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Strainger Things: Discrete Differential Geometry for Transporting Right Ventricular Deformation Across Meshes
Cardiac dynamics have been a focus of image analysis, and their statistical models are used in a wide range of applications: generating synthetic...
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Geometry Parameter Estimation for Sparse X-Ray Log Imaging
We consider geometry parameter estimation in industrial sawmill fan-beam X-ray tomography. In such industrial settings, scanners do not always allow...
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Geometry-Preserving Lie Group Integrators for Differential Equations on the Manifold of Symmetric Positive Definite Matrices
In many applications, one encounters time series that lie on manifolds rather than a Euclidean space. In particular, covariance matrices are...
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Categorical Information Geometry
Information geometry is the study of interactions between random variables by means of metric, divergences, and their geometry. Categorical...
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Neural Differential Radiance Field: Learning the Differential Space Using a Neural Network
We introduce an adjoint-based inverse rendering method using a Neural Differential Radiance Field, i.e. a neural network representation of the...
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On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry
This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence...
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Learning with Symmetric Positive Definite Matrices via Generalized Bures-Wasserstein Geometry
Learning with symmetric positive definite (SPD) matrices has many applications in machine learning. Consequently, understanding the Riemannian...
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A state-of-the-art review on topology and differential geometry-based robotic path planning—part I: planning under static constraints
Autonomous robotics has permeated several industrial, research and consumer robotic applications, of which path planning is an important component....
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Geometry of Saccades and Saccadic Cycles
The paper is devoted to the development of the differential geometry of saccades and saccadic cycles. We recall an interpretation of Donder’s and...
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A state-of-the-art review on topology and differential geometry-based robotic path planning—part II: planning under dynamic constraints
Path planning is an intrinsic component of autonomous robotics, be it industrial, research or consumer robotics. Such avenues experience constraints...
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Ordinary Differential Equations
A differential equation is an equation that contains a function and one or more of its derivatives. They have been studied ever since the invention...
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Approach to Cryptography from Differential Geometry with Example
We propose a public-key encryption scheme that arise from a kind of differential geometry called Finsler geometry. Our approach is first to observe a...
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Element differential method for contact problems with non-conforming contact discretization
In this paper, a new strong-form numerical method, the element differential method (EDM) is employed to solve two- and three-dimensional contact...
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MPEG Geometry-Based Point Cloud Compression (G-PCC) Standard
Advances in 3D representation technology have promoted the development of digital museums, automated driving, and other virtual/augmented reality...
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Geometry of Parametric Binary Choice Models
In this study, we consider parametric binary choice models from the perspective of information geometry. The set of models is a dually flat manifold...
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Learning Differential Invariants of Planar Curves
We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks’ (DNNs) universal...
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