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We present an unsupervised data-driven approach for non-rigid shape matching. Shape matching identifies correspondences between two shapes and is a fundamental step in many computer vision and graphics applications. Our approach is designed…
The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…
We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…
Template matching is a fundamental task in computer vision and has been studied for decades. It plays an essential role in manufacturing industry for estimating the poses of different parts, facilitating downstream tasks such as robotic…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
Establishing accurate point-to-point correspondences between non-rigid 3D shapes remains a critical challenge, particularly under non-isometric deformations and topological noise. Existing functional map pipelines suffer from ambiguities…
In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
Spectral variability significantly impacts the accuracy and convergence of hyperspectral unmixing algorithms. Many methods address complex spectral variability; yet large-scale distortions to the scale of the observed pixel signatures due…
An important operation in geometry processing is finding the correspondences between pairs of shapes. The Gromov-Hausdorff distance, a measure of dissimilarity between metric spaces, has been found to be highly useful for nonrigid shape…
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, $\phi: X \to S$ and $\psi: Y \to S$, coincide exactly. This condition of strict equality, however, is…