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Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…

In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…

This paper concludes a three-part effort aimed at developing a consistent and unified framework for the phase-field modeling of cohesive fracture. Building on the theoretical foundations established in the first two parts, which included a…

A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…

We propose a fully automatic method for fitting a 3D morphable model to single face images in arbitrary pose and lighting. Our approach relies on geometric features (edges and landmarks) and, inspired by the iterated closest point…

We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a…

A popular paradigm for 3D point cloud registration is by extracting 3D keypoint correspondences, then estimating the registration function from the correspondences using a robust algorithm. However, many existing 3D keypoint techniques tend…

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…

The paper develops a solver based on a conforming finite element method for a 3D--1D coupled incompressible flow problem. New coupling conditions are introduced to ensure a suitable bound for the cumulative energy of the model. We study the…

In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both time and space, temporal discretization is based on the…

We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…

We present a suite of techniques for jointly optimizing triangle meshes and shading models to match the appearance of reference scenes. This capability has a number of uses, including appearance-preserving simplification of extremely…

I propose a scheme of constructing classical integrable models in 3+1 discrete dimensions, based on a relaxed version of the problem of factorizing a matrix into the product of four matrices of a special form.

Model merging combines fine-tuned checkpoints into a single multi-task model without retraining. Existing methods - such as task arithmetic, model soups, TIES, and DARE - are computationally efficient and empirically successful, but rely on…

We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a background mesh to curvilinear ones that conform exactly to the…

Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are…

We show that by extending the Laplacian formalism, which was first introduced in the Graphics community to regularize 3D meshes, we can turn the monocular 3D shape reconstruction of a deformable surface given correspondences with a…

Reconstructing 3D scenes from multiple views has made impressive strides in recent years, chiefly by correlating isolated feature points, intensity patterns, or curvilinear structures. In the general setting - without controlled…

We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…