Related papers: Grassmannian Shape Representations for Aerodynamic…
Thin astrophysical discs are very often modelled using the equations of two-dimensional hydrodynamics. We derive an extension of this model that describes more accurately the behaviour of a thin disc in the absence of self-gravity, magnetic…
The paper presents a micromechanical representation of deformation in 2D granular materials. The representation is a generalization of K. Bagi's work and is based upon the void-cell approach of M. Satake. The general representation applies…
We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be…
Position representation is crucial for building position-aware representations in Transformers. Existing position representations suffer from a lack of generalization to test data with unseen lengths or high computational cost. We…
We propose LeafFit, a pipeline that converts 3D Gaussian Splatting (3DGS) of individual plants into editable, instanced mesh assets. While 3DGS faithfully captures complex foliage, its high memory footprint and lack of mesh topology make it…
Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant…
Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations…
In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…
In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no…
In this paper, a novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics is developed for predicting the response of engineering systems and complex physical phenomena. The method utilizes…
This paper reviews several Riemannian metrics and evolution equations in the context of diffeomorphic shape analysis. After a short review of of various approaches at building Riemannian spaces of shapes, with a special focus on the…
A backward biorthogonalization approach is proposed, which modifies biorthogonal functions so as to generate orthogonal projections onto a reduced subspace. The technique is relevant to problems amenable to be represented by a general…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Current diffusion or flow-based generative models for 3D shapes divide to two: distilling pre-trained 2D image diffusion models, and training directly on 3D shapes. When training a diffusion or flow models on 3D shapes a crucial design…
Shape control of deformable objects is a challenging and important robotic problem. This paper proposes a model-free controller using novel 3D global deformation features based on modal analysis. Unlike most existing controllers using…
Classical archetypal analysis is appealing for its interpretability, but its linear geometry can limit performance on data with strongly non-linear structure; at the same time, existing neural extensions improve flexibility while often…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
We present a method for nonrigid registration of 2-D geometric shapes. Our contribution is twofold. First, we extend the classic chamfer-matching energy to a variational functional. Secondly, we introduce a meshless deformation model that…
Multiple shapes must be obtained in the mechanical design process to satisfy the required design specifications. The inverse design problem has been analyzed in previous studies to obtain such shapes. However, finding multiple shapes in a…
In many image analysis problems, the contours of objects carry important statistical information about shape. Such contours are typically affected by deformation variables including scaling, translation, rotation, and reparametrization.…