Related papers: Shape Analysis of Surfaces Using General Elastic M…

This article provides an overview of various notions of shape spaces, including the space of parametrized and unparametrized curves, the space of immersions, the diffeomorphism group and the space of Riemannian metrics. We discuss the…

Designing a network on 3D surface for non-rigid shape analysis is a challenging task. In this work, we propose a novel spectral transform network on 3D surface to learn shape descriptors. The proposed network architecture consists of four…

We propose simple yet effective improvements in point representations and local neighborhood graph construction within the general framework of graph neural networks (GNNs) for 3D point cloud processing. As a first contribution, we propose…

Data-driven methods have become popular to parameterize the effects of mesoscale eddies in ocean models. However, they perform poorly in generalization tasks and may require retuning if the grid resolution or ocean configuration changes. We…

Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to…

Models for areal data are traditionally defined using the neighborhood structure of the regions on which data are observed. The unweighted adjacency matrix of a graph is commonly used to characterize the relationships between locations,…

With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…

We present Geometry in Style, a new method for identity-preserving mesh stylization. Existing techniques either adhere to the original shape through overly restrictive deformations such as bump maps or significantly modify the input shape…

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…

This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…

3D shape models are naturally parameterized using vertices and faces, \ie, composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a…

Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…

We propose an approach to measure surface elastic constants of soft solids. Generally, this requires one to probe interfacial mechanics at around the elastocapillary length scale, which is typically microscopic. Deformations of microscopic…

We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…

We study a wide class of metrics in a Lebesgue space with a standard measure, the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the…

Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a…

We consider the family known as modified or generalized surface quasi-geostrophic equations (mSQG) consisting of the classical inviscid surface quasi-geostrophic (SQG) equation together with a family of regularized active scalars given by…

In this article we introduce a diffeomorphism-invariant Riemannian metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape…

The majority of descriptor-based methods for geometric processing of non-rigid shape rely on hand-crafted descriptors. Recently, learning-based techniques have been shown effective, achieving state-of-the-art results in a variety of tasks.…