Recently,human motion prediction has gained significant attention and achieved notable ***,current methods primarily rely on training and testing with ideal datasets,overlooking the impact of variations in the viewing...
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Recently,human motion prediction has gained significant attention and achieved notable ***,current methods primarily rely on training and testing with ideal datasets,overlooking the impact of variations in the viewing distance and viewing angle,which are commonly encountered in practical *** this study,we address the issue of model invariance by ensuring robust performance despite variations in view distances and *** achieve this,we employed Riemannian geometry methods to constrain the learning process of neural networks,enabling the prediction of invariances using a simple ***,this enhances the application of motion prediction in various *** framework uses Riemannian geometry to encode motion into a novel motion space to achieve prediction with an invariant viewing distance and angle using a simple ***,the specified path transport square-root velocity function is proposed to aid in removing the view-angle equivalence class and encode motion sequences into a flattened *** coding by the geometry method linearizes the optimization problem in a non-flattened space and effectively extracts motion information,allowing the proposed method to achieve competitive performance using a simple *** results on Human 3.6M and CMU MoCap demonstrate that the proposed framework has competitive performance and invariance to the viewing distance and viewing angle.
This thesis studies codings of orbits of Weyl chamber flows on symmetric spacesof non-compact type.Let H be the hyperbolic plane with constant curvature −1 and Γ be a Fuchsiangroup of &...
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This thesis studies codings of orbits of Weyl chamber flows on symmetric spacesof non-compact type.Let H be the hyperbolic plane with constant curvature −1 and Γ be a Fuchsiangroup of finite covolume. Let D be a Dirichlet domain of Γ on H. The main resultshows that the set of cutting sequences of all geodesics in the sense of Morse withrespect to the tessellation of H, formed by the sets gD, g ∈ Γ, is a topologicalMarkov chain if and only if D does not have vertices in H.Also, a background is provided for the study of generalization of continuedfractions to higher dimensions. So-called arithmetic Gauss coding of geodesics onH is described along with its relation with the minus continued fractions. H is aparticular case of a symmetric space of non-compact type, H = SL2R/SO2R, andthe geodesic flow on H implements the Weyl chamber flow on it. A generalizationof the minus continued fractions was suspected by S. Katok and A. Katok to exist,which involves orbits of Weyl chamber flows on symmetric spaces of non-compacttype SLnR/SOnR and their compactifications.
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