonian fashion on a compact symplectic manifold M, then it is classically known that there are at least $\frac {1}{2}\,{\dim M}+1$ fixed points; this follows from Morse theory for the momentum map of the action. In this paper we use Atiyah–Bott–Berline–Vergne (ABBV) localization in equivariant cohomology to prove that this conclusion also holds for symplectic circle actions with non-empty fixed sets, as long as the Chern class map is somewhere injective—the Chern class map assigns to a fixed point the sum of the action weights at the point. We complement this result with less sharp lower bounds on the number of fixed points, under no assumptions; from a dynamical systems viewpoint, our results imply that there is no symplectic periodic flow with exactly one or two equilibrium points on a compact manifold of dimension at least eight.
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Hu, Fei, JongHae Keum, and De-Qi Zhang. "Criteria for the existence of equivariant fibrations on algebraic surfaces and hyperkähler manifolds and equality of automorphisms up to powers: a dynamical viewpoint." Journal of the London Mathematical Society 92, no. 3 (October 27, 2015): 724–35. http://dx.doi.org/10.1112/jlms/jdv045.

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Fujita, Hajime. "Deformation of Dirac operators along orbits and quantization of noncompact Hamiltonian torus manifolds." Canadian Journal of Mathematics, March 9, 2021, 1–31. http://dx.doi.org/10.4153/s0008414x2100016x.

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Abstract We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly noncompact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to noncompact Hamiltonian torus manifolds to define geometric quantization from the viewpoint of index theory. We give two applications. The first one is a proof of a [Q,R]=0 type theorem, which can be regarded as a proof of the Vergne conjecture for abelian case. The other is a Danilov-type formula for toric case in the noncompact setting, which is a localization phenomenon of geometric quantization in the noncompact setting. The proofs are based on the localization of index to lattice points.
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Dissertations / Theses on the topic "Viewpoint Equivariance"

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Garau, Nicola. "Design of Viewpoint-Equivariant Networks to Improve Human Pose Estimation." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/345132.

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Human pose estimation (HPE) is an ever-growing research field, with an increasing number of publications in the computer vision and deep learning fields and it covers a multitude of practical scenarios, from sports to entertainment and from surveillance to medical applications. Despite the impressive results that can be obtained with HPE, there are still many problems that need to be tackled when dealing with real-world applications. Most of the issues are linked to a poor or completely wrong detection of the pose that emerges from the inability of the network to model the viewpoint. This thesis shows how designing viewpoint-equivariant neural networks can lead to substantial improvements in the field of human pose estimation, both in terms of state-of-the-art results and better real-world applications. By jointly learning how to build hierarchical human body poses together with the observer viewpoint, a network can learn to generalise its predictions when dealing with previously unseen viewpoints. As a result, the amount of training data needed can be drastically reduced, simultaneously leading to faster and more efficient training and more robust and interpretable real-world applications.
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Conference papers on the topic "Viewpoint Equivariance"

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Garau, Nicola, Niccolo Bisagno, Piotr Brodka, and Nicola Conci. "DECA: Deep viewpoint-Equivariant human pose estimation using Capsule Autoencoders." In 2021 IEEE/CVF International Conference on Computer Vision (ICCV). IEEE, 2021. http://dx.doi.org/10.1109/iccv48922.2021.01147.

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Yang, Liang, Xiao-Yuan Jing, Fulin He, Fei Ma, and Li Cheng. "Viewpoint-robust Person Re-identification via Deep Residual Equivariant Mapping and Fine-grained Features." In 2019 International Joint Conference on Neural Networks (IJCNN). IEEE, 2019. http://dx.doi.org/10.1109/ijcnn.2019.8852125.

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