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We consider the problem of non-rigid shape matching using the functional map framework. Specifically, we analyze a commonly used approach for regularizing functional maps, which consists in penalizing the failure of the unknown map to…

This work proposes an adaptive framework to solve a robust structural shape optimization problem governed by linear elasticity models that account for uncertainties in the loading and material inputs. A posteriori error estimators are…

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…

In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…

Models for near-rigid shape matching are typically based on distance-related features, in order to infer matches that are consistent with the isometric assumption. However, real shapes from image datasets, even when expected to be related…

This paper is devoted to the study of a novel mixed Finite Element Method for approximating the solutions of fourth order variational problems subjected to a constraint. The first problem we consider consists in establishing the convergence…

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal…

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…

Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…

Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…

In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate…

Finding correspondences between 3D deformable shapes is an important and long-standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in…

Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…

This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…

In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…

We combine the parameterization method for invariant manifolds with the finite element method for elliptic PDEs,to obtain a new computational framework for high order approximation of invariant manifolds attached to unstable equilibrium…

Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…

Establishing a correspondence between two non-rigidly deforming shapes is one of the most fundamental problems in visual computing. Existing methods often show weak resilience when presented with challenges innate to real-world data such as…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…